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First, we'll download the dataset to our local machine. The data consists of characters rendered in a variety of fonts on a 28x28 image. The labels are limited to 'A' through 'J' (10 classes). The training set has about 500k and the testset 19000 labeled examples. Given these sizes, it should be possible to train models quickly on any machine. | url = 'https://commondatastorage.googleapis.com/books1000/'
last_percent_reported = None
data_root = '.' # Change me to store data elsewhere
def download_progress_hook(count, blockSize, totalSize):
"""A hook to report the progress of a download. This is mostly intended for users with
slow internet connections. Reports every 5% change in download progress.
"""
global last_percent_reported
percent = int(count * blockSize * 100 / totalSize)
if last_percent_reported != percent:
if percent % 5 == 0:
sys.stdout.write("%s%%" % percent)
sys.stdout.flush()
else:
sys.stdout.write(".")
sys.stdout.flush()
last_percent_reported = percent
def maybe_download(filename, expected_bytes, force=False):
"""Download a file if not present, and make sure it's the right size."""
dest_filename = os.path.join(data_root, filename)
if force or not os.path.exists(dest_filename):
print('Attempting to download:', filename)
filename, _ = urlretrieve(url + filename, dest_filename, reporthook=download_progress_hook)
print('\nDownload Complete!')
statinfo = os.stat(dest_filename)
if statinfo.st_size == expected_bytes:
print('Found and verified', dest_filename)
else:
raise Exception(
'Failed to verify ' + dest_filename + '. Can you get to it with a browser?')
return dest_filename
train_filename = maybe_download('notMNIST_large.tar.gz', 247336696)
test_filename = maybe_download('notMNIST_small.tar.gz', 8458043) | machine-learning/deep-learning/udacity/ud730/1_notmnist.ipynb | pk-ai/training | mit |
Extract the dataset from the compressed .tar.gz file.
This should give you a set of directories, labeled A through J. | num_classes = 10
np.random.seed(133)
def maybe_extract(filename, force=False):
root = os.path.splitext(os.path.splitext(filename)[0])[0] # remove .tar.gz
if os.path.isdir(root) and not force:
# You may override by setting force=True.
print('%s already present - Skipping extraction of %s.' % (root, filename))
else:
print('Extracting data for %s. This may take a while. Please wait.' % root)
tar = tarfile.open(filename)
sys.stdout.flush()
tar.extractall(data_root)
tar.close()
data_folders = [
os.path.join(root, d) for d in sorted(os.listdir(root))
if os.path.isdir(os.path.join(root, d))]
if len(data_folders) != num_classes:
raise Exception(
'Expected %d folders, one per class. Found %d instead.' % (
num_classes, len(data_folders)))
print(data_folders)
return data_folders
train_folders = maybe_extract(train_filename)
test_folders = maybe_extract(test_filename) | machine-learning/deep-learning/udacity/ud730/1_notmnist.ipynb | pk-ai/training | mit |
Problem 1
Let's take a peek at some of the data to make sure it looks sensible. Each exemplar should be an image of a character A through J rendered in a different font. Display a sample of the images that we just downloaded. Hint: you can use the package IPython.display. | # Solution for Problem 1
import random
print('Displaying images of train folders')
# Looping through train folders and displaying a random image of each folder
for path in train_folders:
image_file = os.path.join(path, random.choice(os.listdir(path)))
display(Image(filename=image_file))
print('Displaying images of test folders')
# Looping through train folders and displaying a random image of each folder
for path in test_folders:
image_file = os.path.join(path, random.choice(os.listdir(path)))
display(Image(filename=image_file)) | machine-learning/deep-learning/udacity/ud730/1_notmnist.ipynb | pk-ai/training | mit |
Now let's load the data in a more manageable format. Since, depending on your computer setup you might not be able to fit it all in memory, we'll load each class into a separate dataset, store them on disk and curate them independently. Later we'll merge them into a single dataset of manageable size.
We'll convert the entire dataset into a 3D array (image index, x, y) of floating point values, normalized to have approximately zero mean and standard deviation ~0.5 to make training easier down the road.
A few images might not be readable, we'll just skip them. | image_size = 28 # Pixel width and height.
pixel_depth = 255.0 # Number of levels per pixel.
def load_letter(folder, min_num_images):
"""Load the data for a single letter label."""
image_files = os.listdir(folder)
dataset = np.ndarray(shape=(len(image_files), image_size, image_size),
dtype=np.float32)
print(folder)
num_images = 0
for image in image_files:
image_file = os.path.join(folder, image)
try:
image_data = (ndimage.imread(image_file).astype(float) -
pixel_depth / 2) / pixel_depth
if image_data.shape != (image_size, image_size):
raise Exception('Unexpected image shape: %s' % str(image_data.shape))
dataset[num_images, :, :] = image_data
num_images = num_images + 1
except IOError as e:
print('Could not read:', image_file, ':', e, '- it\'s ok, skipping.')
dataset = dataset[0:num_images, :, :]
if num_images < min_num_images:
raise Exception('Many fewer images than expected: %d < %d' %
(num_images, min_num_images))
print('Full dataset tensor:', dataset.shape)
print('Mean:', np.mean(dataset))
print('Standard deviation:', np.std(dataset))
return dataset
def maybe_pickle(data_folders, min_num_images_per_class, force=False):
dataset_names = []
for folder in data_folders:
set_filename = folder + '.pickle'
dataset_names.append(set_filename)
if os.path.exists(set_filename) and not force:
# You may override by setting force=True.
print('%s already present - Skipping pickling.' % set_filename)
else:
print('Pickling %s.' % set_filename)
dataset = load_letter(folder, min_num_images_per_class)
try:
with open(set_filename, 'wb') as f:
pickle.dump(dataset, f, pickle.HIGHEST_PROTOCOL)
except Exception as e:
print('Unable to save data to', set_filename, ':', e)
return dataset_names
train_datasets = maybe_pickle(train_folders, 45000)
test_datasets = maybe_pickle(test_folders, 1800) | machine-learning/deep-learning/udacity/ud730/1_notmnist.ipynb | pk-ai/training | mit |
Problem 2
Let's verify that the data still looks good. Displaying a sample of the labels and images from the ndarray. Hint: you can use matplotlib.pyplot. | # Solution for Problem 2
def show_first_image(datasets):
for pickl in datasets:
print('Showing a first image from pickle ', pickl)
try:
with open(pickl, 'rb') as f:
letter_set = pickle.load(f)
plt.imshow(letter_set[0])
except Exception as e:
print('Unable to show image from pickle ', pickl, ':', e)
raise
print('From Training dataset')
show_first_image(train_datasets)
print('From Test Dataset')
show_first_image(test_datasets) | machine-learning/deep-learning/udacity/ud730/1_notmnist.ipynb | pk-ai/training | mit |
Problem 3
Another check: we expect the data to be balanced across classes. Verify that. | def show_dataset_shape(datasets):
for pickl in datasets:
try:
with open(pickl, 'rb') as f:
letter_set = pickle.load(f)
print('Shape of pickle ', pickl, 'is', np.shape(letter_set))
except Exception as e:
print('Unable to show image from pickle ', pickl, ':', e)
raise
print('Shape for Training set')
show_dataset_shape(train_datasets)
print('Shape for Test set')
show_dataset_shape(test_datasets) | machine-learning/deep-learning/udacity/ud730/1_notmnist.ipynb | pk-ai/training | mit |
Merge and prune the training data as needed. Depending on your computer setup, you might not be able to fit it all in memory, and you can tune train_size as needed. The labels will be stored into a separate array of integers 0 through 9.
Also create a validation dataset for hyperparameter tuning. | def make_arrays(nb_rows, img_size):
if nb_rows:
dataset = np.ndarray((nb_rows, img_size, img_size), dtype=np.float32)
labels = np.ndarray(nb_rows, dtype=np.int32)
else:
dataset, labels = None, None
return dataset, labels
def merge_datasets(pickle_files, train_size, valid_size=0):
num_classes = len(pickle_files)
valid_dataset, valid_labels = make_arrays(valid_size, image_size)
train_dataset, train_labels = make_arrays(train_size, image_size)
vsize_per_class = valid_size // num_classes
tsize_per_class = train_size // num_classes
start_v, start_t = 0, 0
end_v, end_t = vsize_per_class, tsize_per_class
end_l = vsize_per_class+tsize_per_class
for label, pickle_file in enumerate(pickle_files):
try:
with open(pickle_file, 'rb') as f:
letter_set = pickle.load(f)
# let's shuffle the letters to have random validation and training set
np.random.shuffle(letter_set)
if valid_dataset is not None:
valid_letter = letter_set[:vsize_per_class, :, :]
valid_dataset[start_v:end_v, :, :] = valid_letter
valid_labels[start_v:end_v] = label
start_v += vsize_per_class
end_v += vsize_per_class
train_letter = letter_set[vsize_per_class:end_l, :, :]
train_dataset[start_t:end_t, :, :] = train_letter
train_labels[start_t:end_t] = label
start_t += tsize_per_class
end_t += tsize_per_class
except Exception as e:
print('Unable to process data from', pickle_file, ':', e)
raise
return valid_dataset, valid_labels, train_dataset, train_labels
"""
train_size = 200000
valid_size = 10000
test_size = 10000
"""
train_size = 20000
valid_size = 1000
test_size = 1000
valid_dataset, valid_labels, train_dataset, train_labels = merge_datasets(
train_datasets, train_size, valid_size)
_, _, test_dataset, test_labels = merge_datasets(test_datasets, test_size)
print('Training:', train_dataset.shape, train_labels.shape)
print('Validation:', valid_dataset.shape, valid_labels.shape)
print('Testing:', test_dataset.shape, test_labels.shape) | machine-learning/deep-learning/udacity/ud730/1_notmnist.ipynb | pk-ai/training | mit |
Next, we'll randomize the data. It's important to have the labels well shuffled for the training and test distributions to match. | def randomize(dataset, labels):
permutation = np.random.permutation(labels.shape[0])
shuffled_dataset = dataset[permutation,:,:]
shuffled_labels = labels[permutation]
return shuffled_dataset, shuffled_labels
train_dataset, train_labels = randomize(train_dataset, train_labels)
test_dataset, test_labels = randomize(test_dataset, test_labels)
valid_dataset, valid_labels = randomize(valid_dataset, valid_labels) | machine-learning/deep-learning/udacity/ud730/1_notmnist.ipynb | pk-ai/training | mit |
Problem 4
Convince yourself that the data is still good after shuffling! | print('Printing Train, validation and test labels after shuffling')
def print_first_10_labels(labels):
printing_labels = []
for i in range(10):
printing_labels.append(labels[[i]])
print(printing_labels)
print_first_10_labels(train_labels)
print_first_10_labels(test_labels)
print_first_10_labels(valid_labels) | machine-learning/deep-learning/udacity/ud730/1_notmnist.ipynb | pk-ai/training | mit |
Finally, let's save the data for later reuse: | pickle_file = os.path.join(data_root, 'notMNIST.pickle')
try:
f = open(pickle_file, 'wb')
save = {
'train_dataset': train_dataset,
'train_labels': train_labels,
'valid_dataset': valid_dataset,
'valid_labels': valid_labels,
'test_dataset': test_dataset,
'test_labels': test_labels,
}
pickle.dump(save, f, pickle.HIGHEST_PROTOCOL)
f.close()
except Exception as e:
print('Unable to save data to', pickle_file, ':', e)
raise
statinfo = os.stat(pickle_file)
print('Compressed pickle size:', statinfo.st_size) | machine-learning/deep-learning/udacity/ud730/1_notmnist.ipynb | pk-ai/training | mit |
Problem 5
By construction, this dataset might contain a lot of overlapping samples, including training data that's also contained in the validation and test set! Overlap between training and test can skew the results if you expect to use your model in an environment where there is never an overlap, but are actually ok if you expect to see training samples recur when you use it.
Measure how much overlap there is between training, validation and test samples.
Optional questions:
- What about near duplicates between datasets? (images that are almost identical)
- Create a sanitized validation and test set, and compare your accuracy on those in subsequent assignments.
Problem 6
Let's get an idea of what an off-the-shelf classifier can give you on this data. It's always good to check that there is something to learn, and that it's a problem that is not so trivial that a canned solution solves it.
Train a simple model on this data using 50, 100, 1000 and 5000 training samples. Hint: you can use the LogisticRegression model from sklearn.linear_model.
