fABBA 1.5.2
An efficient symbolic time series approximation with ABBA.
License: BSD-3-Clause
Requires Python: >=3.8

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fABBA is a fast and accurate symbolic representation method for temporal data. 
It is based on a polygonal chain approximation of the time series followed by an aggregation of the polygonal pieces into groups. 
The aggregation process is sped up by sorting the polygonal pieces and exploiting early termination conditions. 
In contrast to the ABBA method [S. Elsworth and S. Güttel, Data Mining and Knowledge Discovery, 34:1175-1200, 2020], fABBA avoids repeated within-cluster-sum-of-squares computations which reduces its computational complexity significantly.
Furthermore, fABBA is fully tolerance-driven and does not require the number of time series symbols to be specified by the user. 

--------
Install
--------

fABBA has the following essential dependencies for its functionality:

- cython
- numpy
- scipy
- requests


To install the current release via PIP use:

.. code:: bash
    
    pip install fABBA


Download this repository:

.. code:: bash
    
    git clone https://github.com/nla-group/fABBA.git



--------
Examples 
--------

- *Compress and reconstruct a time series*

The following example approximately transforms a time series into a symbolic string representation (`transform`) and then converts the string back into a numerical format (`inverse_transform`). fABBA essentially requires two parameters `tol` and `alpha`. The tolerance `tol` determines how closely the polygonal chain approximation follows the original time series. The parameter `alpha` controls how similar time series pieces need to be in order to be represented by the same symbol. A smaller `tol` means that more polygonal pieces are used and the polygonal chain approximation is more accurate; but on the other hand, it will increase the length of the string representation. A smaller `alpha` typically results in a larger number of symbols. 

The choice of parameters depends on the application, but in practice, one often just wants the polygonal chain to mimic the key features in time series and not to approximate any noise. In this example the time series is a sine wave and the chosen parameters result in the symbolic representation `#$!"!"!"!"!"!"!"%`. Note how the periodicity in the time series is nicely reflected in repetitions in its string representation.

.. code:: python

    import numpy as np
    import matplotlib.pyplot as plt
    from fABBA import fabba_model

    ts = [np.sin(0.05*i) for i in range(1000)]  # original time series
    fabba = fabba_model(tol=0.1, alpha=0.1, sorting='2-norm', scl=1, verbose=0)

    string = fabba.fit_transform(ts)            # string representation of the time series
    print(string)                               # prints BbAaAaAaAaAaAaAaC

    inverse_ts = fabba.inverse_transform(string, ts[0]) # numerical time series reconstruction



- *Adaptive polygonal chain approximation*

Instead of using `transform` which combines the polygonal chain approximation of the time series and the symbolic conversion into one, both steps of fABBA can be performed independently. Here’s how to obtain the compression pieces and reconstruct time series by inversely transforming the pieces:

.. code:: python

    import numpy as np
    from fABBA import compress
    from fABBA import inverse_compress
    ts = [np.sin(0.05*i) for i in range(1000)]
    pieces = compress(ts, tol=0.1)               # pieces is a list of the polygonal chain pieces
    inverse_ts = inverse_compress(pieces, ts[0]) # reconstruct polygonal chain from pieces


Similarly, the digitization can be implemented after compression step as belows:

.. code:: python

    from fABBA import digitize
    from fABBA import inverse_digitize
    string, parameters = digitize(pieces, alpha=0.1, sorting='2-norm', scl=1) # compression of the polygon
    print(''.join(string))                                 # prints BbAaAaAaAaAaAaAaC

    inverse_pieces = inverse_digitize(string, parameters)
    inverse_ts = inverse_compress(inverse_pieces, ts[0])   # numerical time series reconstruction



- *Alternative ABBA approach*

We also provide other clustering based ABBA methods, it is easy to use with the support of scikit-learn tools. The user guidance is as follows

.. code:: python

    import numpy as np
    from sklearn.cluster import KMeans
    from fABBA import ABBAbase

    ts = [np.sin(0.05*i) for i in range(1000)]         # original time series
    #  specifies 5 symbols using kmeans clustering
    kmeans = KMeans(n_clusters=5, random_state=0, init='k-means++', verbose=0)     
    abba = ABBAbase(tol=0.1, scl=1, clustering=kmeans)
    string = abba.fit_transform(ts)                    # string representation of the time series
    print(string)                                      # prints BbAaAaAaAaAaAaAaC
    inverse_ts = abba.inverse_transform(string)        # reconstruction




- *Image compression*

The following example shows how to apply fABBA to image data.

.. code:: python

    import matplotlib.pyplot as plt
    from fABBA.load_datasets import load_images
    from fABBA import image_compress
    from fABBA import image_decompress
    from fABBA import fabba_model
    from cv2 import resize
    img_samples = load_images() # load test images
    img = resize(img_samples[0], (100, 100)) # select the first image for test

    fabba = fabba_model(tol=0.1, alpha=0.01, sorting='2-norm', scl=1, verbose=1)
    string = image_compress(fabba, img) # compress image
    inverse_img = image_decompress(fabba, string) # decompress image



--------
Citation
--------

If you use fABBA in a scientific publication, we would appreciate your citing:

.. code:: bibtex

    @techreport{CG22a,
      title   = {An efficient aggregation method for the symbolic representation of temporal data},
      author  = {Chen, Xinye and G\"{u}ttel, Stefan},
      year    = {2022},
      number  = {arXiv:2201.05697},
      pages   = {23},
      institution = {The University of Manchester},
      address = {UK},
      type    = {arXiv EPrint},
      url     = {https://arxiv.org/abs/2201.05697}
    }