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| import gradio as gr | |
| import numpy as np | |
| from matplotlib import pyplot as plt | |
| from matplotlib.collections import LineCollection | |
| from sklearn import manifold | |
| from sklearn.metrics import euclidean_distances | |
| from sklearn.decomposition import PCA | |
| EPSILON = np.finfo(np.float32).eps | |
| n_samples = 20 | |
| seed = np.random.RandomState(seed=3) | |
| X_true = seed.randint(0, 20, 2 * n_samples).astype(float) | |
| X_true = X_true.reshape((n_samples, 2)) | |
| # Center the data | |
| X_true -= X_true.mean() | |
| similarities = euclidean_distances(X_true) | |
| # Add noise to the similarities | |
| noise = np.random.rand(n_samples, n_samples) | |
| noise = noise + noise.T | |
| noise[np.arange(noise.shape[0]), np.arange(noise.shape[0])] = 0 | |
| similarities += noise | |
| def mds_nmds(n_components, max_iter, eps): | |
| mds = manifold.MDS( | |
| n_components=n_components, | |
| max_iter=max_iter, | |
| eps=eps, | |
| random_state=seed, | |
| dissimilarity="precomputed", | |
| n_jobs=1, | |
| normalized_stress="auto", | |
| ) | |
| pos = mds.fit(similarities).embedding_ | |
| nmds = manifold.MDS( | |
| n_components=n_components, | |
| metric=False, | |
| max_iter=max_iter, | |
| eps=eps, | |
| dissimilarity="precomputed", | |
| random_state=seed, | |
| n_jobs=1, | |
| n_init=1, | |
| normalized_stress="auto", | |
| ) | |
| npos = nmds.fit_transform(similarities, init=pos) | |
| # Rescale the data | |
| pos *= np.sqrt((X_true**2).sum()) / np.sqrt((pos**2).sum()) | |
| npos *= np.sqrt((X_true**2).sum()) / np.sqrt((npos**2).sum()) | |
| # Rotate the data | |
| clf = PCA(n_components=2) | |
| X_true_transformed = clf.fit_transform(X_true) | |
| pos_transformed = clf.fit_transform(pos) | |
| npos_transformed = clf.fit_transform(npos) | |
| return X_true_transformed, pos_transformed, npos_transformed | |
| def plot_similarity_scatter(similarity_threshold=50, n_components=2, max_iter=3000, eps=1e-9, cmap_name='Blues'): | |
| X_true_transformed, pos_transformed, npos_transformed = mds_nmds(n_components, max_iter, eps) | |
| fig = plt.figure() | |
| ax = plt.axes([0.0, 0.0, 1.0, 1.0]) | |
| s = 100 | |
| plt.scatter(X_true_transformed[:, 0], X_true_transformed[:, 1], color="navy", s=s, lw=0, label="True Position") | |
| plt.scatter(pos_transformed[:, 0], pos_transformed[:, 1], color="turquoise", s=s, lw=0, label="MDS") | |
| plt.scatter(npos_transformed[:, 0], npos_transformed[:, 1], color="darkorange", s=s, lw=0, label="NMDS") | |
| plt.legend(scatterpoints=1, loc="best", shadow=False) | |
| similarities_thresholded = similarities.copy() | |
| similarities_thresholded[similarities_thresholded <= int(similarity_threshold)] = 0 | |
| np.fill_diagonal(similarities_thresholded, 0) | |
| # Plot the edges | |
| start_idx, end_idx = np.where(pos_transformed) | |
| segments = [[X_true_transformed[i, :], X_true_transformed[j, :]] for i in range(len(pos_transformed)) for j in range(len(pos_transformed))] | |
| values = np.abs(similarities_thresholded) | |
| lc = LineCollection(segments, zorder=0, cmap=plt.cm.get_cmap(cmap_name), norm=plt.Normalize(0, values.max())) | |
| lc.set_array(similarities_thresholded.flatten()) | |
| lc.set_linewidths(np.full(len(segments), 0.5)) | |
| ax.add_collection(lc) | |
| # Save the plot as a PNG file | |
| plt.savefig("plot.png") | |
| plt.close() | |
| # Return the saved plot file | |
| return "plot.png" | |
| parameters = [ | |
| gr.inputs.Slider(label="Similarity Threshold", minimum=0, maximum=100, step=1, default=50), | |
| gr.inputs.Slider(label="Number of Components", minimum=1, maximum=10, step=1, default=2), | |
| gr.inputs.Slider(label="Max Iterations", minimum=100, maximum=5000, step=100, default=3000), | |
| gr.inputs.Slider(label="Epsilon", minimum=1e-12, maximum=1e-6, step=1e-12, default=1e-9), | |
| gr.inputs.Dropdown(label="Colormap", choices=["Blues_r", "Dark2", "Reds_r", "Purples_r"], default="Blues_r") | |
| ] | |
| iface = gr.Interface( | |
| fn=plot_similarity_scatter, | |
| inputs=parameters, | |
| outputs="image", | |
| title="Multi-dimensional scaling", | |
| description="The scatter plot is generated based on the provided data and similarity matrix. MDS and NMDS techniques are used to project the data points into a two-dimensional space. The points are plotted in the scatter plot, with different colors representing the true positions, MDS positions, and NMDS positions of the data points. The similarity threshold parameter allows you to control the visibility of connections between the points. Points with similarity values below the threshold are not connected by lines in the plot. See the original scikit-learn example here: https://scikit-learn.org/stable/auto_examples/manifold/plot_mds.html", | |
| examples=[ | |
| [50, 2, 3000, 1e-9, "Blues_r"], | |
| [75, 3, 2000, 1e-10, "Dark2"], | |
| [90, 2, 4000, 1e-11, "Reds_r"], | |
| ], | |
| ) | |
| iface.launch() | |