Optional question: train an off-the-shelf model on all the data! | logreg_model_clf = LogisticRegression()
nsamples, nx, ny = train_dataset.shape
d2_train_dataset = train_dataset.reshape((nsamples,nx*ny))
logreg_model_clf.fit(d2_train_dataset, train_labels)
from sklearn.metrics import accuracy_score
nsamples, nx, ny = valid_dataset.shape
d2_valid_dataset = valid_dataset.reshape((nsamples,nx*ny))
print("validation accuracy,", accuracy_score(valid_labels, logreg_model_clf.predict(d2_valid_dataset)))
nsamples, nx, ny = test_dataset.shape
d2_train_dataset = test_dataset.reshape((nsamples,nx*ny))
print("test accuracy,", accuracy_score(test_labels, logreg_model_clf.predict(d2_train_dataset))) | machine-learning/deep-learning/udacity/ud730/1_notmnist.ipynb | pk-ai/training | mit |
Now the Hotels | url = 'http://www.bringfido.com/lodging/city/new_haven_ct_us'
r = Render(url)
result = r.frame.toHtml()
#QString should be converted to string before processed by lxml
formatted_result = str(result.toAscii())
tree = html.fromstring(formatted_result)
#Now using correct Xpath we are fetching URL of archives
archive_links = tree.xpath('//*[@id="results_list"]/div')
print(archive_links)
print('')
for lnk in archive_links:
print(lnk.xpath('div[2]/h1/a/text()')[0])
print(lnk.text_content())
print('*'*25)
| code/.ipynb_checkpoints/bf_qt_scraping-checkpoint.ipynb | mattgiguere/doglodge | mit |
Now Get the Links | links = []
for lnk in archive_links:
print(lnk.xpath('div/h1/a/@href')[0])
links.append(lnk.xpath('div/h1/a/@href')[0])
print('*'*25)
lnk.xpath('//*/div/h1/a/@href')[0]
links | code/.ipynb_checkpoints/bf_qt_scraping-checkpoint.ipynb | mattgiguere/doglodge | mit |
Loading Reviews
Next, we want to step through each page, and scrape the reviews for each hotel. | url_base = 'http://www.bringfido.com'
r.update_url(url_base+links[0])
result = r.frame.toHtml()
#QString should be converted to string before processed by lxml
formatted_result = str(result.toAscii())
tree = html.fromstring(formatted_result)
hotel_description = tree.xpath('//*[@class="body"]/text()')
details = tree.xpath('//*[@class="address"]/text()')
address = details[0]
csczip = details[1]
phone = details[2]
#Now using correct Xpath we are fetching URL of archives
reviews = tree.xpath('//*[@class="review_container"]')
texts = []
titles = []
authors = []
ratings = []
print(reviews)
print('')
for rev in reviews:
titles.append(rev.xpath('div/div[1]/text()')[0])
authors.append(rev.xpath('div/div[2]/text()')[0])
texts.append(rev.xpath('div/div[3]/text()')[0])
ratings.append(rev.xpath('div[2]/img/@src')[0].split('/')[-1][0:1])
print(rev.xpath('div[2]/img/@src')[0].split('/')[-1][0:1])
titles
authors
texts
ratings | code/.ipynb_checkpoints/bf_qt_scraping-checkpoint.ipynb | mattgiguere/doglodge | mit |
Load software and filenames definitions | from fretbursts import *
init_notebook()
from IPython.display import display | out_notebooks/usALEX-5samples-E-corrected-all-ph-out-12d.ipynb | tritemio/multispot_paper | mit |
Data folder: | data_dir = './data/singlespot/'
import os
data_dir = os.path.abspath(data_dir) + '/'
assert os.path.exists(data_dir), "Path '%s' does not exist." % data_dir | out_notebooks/usALEX-5samples-E-corrected-all-ph-out-12d.ipynb | tritemio/multispot_paper | mit |
List of data files: | from glob import glob
file_list = sorted(f for f in glob(data_dir + '*.hdf5') if '_BKG' not in f)
## Selection for POLIMI 2012-11-26 datatset
labels = ['17d', '27d', '7d', '12d', '22d']
files_dict = {lab: fname for lab, fname in zip(labels, file_list)}
files_dict
data_id | out_notebooks/usALEX-5samples-E-corrected-all-ph-out-12d.ipynb | tritemio/multispot_paper | mit |
Data load
Initial loading of the data: | d = loader.photon_hdf5(filename=files_dict[data_id]) | out_notebooks/usALEX-5samples-E-corrected-all-ph-out-12d.ipynb | tritemio/multispot_paper | mit |
Load the leakage coefficient from disk: | leakage_coeff_fname = 'results/usALEX - leakage coefficient DexDem.csv'
leakage = np.loadtxt(leakage_coeff_fname)
print('Leakage coefficient:', leakage) | out_notebooks/usALEX-5samples-E-corrected-all-ph-out-12d.ipynb | tritemio/multispot_paper | mit |
Load the direct excitation coefficient ($d_{exAA}$) from disk: | dir_ex_coeff_fname = 'results/usALEX - direct excitation coefficient dir_ex_aa.csv'
dir_ex_aa = np.loadtxt(dir_ex_coeff_fname)
print('Direct excitation coefficient (dir_ex_aa):', dir_ex_aa) | out_notebooks/usALEX-5samples-E-corrected-all-ph-out-12d.ipynb | tritemio/multispot_paper | mit |
Load the gamma-factor ($\gamma$) from disk: | gamma_fname = 'results/usALEX - gamma factor - all-ph.csv'
gamma = np.loadtxt(gamma_fname)
print('Gamma-factor:', gamma) | out_notebooks/usALEX-5samples-E-corrected-all-ph-out-12d.ipynb | tritemio/multispot_paper | mit |
Update d with the correction coefficients: | d.leakage = leakage
d.dir_ex = dir_ex_aa
d.gamma = gamma | out_notebooks/usALEX-5samples-E-corrected-all-ph-out-12d.ipynb | tritemio/multispot_paper | mit |
Laser alternation selection
At this point we have only the timestamps and the detector numbers: | d.ph_times_t[0][:3], d.ph_times_t[0][-3:]#, d.det_t
print('First and last timestamps: {:10,} {:10,}'.format(d.ph_times_t[0][0], d.ph_times_t[0][-1]))
print('Total number of timestamps: {:10,}'.format(d.ph_times_t[0].size)) | out_notebooks/usALEX-5samples-E-corrected-all-ph-out-12d.ipynb | tritemio/multispot_paper | mit |
We need to define some parameters: donor and acceptor ch, excitation period and donor and acceptor excitiations: | d.add(det_donor_accept=(0, 1), alex_period=4000, D_ON=(2850, 580), A_ON=(900, 2580), offset=0) | out_notebooks/usALEX-5samples-E-corrected-all-ph-out-12d.ipynb | tritemio/multispot_paper | mit |
We should check if everithing is OK with an alternation histogram: | plot_alternation_hist(d) | out_notebooks/usALEX-5samples-E-corrected-all-ph-out-12d.ipynb | tritemio/multispot_paper | mit |
If the plot looks good we can apply the parameters with: | loader.alex_apply_period(d)
print('D+A photons in D-excitation period: {:10,}'.format(d.D_ex[0].sum()))
print('D+A photons in A-excitation period: {:10,}'.format(d.A_ex[0].sum())) | out_notebooks/usALEX-5samples-E-corrected-all-ph-out-12d.ipynb | tritemio/multispot_paper | mit |
Measurements infos
All the measurement data is in the d variable. We can print it: | d | out_notebooks/usALEX-5samples-E-corrected-all-ph-out-12d.ipynb | tritemio/multispot_paper | mit |
Or check the measurements duration: | d.time_max | out_notebooks/usALEX-5samples-E-corrected-all-ph-out-12d.ipynb | tritemio/multispot_paper | mit |
Compute background
Compute the background using automatic threshold: | d.calc_bg(bg.exp_fit, time_s=60, tail_min_us='auto', F_bg=1.7)
dplot(d, timetrace_bg)
d.rate_m, d.rate_dd, d.rate_ad, d.rate_aa | out_notebooks/usALEX-5samples-E-corrected-all-ph-out-12d.ipynb | tritemio/multispot_paper | mit |
Burst search and selection | d.burst_search(L=10, m=10, F=7, ph_sel=Ph_sel('all'))
print(d.ph_sel)
dplot(d, hist_fret);
# if data_id in ['7d', '27d']:
# ds = d.select_bursts(select_bursts.size, th1=20)
# else:
# ds = d.select_bursts(select_bursts.size, th1=30)
ds = d.select_bursts(select_bursts.size, add_naa=False, th1=30)
n_bursts_all = ds.num_bursts[0]
def select_and_plot_ES(fret_sel, do_sel):
ds_fret= ds.select_bursts(select_bursts.ES, **fret_sel)
ds_do = ds.select_bursts(select_bursts.ES, **do_sel)
bpl.plot_ES_selection(ax, **fret_sel)
bpl.plot_ES_selection(ax, **do_sel)
return ds_fret, ds_do
ax = dplot(ds, hist2d_alex, S_max_norm=2, scatter_alpha=0.1)
if data_id == '7d':
fret_sel = dict(E1=0.60, E2=1.2, S1=0.2, S2=0.9, rect=False)
do_sel = dict(E1=-0.2, E2=0.5, S1=0.8, S2=2, rect=True)
ds_fret, ds_do = select_and_plot_ES(fret_sel, do_sel)
elif data_id == '12d':
fret_sel = dict(E1=0.30,E2=1.2,S1=0.131,S2=0.9, rect=False)
do_sel = dict(E1=-0.4, E2=0.4, S1=0.8, S2=2, rect=False)
ds_fret, ds_do = select_and_plot_ES(fret_sel, do_sel)
elif data_id == '17d':
fret_sel = dict(E1=0.01, E2=0.98, S1=0.14, S2=0.88, rect=False)
do_sel = dict(E1=-0.4, E2=0.4, S1=0.80, S2=2, rect=False)
ds_fret, ds_do = select_and_plot_ES(fret_sel, do_sel)
elif data_id == '22d':
fret_sel = dict(E1=-0.16, E2=0.6, S1=0.2, S2=0.80, rect=False)
do_sel = dict(E1=-0.2, E2=0.4, S1=0.85, S2=2, rect=True)
ds_fret, ds_do = select_and_plot_ES(fret_sel, do_sel)
elif data_id == '27d':
fret_sel = dict(E1=-0.1, E2=0.5, S1=0.2, S2=0.82, rect=False)
do_sel = dict(E1=-0.2, E2=0.4, S1=0.88, S2=2, rect=True)
ds_fret, ds_do = select_and_plot_ES(fret_sel, do_sel)
n_bursts_do = ds_do.num_bursts[0]
n_bursts_fret = ds_fret.num_bursts[0]
n_bursts_do, n_bursts_fret
d_only_frac = 1.*n_bursts_do/(n_bursts_do + n_bursts_fret)
print('D-only fraction:', d_only_frac)
dplot(ds_fret, hist2d_alex, scatter_alpha=0.1);
dplot(ds_do, hist2d_alex, S_max_norm=2, scatter=False); | out_notebooks/usALEX-5samples-E-corrected-all-ph-out-12d.ipynb | tritemio/multispot_paper | mit |
Donor Leakage fit | bandwidth = 0.03
E_range_do = (-0.1, 0.15)
E_ax = np.r_[-0.2:0.401:0.0002]
E_pr_do_kde = bext.fit_bursts_kde_peak(ds_do, bandwidth=bandwidth, weights='size',
x_range=E_range_do, x_ax=E_ax, save_fitter=True)
mfit.plot_mfit(ds_do.E_fitter, plot_kde=True, bins=np.r_[E_ax.min(): E_ax.max(): bandwidth])
plt.xlim(-0.3, 0.5)
print("%s: E_peak = %.2f%%" % (ds.ph_sel, E_pr_do_kde*100)) | out_notebooks/usALEX-5samples-E-corrected-all-ph-out-12d.ipynb | tritemio/multispot_paper | mit |
Burst sizes | nt_th1 = 50
dplot(ds_fret, hist_size, which='all', add_naa=False)
xlim(-0, 250)
plt.axvline(nt_th1)
Th_nt = np.arange(35, 120)
nt_th = np.zeros(Th_nt.size)
for i, th in enumerate(Th_nt):
ds_nt = ds_fret.select_bursts(select_bursts.size, th1=th)
nt_th[i] = (ds_nt.nd[0] + ds_nt.na[0]).mean() - th
plt.figure()
plot(Th_nt, nt_th)
plt.axvline(nt_th1)
nt_mean = nt_th[np.where(Th_nt == nt_th1)][0]
nt_mean | out_notebooks/usALEX-5samples-E-corrected-all-ph-out-12d.ipynb | tritemio/multispot_paper | mit |
Fret fit
Max position of the Kernel Density Estimation (KDE): | E_pr_fret_kde = bext.fit_bursts_kde_peak(ds_fret, bandwidth=bandwidth, weights='size')
E_fitter = ds_fret.E_fitter
E_fitter.histogram(bins=np.r_[-0.1:1.1:0.03])
E_fitter.fit_histogram(mfit.factory_gaussian(center=0.5))
E_fitter.fit_res[0].params.pretty_print()
fig, ax = plt.subplots(1, 2, figsize=(14, 4.5))
mfit.plot_mfit(E_fitter, ax=ax[0])
mfit.plot_mfit(E_fitter, plot_model=False, plot_kde=True, ax=ax[1])
print('%s\nKDE peak %.2f ' % (ds_fret.ph_sel, E_pr_fret_kde*100))
display(E_fitter.params*100) | out_notebooks/usALEX-5samples-E-corrected-all-ph-out-12d.ipynb | tritemio/multispot_paper | mit |
Weighted mean of $E$ of each burst: | ds_fret.fit_E_m(weights='size') | out_notebooks/usALEX-5samples-E-corrected-all-ph-out-12d.ipynb | tritemio/multispot_paper | mit |
Gaussian fit (no weights): | ds_fret.fit_E_generic(fit_fun=bl.gaussian_fit_hist, bins=np.r_[-0.1:1.1:0.03], weights=None) | out_notebooks/usALEX-5samples-E-corrected-all-ph-out-12d.ipynb | tritemio/multispot_paper | mit |
Gaussian fit (using burst size as weights): | ds_fret.fit_E_generic(fit_fun=bl.gaussian_fit_hist, bins=np.r_[-0.1:1.1:0.005], weights='size')
E_kde_w = E_fitter.kde_max_pos[0]
E_gauss_w = E_fitter.params.loc[0, 'center']
E_gauss_w_sig = E_fitter.params.loc[0, 'sigma']
E_gauss_w_err = float(E_gauss_w_sig/np.sqrt(ds_fret.num_bursts[0]))
E_gauss_w_fiterr = E_fitter.fit_res[0].params['center'].stderr
E_kde_w, E_gauss_w, E_gauss_w_sig, E_gauss_w_err, E_gauss_w_fiterr | out_notebooks/usALEX-5samples-E-corrected-all-ph-out-12d.ipynb | tritemio/multispot_paper | mit |
Stoichiometry fit
Max position of the Kernel Density Estimation (KDE): | S_pr_fret_kde = bext.fit_bursts_kde_peak(ds_fret, burst_data='S', bandwidth=0.03) #weights='size', add_naa=True)
S_fitter = ds_fret.S_fitter
S_fitter.histogram(bins=np.r_[-0.1:1.1:0.03])
S_fitter.fit_histogram(mfit.factory_gaussian(), center=0.5)
fig, ax = plt.subplots(1, 2, figsize=(14, 4.5))
mfit.plot_mfit(S_fitter, ax=ax[0])
mfit.plot_mfit(S_fitter, plot_model=False, plot_kde=True, ax=ax[1])
print('%s\nKDE peak %.2f ' % (ds_fret.ph_sel, S_pr_fret_kde*100))
display(S_fitter.params*100)
S_kde = S_fitter.kde_max_pos[0]
S_gauss = S_fitter.params.loc[0, 'center']
S_gauss_sig = S_fitter.params.loc[0, 'sigma']
S_gauss_err = float(S_gauss_sig/np.sqrt(ds_fret.num_bursts[0]))
S_gauss_fiterr = S_fitter.fit_res[0].params['center'].stderr
S_kde, S_gauss, S_gauss_sig, S_gauss_err, S_gauss_fiterr | out_notebooks/usALEX-5samples-E-corrected-all-ph-out-12d.ipynb | tritemio/multispot_paper | mit |
The Maximum likelihood fit for a Gaussian population is the mean: | S = ds_fret.S[0]
S_ml_fit = (S.mean(), S.std())
S_ml_fit | out_notebooks/usALEX-5samples-E-corrected-all-ph-out-12d.ipynb | tritemio/multispot_paper | mit |
Computing the weighted mean and weighted standard deviation we get: | weights = bl.fret_fit.get_weights(ds_fret.nd[0], ds_fret.na[0], weights='size', naa=ds_fret.naa[0], gamma=1.)
