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Author: snrazavi

1-MLiP2017_Introduction.pdf

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+import numpy as np
+import matplotlib.pyplot as plt
+import warnings
+
+
+def plot_kmeans_interactive(min_clusters=1, max_clusters=6):
+    #from IPython.html.widgets import interact
+    from ipywidgets import interact
+    from sklearn.metrics.pairwise import euclidean_distances
+    from sklearn.datasets.samples_generator import make_blobs
+
+    with warnings.catch_warnings():
+        warnings.filterwarnings('ignore')
+
+        X, y = make_blobs(n_samples=300, centers=4,
+                          random_state=0, cluster_std=0.60)
+
+        def _kmeans_step(frame=0, n_clusters=4):
+            rng = np.random.RandomState(2)
+            labels = np.zeros(X.shape[0])
+            centers = rng.randn(n_clusters, 2)
+
+            nsteps = frame // 3
+
+            for i in range(nsteps + 1):
+                old_centers = centers
+                if i < nsteps or frame % 3 > 0:
+                    dist = euclidean_distances(X, centers)
+                    labels = dist.argmin(1)
+
+                if i < nsteps or frame % 3 > 1:
+                    centers = np.array([X[labels == j].mean(0)
+                                        for j in range(n_clusters)])
+                    nans = np.isnan(centers)
+                    centers[nans] = old_centers[nans]
+
+
+            # plot the data and cluster centers
+            plt.scatter(X[:, 0], X[:, 1], c=labels, s=50, cmap='rainbow',
+                        vmin=0, vmax=n_clusters - 1);
+            plt.scatter(old_centers[:, 0], old_centers[:, 1], marker='o',
+                        c=np.arange(n_clusters),
+                        s=200, cmap='rainbow')
+            plt.scatter(old_centers[:, 0], old_centers[:, 1], marker='o',
+                        c='black', s=50)
+
+            # plot new centers if third frame
+            if frame % 3 == 2:
+                for i in range(n_clusters):
+                    plt.annotate('', centers[i], old_centers[i], 
+                                 arrowprops=dict(arrowstyle='->', linewidth=1))
+                plt.scatter(centers[:, 0], centers[:, 1], marker='o',
+                            c=np.arange(n_clusters),
+                            s=200, cmap='rainbow')
+                plt.scatter(centers[:, 0], centers[:, 1], marker='o',
+                            c='black', s=50)
+
+            plt.xlim(-4, 4)
+            plt.ylim(-2, 10)
+
+            if frame % 3 == 1:
+                plt.text(3.8, 9.5, "1. Reassign points to nearest centroid",
+                         ha='right', va='top', size=14)
+            elif frame % 3 == 2:
+                plt.text(3.8, 9.5, "2. Update centroids to cluster means",
+                         ha='right', va='top', size=14)
+
+    
+    return interact(_kmeans_step, frame=np.arange(0, 50),
+                    n_clusters=np.arange(min_clusters, max_clusters))
+
+
+def plot_image_components(x, coefficients=None, mean=0, components=None,
+                          imshape=(8, 8), n_components=6, fontsize=12):
+    if coefficients is None:
+        coefficients = x
+        
+    if components is None:
+        components = np.eye(len(coefficients), len(x))
+        
+    mean = np.zeros_like(x) + mean
+        
+
+    fig = plt.figure(figsize=(1.2 * (5 + n_components), 1.2 * 2))
+    g = plt.GridSpec(2, 5 + n_components, hspace=0.3)
+
+    def show(i, j, x, title=None):
+        ax = fig.add_subplot(g[i, j], xticks=[], yticks=[])
+        ax.imshow(x.reshape(imshape), interpolation='nearest')
+        if title:
+            ax.set_title(title, fontsize=fontsize)
+
+    show(slice(2), slice(2), x, "True")
+
+    approx = mean.copy()
+    show(0, 2, np.zeros_like(x) + mean, r'$\mu$')
+    show(1, 2, approx, r'$1 \cdot \mu$')
+
+    for i in range(0, n_components):
+        approx = approx + coefficients[i] * components[i]
+        show(0, i + 3, components[i], r'$c_{0}$'.format(i + 1))
+        show(1, i + 3, approx,
+             r"${0:.2f} \cdot c_{1}$".format(coefficients[i], i + 1))
+        plt.gca().text(0, 1.05, '$+$', ha='right', va='bottom',
+                       transform=plt.gca().transAxes, fontsize=fontsize)
+
+    show(slice(2), slice(-2, None), approx, "Approx")
+
+
+def plot_pca_interactive(data, n_components=6):
+    from sklearn.decomposition import PCA
+    #from IPython.html.widgets import interact
+    from ipywidgets import interact
+
+    pca = PCA(n_components=n_components)
+    Xproj = pca.fit_transform(data)
+
+    def show_decomp(i=0):
+        plot_image_components(data[i], Xproj[i],
+                              pca.mean_, pca.components_)
+    
+    interact(show_decomp, i=(0, data.shape[0] - 1));