S_mean = np.dot(weights, S)/weights.sum()
S_std_dev = np.sqrt(
np.dot(weights, (S - S_mean)**2)/weights.sum())
S_wmean_fit = [S_mean, S_std_dev]
S_wmean_fit | out_notebooks/usALEX-5samples-E-corrected-all-ph-out-12d.ipynb | tritemio/multispot_paper | mit |
Save data to file | sample = data_id | out_notebooks/usALEX-5samples-E-corrected-all-ph-out-12d.ipynb | tritemio/multispot_paper | mit |
The following string contains the list of variables to be saved. When saving, the order of the variables is preserved. | variables = ('sample n_bursts_all n_bursts_do n_bursts_fret '
'E_kde_w E_gauss_w E_gauss_w_sig E_gauss_w_err E_gauss_w_fiterr '
'S_kde S_gauss S_gauss_sig S_gauss_err S_gauss_fiterr '
'E_pr_do_kde nt_mean\n') | out_notebooks/usALEX-5samples-E-corrected-all-ph-out-12d.ipynb | tritemio/multispot_paper | mit |
This is just a trick to format the different variables: | variables_csv = variables.replace(' ', ',')
fmt_float = '{%s:.6f}'
fmt_int = '{%s:d}'
fmt_str = '{%s}'
fmt_dict = {**{'sample': fmt_str},
**{k: fmt_int for k in variables.split() if k.startswith('n_bursts')}}
var_dict = {name: eval(name) for name in variables.split()}
var_fmt = ', '.join([fmt_dict.get(name, fmt_float) % name for name in variables.split()]) + '\n'
data_str = var_fmt.format(**var_dict)
print(variables_csv)
print(data_str)
# NOTE: The file name should be the notebook name but with .csv extension
with open('results/usALEX-5samples-E-corrected-all-ph.csv', 'a') as f:
f.seek(0, 2)
if f.tell() == 0:
f.write(variables_csv)
f.write(data_str) | out_notebooks/usALEX-5samples-E-corrected-all-ph-out-12d.ipynb | tritemio/multispot_paper | mit |
Data folder: | data_dir = './data/singlespot/' | out_notebooks/usALEX-5samples-PR-raw-dir_ex_aa-fit-out-AexAem-17d.ipynb | tritemio/multispot_paper | mit |
Check that the folder exists: | import os
data_dir = os.path.abspath(data_dir) + '/'
assert os.path.exists(data_dir), "Path '%s' does not exist." % data_dir | out_notebooks/usALEX-5samples-PR-raw-dir_ex_aa-fit-out-AexAem-17d.ipynb | tritemio/multispot_paper | mit |
List of data files in data_dir: | from glob import glob
file_list = sorted(f for f in glob(data_dir + '*.hdf5') if '_BKG' not in f)
file_list
## Selection for POLIMI 2012-12-6 dataset
# file_list.pop(2)
# file_list = file_list[1:-2]
# display(file_list)
# labels = ['22d', '27d', '17d', '12d', '7d']
## Selection for P.E. 2012-12-6 dataset
# file_list.pop(1)
# file_list = file_list[:-1]
# display(file_list)
# labels = ['22d', '27d', '17d', '12d', '7d']
## Selection for POLIMI 2012-11-26 datatset
labels = ['17d', '27d', '7d', '12d', '22d']
files_dict = {lab: fname for lab, fname in zip(labels, file_list)}
files_dict
ph_sel_map = {'all-ph': Ph_sel('all'), 'AexAem': Ph_sel(Aex='Aem')}
ph_sel = ph_sel_map[ph_sel_name]
data_id, ph_sel_name | out_notebooks/usALEX-5samples-PR-raw-dir_ex_aa-fit-out-AexAem-17d.ipynb | tritemio/multispot_paper | mit |
Laser alternation selection
At this point we have only the timestamps and the detector numbers: | d.ph_times_t, d.det_t | out_notebooks/usALEX-5samples-PR-raw-dir_ex_aa-fit-out-AexAem-17d.ipynb | tritemio/multispot_paper | mit |
If the plot looks good we can apply the parameters with: | loader.alex_apply_period(d) | out_notebooks/usALEX-5samples-PR-raw-dir_ex_aa-fit-out-AexAem-17d.ipynb | tritemio/multispot_paper | mit |
Burst search and selection | from mpl_toolkits.axes_grid1 import AxesGrid
import lmfit
print('lmfit version:', lmfit.__version__)
assert d.dir_ex == 0
assert d.leakage == 0
d.burst_search(m=10, F=6, ph_sel=ph_sel)
print(d.ph_sel, d.num_bursts)
ds_sa = d.select_bursts(select_bursts.naa, th1=30)
ds_sa.num_bursts | out_notebooks/usALEX-5samples-PR-raw-dir_ex_aa-fit-out-AexAem-17d.ipynb | tritemio/multispot_paper | mit |
Preliminary selection and plots | mask = (d.naa[0] - np.abs(d.na[0] + d.nd[0])) > 30
ds_saw = d.select_bursts_mask_apply([mask])
ds_sas0 = ds_sa.select_bursts(select_bursts.S, S2=0.10)
ds_sas = ds_sa.select_bursts(select_bursts.S, S2=0.15)
ds_sas2 = ds_sa.select_bursts(select_bursts.S, S2=0.20)
ds_sas3 = ds_sa.select_bursts(select_bursts.S, S2=0.25)
ds_st = d.select_bursts(select_bursts.size, add_naa=True, th1=30)
ds_sas.num_bursts
dx = ds_sas0
size = dx.na[0] + dx.nd[0]
s_hist, s_bins = np.histogram(size, bins=np.r_[-15 : 25 : 1], density=True)
s_ax = s_bins[:-1] + 0.5*(s_bins[1] - s_bins[0])
plot(s_ax, s_hist, '-o', alpha=0.5)
dx = ds_sas
size = dx.na[0] + dx.nd[0]
s_hist, s_bins = np.histogram(size, bins=np.r_[-15 : 25 : 1], density=True)
s_ax = s_bins[:-1] + 0.5*(s_bins[1] - s_bins[0])
plot(s_ax, s_hist, '-o', alpha=0.5)
dx = ds_sas2
size = dx.na[0] + dx.nd[0]
s_hist, s_bins = np.histogram(size, bins=np.r_[-15 : 25 : 1], density=True)
s_ax = s_bins[:-1] + 0.5*(s_bins[1] - s_bins[0])
plot(s_ax, s_hist, '-o', alpha=0.5)
dx = ds_sas3
size = dx.na[0] + dx.nd[0]
s_hist, s_bins = np.histogram(size, bins=np.r_[-15 : 25 : 1], density=True)
s_ax = s_bins[:-1] + 0.5*(s_bins[1] - s_bins[0])
plot(s_ax, s_hist, '-o', alpha=0.5)
plt.title('(nd + na) for A-only population using different S cutoff');
dx = ds_sa
alex_jointplot(dx);
dplot(ds_sa, hist_S) | out_notebooks/usALEX-5samples-PR-raw-dir_ex_aa-fit-out-AexAem-17d.ipynb | tritemio/multispot_paper | mit |
A-direct excitation fitting
To extract the A-direct excitation coefficient we need to fit the
S values for the A-only population.
The S value for the A-only population is fitted with different methods:
- Histogram git with 2 Gaussians or with 2 asymmetric Gaussians
(an asymmetric Gaussian has right- and left-side of the peak
decreasing according to different sigmas).
- KDE maximum
In the following we apply these methods using different selection
or weighting schemes to reduce amount of FRET population and make
fitting of the A-only population easier.
Even selection
Here A-only and FRET population are evenly selected. | dx = ds_sa
bin_width = 0.03
bandwidth = 0.03
bins = np.r_[-0.2 : 1 : bin_width]
x_kde = np.arange(bins.min(), bins.max(), 0.0002)
## Weights
weights = None
## Histogram fit
fitter_g = mfit.MultiFitter(dx.S)
fitter_g.histogram(bins=np.r_[-0.2 : 1.2 : bandwidth])
fitter_g.fit_histogram(model = mfit.factory_two_gaussians(p1_center=0.1, p2_center=0.4))
S_hist_orig = fitter_g.hist_pdf
S_2peaks = fitter_g.params.loc[0, 'p1_center']
dir_ex_S2p = S_2peaks/(1 - S_2peaks)
print('Fitted direct excitation (na/naa) [2-Gauss]:', dir_ex_S2p)
## KDE
fitter_g.calc_kde(bandwidth=bandwidth)
fitter_g.find_kde_max(x_kde, xmin=0, xmax=0.15)
S_peak = fitter_g.kde_max_pos[0]
dir_ex_S_kde = S_peak/(1 - S_peak)
print('Fitted direct excitation (na/naa) [KDE]: ', dir_ex_S_kde)
fig, ax = plt.subplots(1, 2, figsize=(14, 4.5))
mfit.plot_mfit(fitter_g, ax=ax[0])
ax[0].set_title('2-Gaussians fit (S_fit = %.2f %%)' % (S_2peaks*100))
mfit.plot_mfit(fitter_g, ax=ax[1], plot_model=False, plot_kde=True)
ax[1].set_title('KDE fit (S_fit = %.2f %%)' % (S_peak*100));
## 2-Asym-Gaussian
fitter_ag = mfit.MultiFitter(dx.S)
fitter_ag.histogram(bins=np.r_[-0.2 : 1.2 : bandwidth])
fitter_ag.fit_histogram(model = mfit.factory_two_asym_gaussians(p1_center=0.1, p2_center=0.4))
#print(fitter_ag.fit_obj[0].model.fit_report())
S_2peaks_a = fitter_ag.params.loc[0, 'p1_center']
dir_ex_S2pa = S_2peaks_a/(1 - S_2peaks_a)
print('Fitted direct excitation (na/naa) [2-Gauss]:', dir_ex_S2pa)
fig, ax = plt.subplots(1, 2, figsize=(14, 4.5))
mfit.plot_mfit(fitter_g, ax=ax[0])
ax[0].set_title('2-Gaussians fit (S_fit = %.2f %%)' % (S_2peaks*100))
mfit.plot_mfit(fitter_ag, ax=ax[1])
ax[1].set_title('2-Asym-Gaussians fit (S_fit = %.2f %%)' % (S_2peaks_a*100)); | out_notebooks/usALEX-5samples-PR-raw-dir_ex_aa-fit-out-AexAem-17d.ipynb | tritemio/multispot_paper | mit |
Zero threshold on nd
Select bursts with:
$$n_d < 0$$. | dx = ds_sa.select_bursts(select_bursts.nd, th1=-100, th2=0)
fitter = bext.bursts_fitter(dx, 'S')
fitter.fit_histogram(model = mfit.factory_gaussian(center=0.1))
S_1peaks_th = fitter.params.loc[0, 'center']
dir_ex_S1p = S_1peaks_th/(1 - S_1peaks_th)
print('Fitted direct excitation (na/naa) [2-Gauss]:', dir_ex_S1p)
mfit.plot_mfit(fitter)
plt.xlim(-0.1, 0.6) | out_notebooks/usALEX-5samples-PR-raw-dir_ex_aa-fit-out-AexAem-17d.ipynb | tritemio/multispot_paper | mit |
Selection 1
Bursts are weighted using $w = f(S)$, where the function $f(S)$ is a
Gaussian fitted to the $S$ histogram of the FRET population. | dx = ds_sa
## Weights
weights = 1 - mfit.gaussian(dx.S[0], fitter_g.params.loc[0, 'p2_center'], fitter_g.params.loc[0, 'p2_sigma'])
weights[dx.S[0] >= fitter_g.params.loc[0, 'p2_center']] = 0
## Histogram fit
fitter_w1 = mfit.MultiFitter(dx.S)
fitter_w1.weights = [weights]
fitter_w1.histogram(bins=np.r_[-0.2 : 1.2 : bandwidth])
fitter_w1.fit_histogram(model = mfit.factory_two_gaussians(p1_center=0.1, p2_center=0.4))
S_2peaks_w1 = fitter_w1.params.loc[0, 'p1_center']
dir_ex_S2p_w1 = S_2peaks_w1/(1 - S_2peaks_w1)
print('Fitted direct excitation (na/naa) [2-Gauss]:', dir_ex_S2p_w1)
## KDE
fitter_w1.calc_kde(bandwidth=bandwidth)
fitter_w1.find_kde_max(x_kde, xmin=0, xmax=0.15)
S_peak_w1 = fitter_w1.kde_max_pos[0]
dir_ex_S_kde_w1 = S_peak_w1/(1 - S_peak_w1)
print('Fitted direct excitation (na/naa) [KDE]: ', dir_ex_S_kde_w1)
def plot_weights(x, weights, ax):
ax2 = ax.twinx()
x_sort = x.argsort()
ax2.plot(x[x_sort], weights[x_sort], color='k', lw=4, alpha=0.4)
ax2.set_ylabel('Weights');
fig, ax = plt.subplots(1, 2, figsize=(14, 4.5))
mfit.plot_mfit(fitter_w1, ax=ax[0])
mfit.plot_mfit(fitter_g, ax=ax[0], plot_model=False, plot_kde=False)
plot_weights(dx.S[0], weights, ax=ax[0])
ax[0].set_title('2-Gaussians fit (S_fit = %.2f %%)' % (S_2peaks_w1*100))
mfit.plot_mfit(fitter_w1, ax=ax[1], plot_model=False, plot_kde=True)
mfit.plot_mfit(fitter_g, ax=ax[1], plot_model=False, plot_kde=False)
plot_weights(dx.S[0], weights, ax=ax[1])
ax[1].set_title('KDE fit (S_fit = %.2f %%)' % (S_peak_w1*100)); | out_notebooks/usALEX-5samples-PR-raw-dir_ex_aa-fit-out-AexAem-17d.ipynb | tritemio/multispot_paper | mit |
Selection 2
Bursts are here weighted using weights $w$:
$$w = n_{aa} - |n_a + n_d|$$ | ## Weights
sizes = dx.nd[0] + dx.na[0] #- dir_ex_S_kde_w3*dx.naa[0]
weights = dx.naa[0] - abs(sizes)
weights[weights < 0] = 0
## Histogram
fitter_w4 = mfit.MultiFitter(dx.S)
fitter_w4.weights = [weights]
fitter_w4.histogram(bins=np.r_[-0.2 : 1.2 : bandwidth])
fitter_w4.fit_histogram(model = mfit.factory_two_gaussians(p1_center=0.1, p2_center=0.4))
S_2peaks_w4 = fitter_w4.params.loc[0, 'p1_center']
dir_ex_S2p_w4 = S_2peaks_w4/(1 - S_2peaks_w4)
print('Fitted direct excitation (na/naa) [2-Gauss]:', dir_ex_S2p_w4)
## KDE
fitter_w4.calc_kde(bandwidth=bandwidth)
fitter_w4.find_kde_max(x_kde, xmin=0, xmax=0.15)
S_peak_w4 = fitter_w4.kde_max_pos[0]
dir_ex_S_kde_w4 = S_peak_w4/(1 - S_peak_w4)
print('Fitted direct excitation (na/naa) [KDE]: ', dir_ex_S_kde_w4)
fig, ax = plt.subplots(1, 2, figsize=(14, 4.5))
mfit.plot_mfit(fitter_w4, ax=ax[0])
mfit.plot_mfit(fitter_g, ax=ax[0], plot_model=False, plot_kde=False)
#plot_weights(dx.S[0], weights, ax=ax[0])
ax[0].set_title('2-Gaussians fit (S_fit = %.2f %%)' % (S_2peaks_w4*100))
mfit.plot_mfit(fitter_w4, ax=ax[1], plot_model=False, plot_kde=True)
mfit.plot_mfit(fitter_g, ax=ax[1], plot_model=False, plot_kde=False)
#plot_weights(dx.S[0], weights, ax=ax[1])
ax[1].set_title('KDE fit (S_fit = %.2f %%)' % (S_peak_w4*100)); | out_notebooks/usALEX-5samples-PR-raw-dir_ex_aa-fit-out-AexAem-17d.ipynb | tritemio/multispot_paper | mit |
Selection 3
Bursts are here selected according to:
$$n_{aa} - |n_a + n_d| > 30$$ | mask = (d.naa[0] - np.abs(d.na[0] + d.nd[0])) > 30
ds_saw = d.select_bursts_mask_apply([mask])
print(ds_saw.num_bursts)
dx = ds_saw
## Weights
weights = None
## 2-Gaussians
fitter_w5 = mfit.MultiFitter(dx.S)
fitter_w5.histogram(bins=np.r_[-0.2 : 1.2 : bandwidth])
fitter_w5.fit_histogram(model = mfit.factory_two_gaussians(p1_center=0.1, p2_center=0.4))
S_2peaks_w5 = fitter_w5.params.loc[0, 'p1_center']
dir_ex_S2p_w5 = S_2peaks_w5/(1 - S_2peaks_w5)
print('Fitted direct excitation (na/naa) [2-Gauss]:', dir_ex_S2p_w5)
## KDE
fitter_w5.calc_kde(bandwidth=bandwidth)
fitter_w5.find_kde_max(x_kde, xmin=0, xmax=0.15)
S_peak_w5 = fitter_w5.kde_max_pos[0]
S_2peaks_w5_fiterr = fitter_w5.fit_res[0].params['p1_center'].stderr
dir_ex_S_kde_w5 = S_peak_w5/(1 - S_peak_w5)
print('Fitted direct excitation (na/naa) [KDE]: ', dir_ex_S_kde_w5)
## 2-Asym-Gaussians
fitter_w5a = mfit.MultiFitter(dx.S)
fitter_w5a.histogram(bins=np.r_[-0.2 : 1.2 : bandwidth])
fitter_w5a.fit_histogram(model = mfit.factory_two_asym_gaussians(p1_center=0.05, p2_center=0.3))
S_2peaks_w5a = fitter_w5a.params.loc[0, 'p1_center']
dir_ex_S2p_w5a = S_2peaks_w5a/(1 - S_2peaks_w5a)
#print(fitter_w5a.fit_obj[0].model.fit_report(min_correl=0.5))
print('Fitted direct excitation (na/naa) [2-Asym-Gauss]:', dir_ex_S2p_w5a)
fig, ax = plt.subplots(1, 3, figsize=(19, 4.5))
mfit.plot_mfit(fitter_w5, ax=ax[0])
mfit.plot_mfit(fitter_g, ax=ax[0], plot_model=False, plot_kde=False)
ax[0].set_title('2-Gaussians fit (S_fit = %.2f %%)' % (S_2peaks_w5*100))
mfit.plot_mfit(fitter_w5, ax=ax[1], plot_model=False, plot_kde=True)
mfit.plot_mfit(fitter_g, ax=ax[1], plot_model=False, plot_kde=False)
ax[1].set_title('KDE fit (S_fit = %.2f %%)' % (S_peak_w5*100));
mfit.plot_mfit(fitter_w5a, ax=ax[2])
mfit.plot_mfit(fitter_g, ax=ax[2], plot_model=False, plot_kde=False)
ax[2].set_title('2-Asym-Gaussians fit (S_fit = %.2f %%)' % (S_2peaks_w5a*100)); | out_notebooks/usALEX-5samples-PR-raw-dir_ex_aa-fit-out-AexAem-17d.ipynb | tritemio/multispot_paper | mit |
Save data to file | sample = data_id
n_bursts_aa = ds_sas.num_bursts[0] | out_notebooks/usALEX-5samples-PR-raw-dir_ex_aa-fit-out-AexAem-17d.ipynb | tritemio/multispot_paper | mit |
The following string contains the list of variables to be saved. When saving, the order of the variables is preserved. | variables = ('sample n_bursts_aa dir_ex_S1p dir_ex_S_kde dir_ex_S2p dir_ex_S2pa '
'dir_ex_S2p_w1 dir_ex_S_kde_w1 dir_ex_S_kde_w4 dir_ex_S_kde_w5 dir_ex_S2p_w5 dir_ex_S2p_w5a '
'S_2peaks_w5 S_2peaks_w5_fiterr\n') | out_notebooks/usALEX-5samples-PR-raw-dir_ex_aa-fit-out-AexAem-17d.ipynb | tritemio/multispot_paper | mit |
This is just a trick to format the different variables: | variables_csv = variables.replace(' ', ',')
fmt_float = '{%s:.6f}'
fmt_int = '{%s:d}'
fmt_str = '{%s}'
fmt_dict = {**{'sample': fmt_str},
**{k: fmt_int for k in variables.split() if k.startswith('n_bursts')}}
var_dict = {name: eval(name) for name in variables.split()}
var_fmt = ', '.join([fmt_dict.get(name, fmt_float) % name for name in variables.split()]) + '\n'
data_str = var_fmt.format(**var_dict)
print(variables_csv)
print(data_str)
# NOTE: The file name should be the notebook name but with .csv extension
with open('results/usALEX-5samples-PR-raw-dir_ex_aa-fit-%s.csv' % ph_sel_name, 'a') as f:
f.seek(0, 2)
if f.tell() == 0:
f.write(variables_csv)
f.write(data_str) | out_notebooks/usALEX-5samples-PR-raw-dir_ex_aa-fit-out-AexAem-17d.ipynb | tritemio/multispot_paper | mit |
1. Get Arxiv data about machine learning
Write a APi querier and extract papers with the terms machine learning or artificial intelligence. Get 2000 results... and play nice! | class Arxiv_querier():
'''
This class takes as an input a query and the number of results, and returns all the parsed results.
Includes routines to deal with multiple pages of results.
'''
def __init__(self,base_url="http://export.arxiv.org/api/query?"):
'''
Initialise
'''
self.base_url = base_url
def query(self,query_string,max_results=100,wait_time=3):
'''
Query the base url
'''
#Attribute query string
#Load base URL
base_url = self.base_url
#Prepare query string
processed_query = re.sub(' ','+',query_string)
self.query_string="_".join(query_string.split(" "))
start=0
pages = 0
#Run the query and store results for as long as the number of results is bigger than the max results
keep_running = True
result_store = []
while keep_running==True:
pages +=1
print(pages)
#Query url (NB the start arg, which will change as we go through different
#pages)
query_url = base_url+'search_query=all:{q}&start={s}&max_results={max_res}'.format(
q=processed_query,s=start,max_res=max_results)
#Download
source = requests.get(query_url)
#Parse the xml and get the entries (papers)
parsed = feedparser.parse(source.content)
#Extract entries
entries = parsed['entries']
#If the number of entries is bigger than the maximum number of results
#this means we need to go to another page. We do that by offseting the
#start with max results
result_store.append(entries)
if len(entries)==max_results:
start+=max_results
#If we have less than max results this means we have run out of
#results and we toggle the keep_running switch off.
if len(entries)<max_results:
keep_running=False
time.sleep(wait_time)
#Save results in a flat list
self.entry_results = [x for el in result_store for x in el]
def extract_data(self):
'''
Here we extract data from the entries
'''
#Load entries
entries = self.entry_results
#Create df
output = pd.concat([pd.DataFrame({
'query':self.query_string,
'id':x['id'],
'link':x['link'],
'title':x['title'],
'authors':", ".join([el['name'] for el in x['authors']]),
'summary':x['summary'],
'updated':x['updated'],
'published':x['published'],
'category':x['arxiv_primary_category']['term'],
'pdf':str([el['href'] for el in x['links'] if el['type']=='application/pdf'][0]
)},index=[0]) for x in entries]).reset_index(drop=True)
output['year_published'] = [x.split("-")[0] for x in output['published']]
self.output_df = output
query_terms = ['artificial intelligence','machine learning','deep learning']
#There are some inconsistencies in the number of results so we run the query three times for each
#term and remove duplicated results
def extract_arxiv_data(term,max_results=1000,wait_time=10, tests=3):
'''
This function initialises the Arxiv_querier class, extracts the data and outputs it
'''
print(term)
collected = []
#We collect the data thrice
for i in np.arange(tests):
print('run'+ ' ' +str(i))
initialised = Arxiv_querier()
initialised.query(term,max_results,wait_time)
initialised.extract_data()
out = initialised.output_df
collected.append(out)
#We concatenate the dfs and remove the duplicates.
output = pd.concat(collected)
output_no_dupes = output.drop_duplicates('id')
#Return both
return([output,output_no_dupes])
arxiv_ai_results_three = [extract_arxiv_data(term=q) for q in query_terms]
all_papers = pd.concat([x[1] for x in arxiv_ai_results_three]).drop_duplicates('id').reset_index(drop=True)
print(all_papers.shape)
all_papers.head()
all_papers.to_csv(int_data+'/{today}_ai_papers.csv'.format(today=today_str),index=False) | notebooks/ml_topic_analysis_exploration.ipynb | Juan-Mateos/coll_int_ai_case | mit |
2. Some exploratory analysis | from nltk.corpus import stopwords
from nltk.tokenize import word_tokenize, sent_tokenize, RegexpTokenizer, PunktSentenceTokenizer
from nltk.stem import WordNetLemmatizer, SnowballStemmer, PorterStemmer
import scipy
import ast
import string as st
from bs4 import BeautifulSoup
import gensim
from gensim.models.coherencemodel import CoherenceModel
from sklearn.feature_extraction.text import TfidfVectorizer
from itertools import product
stopwords_c = stopwords.words('english')
stemmer = PorterStemmer()
lemmatizer= WordNetLemmatizer()
#Read papers
all_papers = pd.read_csv(int_data+'/19_8_2017_ai_papers.csv'.format(today=today_str))
#Let's begin by looking at years
#When where they published?
#Year distribution
year_pubs = all_papers['year_published'].value_counts()
year_pubs.index = [int(x) for x in year_pubs.index]
fig,ax = plt.subplots(figsize=(10,5))
year_pubs_sorted = year_pubs[sorted(year_pubs.index)]
year_pubs_subset = year_pubs_sorted[year_pubs_sorted.index>1991]
ax.plot(np.arange(1993,2018),year_pubs_subset.cumsum(),color='red')
ax.bar(np.arange(1993,2018),year_pubs_subset)
ax.hlines(xmin=1993,xmax=2017,y=[10000,20000,30000,40000],colors='green',linestyles='dashed',alpha=0.7)
ax.set_title("Papers on AI, ML and DL, total per year (bar) and cumulative (red)",size=14)
#What are the categories of the papers? Are we capturing what we think we are capturing
#Top 20
all_papers['category'].value_counts()[:20] | notebooks/ml_topic_analysis_exploration.ipynb | Juan-Mateos/coll_int_ai_case | mit |
See <a href='https://arxiv.org/help/api/user-manual'>here</a> for abbreviations of categories.
In a nutshell, AI is AI, LG is 'Learning', CV is 'Computer Vision', 'CL' is 'computation and language' and NE is 'Neural and Evolutionary computing'. SL.ML is kind of self-explanatory. We seem to be picking up the main things | #NB do we want to remove hyphens?
punct = re.sub('-','',st.punctuation)
def comp_sentence(sentence):
'''
Takes a sentence and pre-processes it.
The output is the sentence as a bag of words
'''
#Remove line breaks and hyphens
sentence = re.sub('\n',' ',sentence)
sentence = re.sub('-',' ',sentence)
#Lowercase and tokenise
text_lowered = [x.lower() for x in sentence.split(" ")]
#Remove signs and digits
text_no_signs_digits = ["".join([x for x in el if x not in punct+st.digits]) for
el in text_lowered]
#Remove stop words, single letters
text_stopped = [w for w in text_no_signs_digits if w not in stopwords_c and
len(w)>1]
#Stem
text_lemmatised = [lemmatizer.lemmatize(w) for w in text_stopped]
#Output
return(text_lemmatised)
#Process text
clean_corpus = [comp_sentence(x) for x in all_papers['summary']]
#We remove rate words
word_freqs = pd.Series([x for el in clean_corpus for x in el]).value_counts()
word_freqs[:30]
rare_words = word_freqs.index[word_freqs<=2]
rare_words[:10] | notebooks/ml_topic_analysis_exploration.ipynb | Juan-Mateos/coll_int_ai_case | mit |
Lots of the rare words seem to be typos and so forth. We remove them | #Removing rare words
clean_corpus_no_rare = [[x for x in el if x not in rare_words] for el in clean_corpus] | notebooks/ml_topic_analysis_exploration.ipynb | Juan-Mateos/coll_int_ai_case | mit |
2 NLP (topic modelling & word embeddings) | #Identify 2-grams (frequent in science!)
bigram_transformer = gensim.models.Phrases(clean_corpus_no_rare)
#Train the model on the corpus
#Let's do a bit of grid search
#model = gensim.models.Word2Vec(bigram_transformer[clean_corpus], size=360, window=15, min_count=2, iter=20)
model.most_similar('ai_safety')
model.most_similar('complexity')
model.most_similar('github')
#Create 3 different dictionaries and bows depending on word sizes
def remove_words_below_threshold(corpus,threshold):
'''
Takes a list of terms and removes any which are below a threshold of occurrences
'''
#Produce token frequencies
token_frequencies = pd.Series([x for el in corpus for x in el]).value_counts()
#Identify tokens to drop (below a threshold)
tokens_to_drop = token_frequencies.index[token_frequencies<=threshold]
#Processed corpus
processed_corpus = [[x for x in el if x not in tokens_to_drop] for el in corpus]
#Dictionary
dictionary = gensim.corpora.Dictionary(processed_corpus)
corpus_bow = [dictionary.doc2bow(x) for x in processed_corpus]
return([dictionary,corpus_bow,processed_corpus])
#Initial model run to see what comes out.
#Transform corpus to bigrams
transformed_corpus = bigram_transformer[clean_corpus]
corpora_to_process = {str(x):remove_words_below_threshold(transformed_corpus,x) for x in [1,2,5,10]}
#Need to turn this into a function.
#Topic modelling
#Parameters for Grid search.
lda_params = list(product([100,200,300],[2,5]))
#Model container
lda_models = []
for x in lda_params:
#Print stage
print('{x}_{y}'.format(x=x[0],y=x[1]))
#Load corpus and dict
dictionary = corpora_to_process[str(x[1])][0]
corpus_bow = corpora_to_process[str(x[1])][1]
corpus = corpora_to_process[str(x[1])][2]
print('training')
#Train model
mod = gensim.models.LdaModel(corpus_bow,num_topics=x[0],id2word=dictionary,
passes=10,iterations=50)
print('coherence')
#Extract coherence
cm = CoherenceModel(mod,texts=corpus,
dictionary=dictionary,coherence='u_mass')
#Get value
try:
coherence_value = cm.get_coherence()
except:
print('coherence_error')
coherence_value='error'
lda_models.append([x,mod,[coherence_value,cm]])
with open(mod_path+'/{t}_ai_topic_models.p'.format(t=today_str),'wb') as outfile:
pickle.dump(lda_models,outfile)
#Visualiase model performance
model_eval = pd.DataFrame([[x[0][0],x[0][1],x[2][0]] for x in lda_models],columns=['topics','word_lim','coherence'])
fig,ax = plt.subplots(figsize=(10,5))
cols = ['red','green','blue']
legs = []
for num,x in enumerate(set(model_eval['word_lim'])):
subset = model_eval.loc[[z == x for z in model_eval['word_lim']],:]
ax.plot(subset.loc[:,'topics'],subset.loc[:,'coherence'],color=cols[num-1])
legs.append([cols[num-1],x])
ax.legend(labels=[x[1] for x in legs],title='Min word count')
ax.set_title('Model performance with different parameters')
with open(mod_path+'/19_8_2017_ai_topic_models.p','rb') as infile:
lda_models = pickle.load(infile)
check_model= lda_models[1][1]
#Explore topics via LDAvis
import pyLDAvis.gensim
pyLDAvis.enable_notebook()
pyLDAvis.gensim.prepare(
#Insert best model/corpus/topics here
check_model,
corpora_to_process[str(5)][1],
corpora_to_process[str(5)][0])
#Can we extract the relevant terms for the topics as in Sievert and Shirley in order to name them?
#First - create a matrix with top 30 terms per topic
top_30_kws = [check_model.get_topic_terms(topicid=n,topn=1000) for n in np.arange(0,100)]
#Keyword df where the columns are tokens and the rows are topics
top_30_kws_df = pd.concat([pd.DataFrame([x[1] for x in el],
index=[x[0] for x in el]) for el in top_30_kws],
axis=1).fillna(0).T.reset_index(drop=True)
#This is the dictionary
selected_dictionary = corpora_to_process[str(5)][0]
#Total number of terms in the document
total_terms = np.sum([vals for vals in selected_dictionary.dfs.values()])
#Appearances of different terms
document_freqs = pd.Series([v for v in selected_dictionary.dfs.values()],
index=[k for k in selected_dictionary.dfs.keys()])[top_30_kws_df.columns]/total_terms
#Normalise the terms (divide the vector of probabilities of each keywords in each topic by the totals)
top_30_kws_normalised = top_30_kws_df.apply(lambda x: x/document_freqs,axis=0)
#Now we want to extract, for each topic, the relevance score.
def relevance_score(prob_in_topic,prob_in_corpus,id2word_lookup,lambda_par = 0.6):
'''
Combines the probabilities using the definition in Sievert and Shirley and returns the top 5 named
#terms for each topic
'''
#Create dataframe
combined = pd.concat([prob_in_topic,prob_in_corpus],axis=1)
combined.columns=['prob_in_topic','prob_in_corpus']
#Create relevance metric
combined['relevance'] = lambda_par*combined['prob_in_topic'] + (1-lambda_par)*combined['prob_in_corpus']
#Top words
top_ids = list(combined.sort_values('relevance',ascending=False).index[:5])
#Top words
top_words = "_".join([id2word_lookup[this_id] for this_id in top_ids])
return(top_words)
relevance_scores = [relevance_score(top_30_kws_df.iloc[n,:],
top_30_kws_normalised.iloc[n,:],
dictionary.id2token,lambda_par=0.6) for n in np.arange(len(top_30_kws_df))]
%%time
#Create a df with the topic predictions.
paper_preds = check_model[corpora_to_process[str(5)][1]]
paper_topics_df = pd.concat([pd.DataFrame([x[1] for x in el],index=[x[0] for x in el]) for el in paper_preds],
axis=1).T
#Replace NAs with zeros and drop pointless index
paper_topics_df.fillna(value=0,inplace=True)
paper_topics_df.reset_index(drop=True,inplace=True)
paper_topics_df.columns = relevance_scores
paper_topics_df.to_csv(int_data+'/{t}_paper_topic_mix.csv'.format(t=today_str),index=False)
#paper_topics_df = pd.read_csv(int_data+'/{t}_paper_topic_mix.csv')
#Quick test of Deep learning papers
#These are papers with a topic that seems to capture deep learning
dl_papers = [x>0.05 for x in paper_topics_df['network_training_model_deep_deep_learning']]
dl_papers_metadata = pd.concat([pd.Series(dl_papers),all_papers],axis=1)
paper_frequencies = pd.crosstab(dl_papers_metadata.year_published,dl_papers_metadata[0])
paper_frequencies.columns=['no_dl','dl']
fig,ax = plt.subplots(figsize=(10,5))
paper_frequencies.plot.bar(stacked=True,ax=ax)
ax.set_title('Number of papers in the DL \'topic\'')
ax.legend(labels=['Not ANN/DL related','NN/DL topic >0.05']) | notebooks/ml_topic_analysis_exploration.ipynb | Juan-Mateos/coll_int_ai_case | mit |
Some of this is interesting. Doesn't seem to be picking up the policy related terms (safety, discrimination)
Next stages - focus on policy related terms. Can we look for papers in keyword dictionaries identified through the word embeddings?
Obtain Google Scholar data | #How many authors are there in the data? Can we collect all their institutions from Google Scholar
paper_authors = pd.Series([x for el in all_papers['authors'] for x in el.split(", ")])
paper_authors_unique = paper_authors.drop_duplicates()
len(paper_authors_unique) | notebooks/ml_topic_analysis_exploration.ipynb | Juan-Mateos/coll_int_ai_case | mit |
We have 68,000 authors. It might take a while to get their data from Google Scholar | #Top authors and frequencies
authors_freq = paper_authors.value_counts()
fig,ax=plt.subplots(figsize=(10,3))
ax.hist(authors_freq,bins=30)
ax.set_title('Distribution of publications')
#Pretty skewed distribution!
print(authors_freq.describe())
np.sum(authors_freq>2) | notebooks/ml_topic_analysis_exploration.ipynb | Juan-Mateos/coll_int_ai_case | mit |
Less than 10,000 authors with 3+ papers in the data | get_scholar_data(
%%time
#Test run
import scholarly
@ratelim.patient(max_calls=30,time_interval=60)
def get_scholar_data(scholarly_object):
''''''
try:
scholarly_object = next(scholarly_object)
metadata = {}
metadata['name']=scholarly_object.name
metadata['affiliation'] = scholarly_object.affiliation
metadata['interests'] = scholarly_object.interests
return(metadata)
except:
return('nothing')
#Extract information from each query (it is a generator)
#Get data
#ml_author_gscholar=[]
for num,x in enumerate(paper_authors_unique[1484:]):
if num % 100 == 0:
print(str(num)+":"+x)
result = get_scholar_data(scholarly.search_author(x))
ml_author_gscholar.append(result)
len(ml_author_gscholar) | notebooks/ml_topic_analysis_exploration.ipynb | Juan-Mateos/coll_int_ai_case | mit |
1. General Mixture Models
pomegranate has a very efficient implementation of mixture models, particularly Gaussian mixture models. Lets take a look at how fast pomegranate is versus sklearn, and then see how much faster parallelization can get it to be. | n, d, k = 1000000, 5, 3
X, y = create_dataset(n, d, k)
print "sklearn GMM"
%timeit GaussianMixture(n_components=k, covariance_type='full', max_iter=15, tol=1e-10).fit(X)
print
print "pomegranate GMM"
%timeit GeneralMixtureModel.from_samples(MultivariateGaussianDistribution, k, X, max_iterations=15, stop_threshold=1e-10)
print
print "pomegranate GMM (4 jobs)"
%timeit GeneralMixtureModel.from_samples(MultivariateGaussianDistribution, k, X, n_jobs=4, max_iterations=15, stop_threshold=1e-10) | tutorials/old/Tutorial_7_Parallelization.ipynb | jmschrei/pomegranate | mit |
It looks like on a large dataset not only is pomegranate faster than sklearn at performing 15 iterations of EM on 3 million 5 dimensional datapoints with 3 clusters, but the parallelization is able to help in speeding things up.
Lets now take a look at the time it takes to make predictions using GMMs. Lets fit the model to a small amount of data, and then predict a larger amount of data drawn from the same underlying distributions. | d, k = 25, 2
X, y = create_dataset(1000, d, k)
a = GaussianMixture(k, n_init=1, max_iter=25).fit(X)
b = GeneralMixtureModel.from_samples(MultivariateGaussianDistribution, k, X, max_iterations=25)
del X, y
n = 1000000
X, y = create_dataset(n, d, k)
print "sklearn GMM"
%timeit -n 1 a.predict_proba(X)
print
print "pomegranate GMM"
%timeit -n 1 b.predict_proba(X)
print
print "pomegranate GMM (4 jobs)"
%timeit -n 1 b.predict_proba(X, n_jobs=4) | tutorials/old/Tutorial_7_Parallelization.ipynb | jmschrei/pomegranate | mit |
It looks like pomegranate can be slightly slower than sklearn when using a single processor, but that it can be parallelized to get faster performance. At the same time, predictions at this level happen so quickly (millions per second) that this may not be the most reliable test for parallelization.
To ensure that we're getting the exact same results just faster, lets subtract the predictions from each other and make sure that the sum is equal to 0. | print (b.predict_proba(X) - b.predict_proba(X, n_jobs=4)).sum() | tutorials/old/Tutorial_7_Parallelization.ipynb | jmschrei/pomegranate | mit |
Great, no difference between the two.
Lets now make sure that pomegranate and sklearn are learning basically the same thing. Lets fit both models to some 2 dimensional 2 component data and make sure that they both extract the underlying clusters by plotting them. | d, k = 2, 2
X, y = create_dataset(1000, d, k, alpha=2)
a = GaussianMixture(k, n_init=1, max_iter=25).fit(X)
b = GeneralMixtureModel.from_samples(MultivariateGaussianDistribution, k, X, max_iterations=25)
y1, y2 = a.predict(X), b.predict(X)
plt.figure(figsize=(16,6))
plt.subplot(121)
plt.title("sklearn clusters", fontsize=14)
plt.scatter(X[y1==0, 0], X[y1==0, 1], color='m', edgecolor='m')
plt.scatter(X[y1==1, 0], X[y1==1, 1], color='c', edgecolor='c')
plt.subplot(122)
plt.title("pomegranate clusters", fontsize=14)
plt.scatter(X[y2==0, 0], X[y2==0, 1], color='m', edgecolor='m')
plt.scatter(X[y2==1, 0], X[y2==1, 1], color='c', edgecolor='c') | tutorials/old/Tutorial_7_Parallelization.ipynb | jmschrei/pomegranate | mit |
It looks like we're getting the same basic results for the two. The two algorithms are initialized a bit differently, and so it can be difficult to directly compare the results between them, but it looks like they're getting roughly the same results.
3. Multivariate Gaussian HMM
Now let's move on to training a hidden Markov model with multivariate Gaussian emissions with a diagonal covariance matrix. We'll randomly generate some Gaussian distributed numbers and use pomegranate with either one or four threads to fit our model to the data. | X = numpy.random.randn(1000, 500, 50)
print "pomegranate Gaussian HMM (1 job)"
%timeit -n 1 -r 1 HiddenMarkovModel.from_samples(NormalDistribution, 5, X, max_iterations=5)
print
print "pomegranate Gaussian HMM (2 jobs)"
%timeit -n 1 -r 1 HiddenMarkovModel.from_samples(NormalDistribution, 5, X, max_iterations=5, n_jobs=2)
print
print "pomegranate Gaussian HMM (2 jobs)"
%timeit -n 1 -r 1 HiddenMarkovModel.from_samples(NormalDistribution, 5, X, max_iterations=5, n_jobs=4) | tutorials/old/Tutorial_7_Parallelization.ipynb | jmschrei/pomegranate | mit |
All we had to do was pass in the n_jobs parameter to the fit function in order to get a speed improvement. It looks like we're getting a really good speed improvement, as well! This is mostly because the HMM algorithms perform a lot more operations than the other models, and so spend the vast majority of time with the GIL released. You may not notice as strong speedups when using a MultivariateGaussianDistribution because BLAS uses multithreaded operations already internally, even when only one job is specified.
Now lets look at the prediction function to make sure the we're getting speedups there as well. You'll have to use a wrapper function to parallelize the predictions for a HMM because it returns an annotated sequence rather than a single value like a classic machine learning model might. | model = HiddenMarkovModel.from_samples(NormalDistribution, 5, X, max_iterations=2, verbose=False)
print "pomegranate Gaussian HMM (1 job)"
%timeit predict_proba(model, X)
print
print "pomegranate Gaussian HMM (2 jobs)"
%timeit predict_proba(model, X, n_jobs=2) | tutorials/old/Tutorial_7_Parallelization.ipynb | jmschrei/pomegranate | mit |
Great, we're getting a really good speedup on that as well! Looks like the parallel processing is more efficient with a bigger, more complex model, than with a simple one. This can make sense, because all inference/training is more complex, and so there is more time with the GIL released compared to with the simpler operations.
4. Mixture of Hidden Markov Models
Let's stack another layer onto this model by making it a mixture of these hidden Markov models, instead of a single one. At this point we're sticking a multivariate Gaussian HMM into a mixture and we're going to train this big thing in parallel. | def create_model(mus):
n = mus.shape[0]
starts = numpy.zeros(n)
starts[0] = 1.
ends = numpy.zeros(n)
ends[-1] = 0.5
transition_matrix = numpy.zeros((n, n))
distributions = []
for i in range(n):
transition_matrix[i, i] = 0.5
if i < n - 1:
transition_matrix[i, i+1] = 0.5
distribution = IndependentComponentsDistribution([NormalDistribution(mu, 1) for mu in mus[i]])
distributions.append(distribution)
model = HiddenMarkovModel.from_matrix(transition_matrix, distributions, starts, ends)
return model
def create_mixture(mus):
hmms = [create_model(mu) for mu in mus]
return GeneralMixtureModel(hmms)
n, d = 50, 10
mus = [(numpy.random.randn(d, n)*0.2 + numpy.random.randn(n)*2).T for i in range(2)]
model = create_mixture(mus)
X = numpy.random.randn(400, 150, d)
print "pomegranate Mixture of Gaussian HMMs (1 job)"
%timeit model.fit(X, max_iterations=5)
print
model = create_mixture(mus)
print "pomegranate Mixture of Gaussian HMMs (2 jobs)"
%timeit model.fit(X, max_iterations=5, n_jobs=2) | tutorials/old/Tutorial_7_Parallelization.ipynb | jmschrei/pomegranate | mit |
Looks like we're getting a really nice speed improvement when training this complex model. Let's take a look now at the time it takes to do inference with it. | model = create_mixture(mus)
print "pomegranate Mixture of Gaussian HMMs (1 job)"
%timeit model.predict_proba(X)
print
model = create_mixture(mus)
print "pomegranate Mixture of Gaussian HMMs (2 jobs)"
%timeit model.predict_proba(X, n_jobs=2) | tutorials/old/Tutorial_7_Parallelization.ipynb | jmschrei/pomegranate | mit |
The inner product of blades in GAlgebra is zero if either operand is a scalar:
$$\begin{split}\begin{aligned}
{\boldsymbol{A}}{r}{\wedge}{\boldsymbol{B}}{s} &\equiv {\left <{{\boldsymbol{A}}{r}{\boldsymbol{B}}{s}} \right >{r+s}} \
{\boldsymbol{A}}{r}\cdot{\boldsymbol{B}}{s} &\equiv {\left { { \begin{array}{cc}
r\mbox{ and }s \ne 0: & {\left <{{\boldsymbol{A}}{r}{\boldsymbol{B}}{s}} \right >{{\left |{r-s}\right |}}} \
r\mbox{ or }s = 0: & 0 \end{array}} \right }}
\end{aligned}\end{split}$$
This definition comes from David Hestenes and Garret Sobczyk, “Clifford Algebra to Geometric Calculus,” Kluwer Academic Publishers, 1984.
In some other literature, the inner product is defined without the exceptional case for scalar part and the definition above is known as "the modified Hestenes inner product" (this name comes from the source code of GAViewer). | c|a
a|c
c|A
A|c | examples/ipython/inner_product.ipynb | arsenovic/galgebra | bsd-3-clause |
$ab=a \wedge b + a \cdot b$ holds for vectors: | a*b
a^b
a|b
(a*b)-(a^b)-(a|b) | examples/ipython/inner_product.ipynb | arsenovic/galgebra | bsd-3-clause |
$aA=a \wedge A + a \cdot A$ holds for the products between vectors and multivectors: | a*A
a^A
a|A
(a*A)-(a^A)-(a|A) | examples/ipython/inner_product.ipynb | arsenovic/galgebra | bsd-3-clause |
$AB=A \wedge B + A \cdot B$ does NOT hold for the products between multivectors and multivectors: | A*B
A|B
(A*B)-(A^B)-(A|B)
(A<B)+(A|B)+(A>B)-A*B | examples/ipython/inner_product.ipynb | arsenovic/galgebra | bsd-3-clause |
Toolkit: Visualization Functions
This class will introduce 3 different visualizations that can be used with the two different classification type neural networks and regression neural networks.
Confusion Matrix - For any type of classification neural network.
ROC Curve - For binary classification.
Lift Curve - For regression neural networks.
The code used to produce these visualizations is shown here: | %matplotlib inline
import matplotlib.pyplot as plt
from sklearn.metrics import roc_curve, auc
# Plot a confusion matrix.
# cm is the confusion matrix, names are the names of the classes.
def plot_confusion_matrix(cm, names, title='Confusion matrix', cmap=plt.cm.Blues):
plt.imshow(cm, interpolation='nearest', cmap=cmap)
plt.title(title)
plt.colorbar()
tick_marks = np.arange(len(names))
plt.xticks(tick_marks, names, rotation=45)
plt.yticks(tick_marks, names)
plt.tight_layout()
plt.ylabel('True label')
plt.xlabel('Predicted label')
# Plot an ROC. pred - the predictions, y - the expected output.
def plot_roc(pred,y):
fpr, tpr, _ = roc_curve(y_test, pred)
roc_auc = auc(fpr, tpr)
plt.figure()
plt.plot(fpr, tpr, label='ROC curve (area = %0.2f)' % roc_auc)
plt.plot([0, 1], [0, 1], 'k--')
plt.xlim([0.0, 1.0])
plt.ylim([0.0, 1.05])
plt.xlabel('False Positive Rate')
plt.ylabel('True Positive Rate')
plt.title('Receiver Operating Characteristic (ROC)')
plt.legend(loc="lower right")
plt.show()
# Plot a lift curve. pred - the predictions, y - the expected output.
def chart_regression(pred,y):
t = pd.DataFrame({'pred' : pred.flatten(), 'y' : y_test.flatten()})
t.sort_values(by=['y'],inplace=True)
a = plt.plot(t['y'].tolist(),label='expected')
b = plt.plot(t['pred'].tolist(),label='prediction')
plt.ylabel('output')
plt.legend()
plt.show() | t81_558_class4_class_reg.ipynb | jbliss1234/ML | apache-2.0 |
Binary Classification
Binary classification is used to create a model that classifies between only two classes. These two classes are often called "positive" and "negative". Consider the following program that uses the wcbreast_wdbc dataset to classify if a breast tumor is cancerous (malignant) or not (benign). The iris dataset is not binary, because there are three classes (3 types of iris). | import os
import pandas as pd
from sklearn.cross_validation import train_test_split
import tensorflow.contrib.learn as skflow
import numpy as np
from sklearn import metrics
path = "./data/"
filename = os.path.join(path,"wcbreast_wdbc.csv")
df = pd.read_csv(filename,na_values=['NA','?'])
# Encode feature vector
df.drop('id',axis=1,inplace=True)
encode_numeric_zscore(df,'mean_radius')
encode_text_index(df,'mean_texture')
encode_text_index(df,'mean_perimeter')
encode_text_index(df,'mean_area')
encode_text_index(df,'mean_smoothness')
encode_text_index(df,'mean_compactness')
encode_text_index(df,'mean_concavity')
encode_text_index(df,'mean_concave_points')
encode_text_index(df,'mean_symmetry')
encode_text_index(df,'mean_fractal_dimension')
encode_text_index(df,'se_radius')
encode_text_index(df,'se_texture')
encode_text_index(df,'se_perimeter')
encode_text_index(df,'se_area')
encode_text_index(df,'se_smoothness')
encode_text_index(df,'se_compactness')
encode_text_index(df,'se_concavity')
encode_text_index(df,'se_concave_points')
encode_text_index(df,'se_symmetry')
encode_text_index(df,'se_fractal_dimension')
encode_text_index(df,'worst_radius')
encode_text_index(df,'worst_texture')
encode_text_index(df,'worst_perimeter')
encode_text_index(df,'worst_area')
encode_text_index(df,'worst_smoothness')
encode_text_index(df,'worst_compactness')
encode_text_index(df,'worst_concavity')
encode_text_index(df,'worst_concave_points')
encode_text_index(df,'worst_symmetry')
encode_text_index(df,'worst_fractal_dimension')
diagnosis = encode_text_index(df,'diagnosis')
num_classes = len(diagnosis)
# Create x & y for training
# Create the x-side (feature vectors) of the training
x, y = to_xy(df,'diagnosis')
# Split into train/test
x_train, x_test, y_train, y_test = train_test_split(
x, y, test_size=0.25, random_state=42)
# Create a deep neural network with 3 hidden layers of 10, 20, 10
classifier = skflow.TensorFlowDNNClassifier(hidden_units=[10, 20, 10], n_classes=num_classes,
steps=10000)
# Early stopping
early_stop = skflow.monitors.ValidationMonitor(x_test, y_test,
early_stopping_rounds=200, print_steps=50, n_classes=num_classes)
# Fit/train neural network
classifier.fit(x_train, y_train, early_stop)
# Measure accuracy
score = metrics.accuracy_score(y, classifier.predict(x))
print("Final accuracy: {}".format(score))
| t81_558_class4_class_reg.ipynb | jbliss1234/ML | apache-2.0 |
Confusion Matrix
The confusion matrix is a common visualization for both binary and larger classification problems. Often a model will have difficulty differentiating between two classes. For example, a neural network might be really good at telling the difference between cats and dogs, but not so good at telling the difference between dogs and wolves. The following code generates a confusion matrix: | import numpy as np
from sklearn import svm, datasets
from sklearn.cross_validation import train_test_split
from sklearn.metrics import confusion_matrix
pred = classifier.predict(x_test)
# Compute confusion matrix
cm = confusion_matrix(y_test, pred)
np.set_printoptions(precision=2)
print('Confusion matrix, without normalization')
print(cm)
plt.figure()
plot_confusion_matrix(cm, diagnosis)
# Normalize the confusion matrix by row (i.e by the number of samples
# in each class)
cm_normalized = cm.astype('float') / cm.sum(axis=1)[:, np.newaxis]
print('Normalized confusion matrix')
print(cm_normalized)
plt.figure()
plot_confusion_matrix(cm_normalized, diagnosis, title='Normalized confusion matrix')
plt.show() | t81_558_class4_class_reg.ipynb | jbliss1234/ML | apache-2.0 |
The above two confusion matrixes show the same network. The bottom (normalized) is the type you will normally see. Notice the two labels. The label "B" means benign (no cancer) and the label "M" means malignant (cancer). The left-right (x) axis are the predictions, the top-bottom) are the expected outcomes. A perfect model (that never makes an error) has a dark blue diagonal that runs from top-left to bottom-right.
To read, consider the top-left square. This square indicates "true labeled" of B and also "predicted label" of B. This is good! The prediction matched the truth. The blueness of this box represents how often "B" is classified correct. It is not darkest blue. This is because the square to the right(which is off the perfect diagonal) has some color. This square indicates truth of "B" but prediction of "M". The white square, at the bottom-left, indicates a true of "M" but predicted of "B". The whiteness indicates this rarely happens.
Your conclusion from the above chart is that the model sometimes classifies "B" as "M" (a false negative), but never mis-classifis "M" as "B". Always look for the dark diagonal, this is good!
ROC Curves
ROC curves can be a bit confusing. However, they are very common. It is important to know how to read them. Even their name is confusing. Do not worry about their name, it comes from electrical engineering (EE).
Binary classification is common in medical testing. Often you want to diagnose if someone has a disease. This can lead to two types of errors, know as false positives and false negatives:
False Positive - Your test (neural network) indicated that the patient had the disease; however, the patient did not have the disease.
False Negative - Your test (neural network) indicated that the patient did not have the disease; however, the patient did have the disease.
True Positive - Your test (neural network) correctly identified that the patient had the disease.
True Negative - Your test (neural network) correctly identified that the patient did not have the disease.
Types of errors:
Neural networks classify in terms of probbility of it being positive. However, at what probability do you give a positive result? Is the cutoff 50%? 90%? Where you set this cutoff is called the threshold. Anything above the cutoff is positive, anything below is negative. Setting this cutoff allows the model to be more sensative or specific:
The following shows a more sensitive cutoff:
An ROC curve measures how good a model is regardless of the cutoff. The following shows how to read a ROC chart:
The following code shows an ROC chart for the breast cancer neural network. The area under the curve (AUC) is also an important measure. The larger the AUC, the better. | pred = classifier.predict_proba(x_test)
pred = pred[:,1] # Only positive cases
# print(pred[:,1])
plot_roc(pred,y_test)
| t81_558_class4_class_reg.ipynb | jbliss1234/ML | apache-2.0 |
Classification
We've already seen multi-class classification, with the iris dataset. Confusion matrixes work just fine with 3 classes. The following code generates a confusion matrix for iris. | import os
import pandas as pd
from sklearn.cross_validation import train_test_split
import tensorflow.contrib.learn as skflow
import numpy as np
path = "./data/"
filename = os.path.join(path,"iris.csv")
df = pd.read_csv(filename,na_values=['NA','?'])
# Encode feature vector
encode_numeric_zscore(df,'petal_w')
encode_numeric_zscore(df,'petal_l')
encode_numeric_zscore(df,'sepal_w')
encode_numeric_zscore(df,'sepal_l')
species = encode_text_index(df,"species")
num_classes = len(species)
# Create x & y for training
# Create the x-side (feature vectors) of the training
x, y = to_xy(df,'species')
# Split into train/test
x_train, x_test, y_train, y_test = train_test_split(
x, y, test_size=0.25, random_state=45)
# as much as I would like to use 42, it gives a perfect result, and a boring confusion matrix!
# Create a deep neural network with 3 hidden layers of 10, 20, 10
classifier = skflow.TensorFlowDNNClassifier(hidden_units=[10, 20, 10], n_classes=num_classes,
steps=10000)
# Early stopping
early_stop = skflow.monitors.ValidationMonitor(x_test, y_test,
early_stopping_rounds=200, print_steps=50, n_classes=num_classes)
# Fit/train neural network
classifier.fit(x_train, y_train, early_stop)
import numpy as np
from sklearn import svm, datasets
from sklearn.cross_validation import train_test_split
from sklearn.metrics import confusion_matrix
pred = classifier.predict(x_test)
# Compute confusion matrix
cm = confusion_matrix(y_test, pred)
np.set_printoptions(precision=2)
print('Confusion matrix, without normalization')
print(cm)
plt.figure()
plot_confusion_matrix(cm, species)
# Normalize the confusion matrix by row (i.e by the number of samples
# in each class)
cm_normalized = cm.astype('float') / cm.sum(axis=1)[:, np.newaxis]
print('Normalized confusion matrix')
print(cm_normalized)
plt.figure()
plot_confusion_matrix(cm_normalized, species, title='Normalized confusion matrix')
plt.show() | t81_558_class4_class_reg.ipynb | jbliss1234/ML | apache-2.0 |
See the strong diagonal? Iris is easy. See the light blue near the bottom? Sometimes virginica is confused for versicolor.
Regression
We've already seen regression with the MPG dataset. Regression uses its own set of visualizations, one of the most common is the lift chart. The following code generates a lift chart. | import tensorflow.contrib.learn as skflow
import pandas as pd
import os
import numpy as np
from sklearn import metrics
from scipy.stats import zscore
path = "./data/"
filename_read = os.path.join(path,"auto-mpg.csv")
df = pd.read_csv(filename_read,na_values=['NA','?'])
# create feature vector
missing_median(df, 'horsepower')
df.drop('name',1,inplace=True)
encode_numeric_zscore(df, 'horsepower')
encode_numeric_zscore(df, 'weight')
encode_numeric_zscore(df, 'cylinders')
encode_numeric_zscore(df, 'displacement')
encode_numeric_zscore(df, 'acceleration')
encode_text_dummy(df, 'origin')
# Encode to a 2D matrix for training
x,y = to_xy(df,['mpg'])
# Split into train/test
x_train, x_test, y_train, y_test = train_test_split(
x, y, test_size=0.25, random_state=42)
# Create a deep neural network with 3 hidden layers of 50, 25, 10
regressor = skflow.TensorFlowDNNRegressor(hidden_units=[50, 25, 10], steps=5000)
# Early stopping
early_stop = skflow.monitors.ValidationMonitor(x_test, y_test,
early_stopping_rounds=200, print_steps=50)
# Fit/train neural network
regressor.fit(x_train, y_train, early_stop)
pred = regressor.predict(x_test)
chart_regression(pred,y_test) | t81_558_class4_class_reg.ipynb | jbliss1234/ML | apache-2.0 |
Reordering the Callendar-Van Duzen equation we obtain the following
$$ AT+BT^2+C(T-100)T^3 =\frac{R(T)}{R_0}-1 \enspace,$$
which we can write in matrix form as $Mx=p$, where
$$\begin{bmatrix} T_1 & T_1^2 & (T_1-100)T_1^3 \ T_2 & T_2^2 & (T_2-100)T_2^3 \ T_3 & T_3^2 & (T_3-100)T_3^3\end{bmatrix} \begin{bmatrix} A\ B \ C\end{bmatrix} = \begin{bmatrix} \frac{R(T_1)}{R_0}-1 \ \frac{R(T_2)}{R_0}-1 \ \frac{R(T_3)}{R_0}-1\end{bmatrix} \enspace.$$
Because $M$ is square we can solve by computing $M^{-1}$ directly. | R0=25;
M=np.array([[T_exp[0],(T_exp[0])**2,(T_exp[0]-100)*(T_exp[0])**3],[T_exp[1],(T_exp[1])**2,(T_exp[1]-100)*(T_exp[1])**3],[T_exp[2],(T_exp[2])**2,(T_exp[2]-100)*(T_exp[2])**3]]);
p=np.array([[(R_exp[0]/R0)-1],[(R_exp[1]/R0)-1],[(R_exp[2]/R0)-1]]);
x = np.linalg.solve(M,p) #solve linear equations system
np.set_printoptions(precision=3)
print('M')
print(M)
print('\n')
print('p')
print(p)
print('\n')
print('x')
print(x) | notebooks/Ex_2_3.ipynb | agmarrugo/sensors-actuators | mit |
We have found the coeffiecients $A$, $B$, and $C$ necessary to describe the sensor's transfer function. Now we plot it from -200 C a 600 C. | A=x[0];B=x[1];C=x[2];
T_range= np.arange(start = -200, stop = 601, step = 1);
R_funT= R0*(1+A[0]*T_range+B[0]*(T_range)**2+C[0]*(T_range-100)*(T_range)**3);
plt.plot(T_range,R_funT,T_exp[0],R_exp[0],'ro',T_exp[1],R_exp[1],'ro',T_exp[2],R_exp[2],'ro');
plt.ylabel('Sensor resistance [Ohm]')
plt.xlabel('Temperature [C]')
plt.show()
| notebooks/Ex_2_3.ipynb | agmarrugo/sensors-actuators | mit |
Reddy Mikks model
Given the following variables:
$\begin{aligned}
x_1 = \textrm{Tons of exterior paint produced daily} \newline
x_2 = \textrm{Tons of interior paint produced daily}
\end{aligned}$
and knowing that we want to maximize the profit, where \$5000 is the profit from exterior paint and \$4000 is the profit from a ton of interior paint, the Reddy Mikks model is:
$$\textrm{Maximize } z = 5x_1 + 4x_2$$
subject to
$$6x_1 + 4x_2 \le 24$$
$$x_1 + 2x_2 \le 6$$
$$-x_1 + x_2 \le 1$$
$$x_2 \le 2$$
$$x_1, x_2 \ge 0$$ | reddymikks = pywraplp.Solver('Reddy_Mikks', pywraplp.Solver.GLOP_LINEAR_PROGRAMMING)
x1 = reddymikks.NumVar(0, reddymikks.infinity(), 'x1')
x2 = reddymikks.NumVar(0, reddymikks.infinity(), 'x2')
reddymikks.Add(6*x1 + 4*x2 <= 24)
reddymikks.Add(x1 + 2*x2 <= 6)
reddymikks.Add(-x1 + x2 <= 1)
reddymikks.Add(x2 <= 2)
profit = reddymikks.Objective()
profit.SetCoefficient(x1, 5)
profit.SetCoefficient(x2, 4)
profit.SetMaximization()
status = reddymikks.Solve()
if status not in [reddymikks.OPTIMAL, reddymikks.FEASIBLE]:
raise Exception('No feasible solution found')
print("The company should produce",round(x1.solution_value(),2),"tons of exterior paint")
print("The company should produce",round(x2.solution_value(),2),"tons of interior paint")
print("The optimal profit is", profit.Value(), 'thousand USD') | Linear Programming with OR-Tools.ipynb | rayjustinhuang/DataAnalysisandMachineLearning | mit |
More simple problems
A company that operates 10 hours a day manufactures two products on three sequential processes. The following data characterizes the problem: | import pandas as pd
problemdata = pd.DataFrame({'Process 1': [10, 5], 'Process 2':[6, 20], 'Process 3':[8, 10], 'Unit profit':[20, 30]})
problemdata.index = ['Product 1', 'Product 2']
problemdata | Linear Programming with OR-Tools.ipynb | rayjustinhuang/DataAnalysisandMachineLearning | mit |
Where there are 10 hours a day dedicated to production. Process times are given in minutes per unit while profit is given in USD.
The optimal mix of the two products would be characterized by the following model:
$\begin{aligned}
x_1 = \textrm{Units of product 1} \newline
x_2 = \textrm{Units of product 2}
\end{aligned}$
$$\textrm{Maximize } z = 20x_1 + 30x_2$$
subject to
$$\begin{array}{rcl}
10x_1 + 5x_2 \le 600 \newline
6x_1 + 20x_2 \le 600 \newline
8x_1 + 10x_2 \le 600 \newline
x_1, x_2 \ge 0
\end{array}$$
(we will assume that continuous solution values are acceptable for this problem) | simpleprod = pywraplp.Solver('Simple_Production', pywraplp.Solver.GLOP_LINEAR_PROGRAMMING)
x1 = simpleprod.NumVar(0, simpleprod.infinity(), 'x1')
x2 = simpleprod.NumVar(0, simpleprod.infinity(), 'x2')
for i in problemdata.columns[:-1]:
simpleprod.Add(problemdata.loc[problemdata.index[0], i]*x1 + problemdata.loc[problemdata.index[1], i]*x2 <= 600)
profit = simpleprod.Objective()
profit.SetCoefficient(x1, 20)
profit.SetCoefficient(x2, 30)
profit.SetMaximization()
status = simpleprod.Solve()
if status not in [simpleprod.OPTIMAL, simpleprod.FEASIBLE]:
raise Exception('No feasible solution found')
print("The company should produce",round(x1.solution_value(),2),"units of product 1")
print("The company should produce",round(x2.solution_value(),2),"units of product 2")
print("The optimal profit is", round(profit.Value(),2), 'USD') | Linear Programming with OR-Tools.ipynb | rayjustinhuang/DataAnalysisandMachineLearning | mit |
1. Download Text8 Corpus | import os.path
if not os.path.isfile('text8'):
!wget -c http://mattmahoney.net/dc/text8.zip
!unzip text8.zip | docs/notebooks/nmslibtutorial.ipynb | RaRe-Technologies/gensim | lgpl-2.1 |
Import & Set up Logging
I'm not going to set up logging due to the verbose input displaying in notebooks, but if you want that, uncomment the lines in the cell below. | LOGS = False
if LOGS:
import logging
logging.basicConfig(format='%(asctime)s : %(levelname)s : %(message)s', level=logging.INFO) | docs/notebooks/nmslibtutorial.ipynb | RaRe-Technologies/gensim | lgpl-2.1 |
2. Build Word2Vec Model | from gensim.models import Word2Vec, KeyedVectors
from gensim.models.word2vec import Text8Corpus
# Using params from Word2Vec_FastText_Comparison
params = {
'alpha': 0.05,
'size': 100,
'window': 5,
'iter': 5,
'min_count': 5,
'sample': 1e-4,
'sg': 1,
'hs': 0,
'negative': 5
}
model = Word2Vec(Text8Corpus('text8'), **params)
print(model) | docs/notebooks/nmslibtutorial.ipynb | RaRe-Technologies/gensim | lgpl-2.1 |
See the Word2Vec tutorial for how to initialize and save this model.
Comparing the traditional implementation, Annoy and Nmslib approximation | # Set up the model and vector that we are using in the comparison
from gensim.similarities.index import AnnoyIndexer
from gensim.similarities.nmslib import NmslibIndexer
model.init_sims()
annoy_index = AnnoyIndexer(model, 300)
nmslib_index = NmslibIndexer(model, {'M': 100, 'indexThreadQty': 1, 'efConstruction': 100}, {'efSearch': 10})
# Dry run to make sure both indices are fully in RAM
vector = model.wv.syn0norm[0]
print(model.most_similar([vector], topn=5, indexer=annoy_index))
print(model.most_similar([vector], topn=5, indexer=nmslib_index))
print(model.most_similar([vector], topn=5))
import time
import numpy as np
def avg_query_time(annoy_index=None, queries=1000):
"""
Average query time of a most_similar method over 1000 random queries,
uses annoy if given an indexer
"""
total_time = 0
for _ in range(queries):
rand_vec = model.wv.syn0norm[np.random.randint(0, len(model.wv.vocab))]
start_time = time.clock()
model.most_similar([rand_vec], topn=5, indexer=annoy_index)
total_time += time.clock() - start_time
return total_time / queries
queries = 10000
gensim_time = avg_query_time(queries=queries)
annoy_time = avg_query_time(annoy_index, queries=queries)
nmslib_time = avg_query_time(nmslib_index, queries=queries)
print("Gensim (s/query):\t{0:.5f}".format(gensim_time))
print("Annoy (s/query):\t{0:.5f}".format(annoy_time))
print("Nmslib (s/query):\t{0:.5f}".format(nmslib_time))
speed_improvement_gensim = gensim_time / nmslib_time
speed_improvement_annoy = annoy_time / nmslib_time
print ("\nNmslib is {0:.2f} times faster on average on this particular run".format(speed_improvement_gensim))
print ("\nNmslib is {0:.2f} times faster on average than annoy on this particular run".format(speed_improvement_annoy))
| docs/notebooks/nmslibtutorial.ipynb | RaRe-Technologies/gensim | lgpl-2.1 |
3. Construct Nmslib Index with model & make a similarity query
Creating an indexer
An instance of NmslibIndexer needs to be created in order to use Nmslib in gensim. The NmslibIndexer class is located in gensim.similarities.nmslib
NmslibIndexer() takes three parameters:
model: A Word2Vec or Doc2Vec model
index_params: Parameters for building nmslib indexer. index_params effects the build time and the index size. The example is {'M': 100, 'indexThreadQty': 1, 'efConstruction': 100}. Increasing the value of M and efConstruction improves the accuracy of search. However this also leads to longer indexing times. indexThreadQty is the number of thread.
query_time_params: Parameters for querying on nmslib indexer. query_time_params effects the query time and the search accuracy. The example is {'efSearch': 100}. A larger efSearch will give more accurate results, but larger query time.
More information can be found here. The relationship between parameters, build/query time, and accuracy will be investigated later in the tutorial.
Now that we are ready to make a query, lets find the top 5 most similar words to "science" in the Text8 corpus. To make a similarity query we call Word2Vec.most_similar like we would traditionally, but with an added parameter, indexer. The only supported indexerers in gensim as of now are Annoy and Nmslib. | # Building nmslib indexer
nmslib_index = NmslibIndexer(model, {'M': 100, 'indexThreadQty': 1, 'efConstruction': 100}, {'efSearch': 10})
# Derive the vector for the word "science" in our model
vector = model["science"]
# The instance of AnnoyIndexer we just created is passed
approximate_neighbors = model.most_similar([vector], topn=11, indexer=nmslib_index)
# Neatly print the approximate_neighbors and their corresponding cosine similarity values
print("Approximate Neighbors")
for neighbor in approximate_neighbors:
print(neighbor)
normal_neighbors = model.most_similar([vector], topn=11)
print("\nNormal (not nmslib-indexed) Neighbors")
for neighbor in normal_neighbors:
print(neighbor) | docs/notebooks/nmslibtutorial.ipynb | RaRe-Technologies/gensim | lgpl-2.1 |
Analyzing the results
The closer the cosine similarity of a vector is to 1, the more similar that word is to our query, which was the vector for "science". In this case the results are almostly same.
4. Verify & Evaluate performance
Persisting Indexes
You can save and load your indexes from/to disk to prevent having to construct them each time. This will create two files on disk, fname and fname.d. Both files are needed to correctly restore all attributes. | import os
fname = '/tmp/mymodel.index'
# Persist index to disk
nmslib_index.save(fname)
# Load index back
if os.path.exists(fname):
nmslib_index2 = NmslibIndexer.load(fname)
nmslib_index2.model = model
# Results should be identical to above
vector = model["science"]
approximate_neighbors2 = model.most_similar([vector], topn=11, indexer=nmslib_index2)
for neighbor in approximate_neighbors2:
print(neighbor)
assert approximate_neighbors == approximate_neighbors2 | docs/notebooks/nmslibtutorial.ipynb | RaRe-Technologies/gensim | lgpl-2.1 |
Be sure to use the same model at load that was used originally, otherwise you will get unexpected behaviors.
Save memory by memory-mapping indices saved to disk
Nmslib library has a useful feature that indices can be memory-mapped from disk. It saves memory when the same index is used by several processes.
Below are two snippets of code. First one has a separate index for each process. The second snipped shares the index between two processes via memory-mapping. The second example uses less total RAM as it is shared. | # Remove verbosity from code below (if logging active)
if LOGS:
logging.disable(logging.CRITICAL)
from multiprocessing import Process
import psutil | docs/notebooks/nmslibtutorial.ipynb | RaRe-Technologies/gensim | lgpl-2.1 |
Bad Example: Two processes load the Word2vec model from disk and create there own Nmslib indices from that model. | %%time
model.save('/tmp/mymodel.pkl')
def f(process_id):
print('Process Id: {}'.format(os.getpid()))
process = psutil.Process(os.getpid())
new_model = Word2Vec.load('/tmp/mymodel.pkl')
vector = new_model["science"]
nmslib_index = NmslibIndexer(new_model, {'M': 100, 'indexThreadQty': 1, 'efConstruction': 100}, {'efSearch': 10})
approximate_neighbors = new_model.most_similar([vector], topn=5, indexer=nmslib_index)
print('\nMemory used by process {}: {}\n---'.format(os.getpid(), process.memory_info()))
# Creating and running two parallel process to share the same index file.
p1 = Process(target=f, args=('1',))
p1.start()
p1.join()
p2 = Process(target=f, args=('2',))
p2.start()
p2.join() | docs/notebooks/nmslibtutorial.ipynb | RaRe-Technologies/gensim | lgpl-2.1 |
Good example. Two processes load both the Word2vec model and index from disk and memory-map the index | %%time
model.save('/tmp/mymodel.pkl')
def f(process_id):
print('Process Id: {}'.format(os.getpid()))
process = psutil.Process(os.getpid())
new_model = Word2Vec.load('/tmp/mymodel.pkl')
vector = new_model["science"]
nmslib_index = NmslibIndexer.load('/tmp/mymodel.index')
nmslib_index.model = new_model
approximate_neighbors = new_model.most_similar([vector], topn=5, indexer=nmslib_index)
print('\nMemory used by process {}: {}\n---'.format(os.getpid(), process.memory_info()))
# Creating and running two parallel process to share the same index file.
p1 = Process(target=f, args=('1',))
p1.start()
p1.join()
p2 = Process(target=f, args=('2',))
p2.start()
p2.join() | docs/notebooks/nmslibtutorial.ipynb | RaRe-Technologies/gensim | lgpl-2.1 |
5. Evaluate relationship of parameters to initialization/query time and accuracy, compared with annoy | import matplotlib.pyplot as plt
%matplotlib inline | docs/notebooks/nmslibtutorial.ipynb | RaRe-Technologies/gensim | lgpl-2.1 |
Build dataset of Initialization times and accuracy measures | exact_results = [element[0] for element in model.most_similar([model.wv.syn0norm[0]], topn=100)]
# For calculating query time
queries = 1000
def create_evaluation_graph(x_values, y_values_init, y_values_accuracy, y_values_query, param_name):
plt.figure(1, figsize=(12, 6))
plt.subplot(231)
plt.plot(x_values, y_values_init)
plt.title("{} vs initalization time".format(param_name))
plt.ylabel("Initialization time (s)")
plt.xlabel(param_name)
plt.subplot(232)
plt.plot(x_values, y_values_accuracy)
plt.title("{} vs accuracy".format(param_name))
plt.ylabel("% accuracy")
plt.xlabel(param_name)
plt.tight_layout()
plt.subplot(233)
plt.plot(y_values_init, y_values_accuracy)
plt.title("Initialization time vs accuracy")
plt.ylabel("% accuracy")
plt.xlabel("Initialization time (s)")
plt.tight_layout()
plt.subplot(234)
plt.plot(x_values, y_values_query)
plt.title("{} vs query time".format(param_name))
plt.ylabel("query time")
plt.xlabel(param_name)
plt.tight_layout()
plt.subplot(235)
plt.plot(y_values_query, y_values_accuracy)
plt.title("query time vs accuracy")
plt.ylabel("% accuracy")
plt.xlabel("query time (s)")
plt.tight_layout()
plt.show()
def evaluate_nmslib_performance(parameter, is_parameter_query, parameter_start, parameter_end, parameter_step):
nmslib_x_values = []
nmslib_y_values_init = []
nmslib_y_values_accuracy = []
nmslib_y_values_query = []
index_params = {'M': 100, 'indexThreadQty': 10, 'efConstruction': 100, 'post': 0}
query_params = {'efSearch': 100}
for x in range(parameter_start, parameter_end, parameter_step):
nmslib_x_values.append(x)
start_time = time.time()
if is_parameter_query:
query_params[parameter] = x
else:
index_params[parameter] = x
nmslib_index = NmslibIndexer(model
, index_params
, query_params)
nmslib_y_values_init.append(time.time() - start_time)
approximate_results = model.most_similar([model.wv.syn0norm[0]], topn=100, indexer=nmslib_index)
top_words = [result[0] for result in approximate_results]
nmslib_y_values_accuracy.append(len(set(top_words).intersection(exact_results)))
nmslib_y_values_query.append(avg_query_time(nmslib_index, queries=queries))
create_evaluation_graph(nmslib_x_values,
nmslib_y_values_init,
nmslib_y_values_accuracy,
nmslib_y_values_query,
parameter)
# Evaluate nmslib indexer, changing the parameter M
evaluate_nmslib_performance("M", False, 50, 401, 50)
# Evaluate nmslib indexer, changing the parameter efConstruction
evaluate_nmslib_performance("efConstruction", False, 50, 1001, 100)
# Evaluate nmslib indexer, changing the parameter efSearch
evaluate_nmslib_performance("efSearch", True, 50, 401, 100)
# Evaluate annoy indexer, changing the parameter num_tree
annoy_x_values = []
annoy_y_values_init = []
annoy_y_values_accuracy = []
annoy_y_values_query = []
for x in range(100, 401, 50):
annoy_x_values.append(x)
start_time = time.time()
annoy_index = AnnoyIndexer(model, x)
annoy_y_values_init.append(time.time() - start_time)
approximate_results = model.most_similar([model.wv.syn0norm[0]], topn=100, indexer=annoy_index)
top_words = [result[0] for result in approximate_results]
annoy_y_values_accuracy.append(len(set(top_words).intersection(exact_results)))
annoy_y_values_query.append(avg_query_time(annoy_index, queries=queries))
create_evaluation_graph(annoy_x_values,
annoy_y_values_init,
annoy_y_values_accuracy,
annoy_y_values_query,
"num_tree")
# nmslib indexer changing the parameter M, efConstruction, efSearch
nmslib_y_values_init = []
nmslib_y_values_accuracy = []
nmslib_y_values_query = []
for M in [100, 200]:
for efConstruction in [100, 200]:
for efSearch in [100, 200]:
start_time = time.time()
nmslib_index = NmslibIndexer(model,
{'M': M, 'indexThreadQty': 10, 'efConstruction': efConstruction, 'post': 0},
{'efSearch': efSearch})
nmslib_y_values_init.append(time.time() - start_time)
approximate_results = model.most_similar([model.wv.syn0norm[0]], topn=100, indexer=nmslib_index)
top_words = [result[0] for result in approximate_results]
nmslib_y_values_accuracy.append(len(set(top_words).intersection(exact_results)))
nmslib_y_values_query.append(avg_query_time(nmslib_index, queries=queries))
# Make a comparison between annoy and nmslib indexer
plt.figure(1, figsize=(12, 6))
plt.subplot(121)
plt.scatter(nmslib_y_values_init, nmslib_y_values_accuracy, label="nmslib", color='r', marker='o')
plt.scatter(annoy_y_values_init, annoy_y_values_accuracy, label="annoy", color='b', marker='x')
plt.legend()
plt.title("Initialization time vs accuracy. Upper left is better.")
plt.ylabel("% accuracy")
plt.xlabel("Initialization time (s)")
plt.subplot(122)
plt.scatter(nmslib_y_values_query, nmslib_y_values_accuracy, label="nmslib", color='r', marker='o')
plt.scatter(annoy_y_values_query, annoy_y_values_accuracy, label="annoy", color='b', marker='x')
plt.legend()
plt.title("Query time vs accuracy. Upper left is better.")
plt.ylabel("% accuracy")
plt.xlabel("Query time (s)")
plt.xlim(min(nmslib_y_values_query+annoy_y_values_query), max(nmslib_y_values_query+annoy_y_values_query))
plt.tight_layout()
plt.show() | docs/notebooks/nmslibtutorial.ipynb | RaRe-Technologies/gensim | lgpl-2.1 |
6. Work with Google word2vec files
Our model can be exported to a word2vec C format. There is a binary and a plain text word2vec format. Both can be read with a variety of other software, or imported back into gensim as a KeyedVectors object. | # To export our model as text
model.wv.save_word2vec_format('/tmp/vectors.txt', binary=False)
from smart_open import open
# View the first 3 lines of the exported file
# The first line has the total number of entries and the vector dimension count.
# The next lines have a key (a string) followed by its vector.
with open('/tmp/vectors.txt') as myfile:
for i in range(3):
print(myfile.readline().strip())
# To import a word2vec text model
wv = KeyedVectors.load_word2vec_format('/tmp/vectors.txt', binary=False)
# To export our model as binary
model.wv.save_word2vec_format('/tmp/vectors.bin', binary=True)
# To import a word2vec binary model
wv = KeyedVectors.load_word2vec_format('/tmp/vectors.bin', binary=True)
# To create and save Nmslib Index from a loaded `KeyedVectors` object
nmslib_index = NmslibIndexer(wv,
{'M': 100, 'indexThreadQty': 1, 'efConstruction': 100}, {'efSearch': 100})
nmslib_index.save('/tmp/mymodel.index')
# Load and test the saved word vectors and saved nmslib index
wv = KeyedVectors.load_word2vec_format('/tmp/vectors.bin', binary=True)
nmslib_index = NmslibIndexer.load('/tmp/mymodel.index')
nmslib_index.model = wv
vector = wv["cat"]
approximate_neighbors = wv.most_similar([vector], topn=11, indexer=nmslib_index)
# Neatly print the approximate_neighbors and their corresponding cosine similarity values
print("Approximate Neighbors")
for neighbor in approximate_neighbors:
print(neighbor)
normal_neighbors = wv.most_similar([vector], topn=11)
print("\nNormal (not Nmslib-indexed) Neighbors")
for neighbor in normal_neighbors:
print(neighbor) | docs/notebooks/nmslibtutorial.ipynb | RaRe-Technologies/gensim | lgpl-2.1 |
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