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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));

Assignments/MLiP2017-ex1-CIFAR10-and-Neural-Networks.ipynb

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+import numpy as np
+import matplotlib.pyplot as plt
+
+
+def plot_2d_separator(classifier, X, fill=False, ax=None, eps=None):
+    if eps is None:
+        eps = X.std() / 2.
+    x_min, x_max = X[:, 0].min() - eps, X[:, 0].max() + eps
+    y_min, y_max = X[:, 1].min() - eps, X[:, 1].max() + eps
+    xx = np.linspace(x_min, x_max, 100)
+    yy = np.linspace(y_min, y_max, 100)
+
+    X1, X2 = np.meshgrid(xx, yy)
+    X_grid = np.c_[X1.ravel(), X2.ravel()]
+    try:
+        decision_values = classifier.decision_function(X_grid)
+        levels = [0]
+        fill_levels = [decision_values.min(), 0, decision_values.max()]
+    except AttributeError:
+        # no decision_function
+        decision_values = classifier.predict_proba(X_grid)[:, 1]
+        levels = [.5]
+        fill_levels = [0, .5, 1]
+
+    if ax is None:
+        ax = plt.gca()
+    if fill:
+        ax.contourf(X1, X2, decision_values.reshape(X1.shape),
+                    levels=fill_levels, colors=['blue', 'red'])
+    else:
+        ax.contour(X1, X2, decision_values.reshape(X1.shape), levels=levels,
+                   colors="black")
+    ax.set_xlim(x_min, x_max)
+    ax.set_ylim(y_min, y_max)
+    ax.set_xticks(())
+    ax.set_yticks(())
+
+
+if __name__ == '__main__':
+    from sklearn.datasets import make_blobs
+    from sklearn.linear_model import LogisticRegression
+    X, y = make_blobs(centers=2, random_state=42)
+    clf = LogisticRegression().fit(X, y)
+    plot_2d_separator(clf, X, fill=True)
+    plt.scatter(X[:, 0], X[:, 1], c=y)
+    plt.show()

Assignments/‌excesizes/MLiP-ex1-Neural_Networks_for_CIFAR10.pdf

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+# Taken from example in scikit-learn examples
+# Authors: Fabian Pedregosa <fabian.pedregosa@inria.fr>
+#          Olivier Grisel <olivier.grisel@ensta.org>
+#          Mathieu Blondel <mathieu@mblondel.org>
+#          Gael Varoquaux
+# License: BSD 3 clause (C) INRIA 2011
+
+import numpy as np
+import matplotlib.pyplot as plt
+from matplotlib import offsetbox
+from sklearn import datasets, decomposition
+
+
+def digits_plot():
+    digits = datasets.load_digits(n_class=6)
+    n_digits = 500
+    X = digits.data[:n_digits]
+    y = digits.target[:n_digits]
+    n_samples, n_features = X.shape
+
+    def plot_embedding(X, title=None):
+        x_min, x_max = np.min(X, 0), np.max(X, 0)
+        X = (X - x_min) / (x_max - x_min)
+
+        plt.figure()
+        ax = plt.subplot(111)
+        for i in range(X.shape[0]):
+            plt.text(X[i, 0], X[i, 1], str(digits.target[i]),
+                     color=plt.cm.Set1(y[i] / 10.),
+                     fontdict={'weight': 'bold', 'size': 9})
+
+        if hasattr(offsetbox, 'AnnotationBbox'):
+            # only print thumbnails with matplotlib > 1.0
+            shown_images = np.array([[1., 1.]])  # just something big
+            for i in range(X.shape[0]):
+                dist = np.sum((X[i] - shown_images) ** 2, 1)
+                if np.min(dist) < 1e5:
+                    # don't show points that are too close
+                    # set a high threshold to basically turn this off
+                    continue
+                shown_images = np.r_[shown_images, [X[i]]]
+                imagebox = offsetbox.AnnotationBbox(
+                    offsetbox.OffsetImage(digits.images[i], cmap=plt.cm.gray_r),
+                    X[i])
+                ax.add_artist(imagebox)
+        plt.xticks([]), plt.yticks([])
+        if title is not None:
+            plt.title(title)
+
+    n_img_per_row = 10
+    img = np.zeros((10 * n_img_per_row, 10 * n_img_per_row))
+    for i in range(n_img_per_row):
+        ix = 10 * i + 1
+        for j in range(n_img_per_row):
+            iy = 10 * j + 1
+            img[ix:ix + 8, iy:iy + 8] = X[i * n_img_per_row + j].reshape((8, 8))
+
+    plt.imshow(img, cmap=plt.cm.binary)
+    plt.xticks([])
+    plt.yticks([])
+    plt.title('A selection from the 64-dimensional digits dataset')
+    print("Computing PCA projection")
+    pca = decomposition.PCA(n_components=2).fit(X)
+    X_pca = pca.transform(X)
+    plot_embedding(X_pca, "Principal Components projection of the digits")
+    plt.figure()
+    plt.title("First Principal Component")
+    plt.matshow(pca.components_[0, :].reshape(8, 8), cmap="gray")
+    plt.axis('off')
+    plt.figure()
+    plt.title("Second Principal Component")
+    plt.matshow(pca.components_[1, :].reshape(8, 8), cmap="gray")
+    plt.axis('off')
+    plt.show()

MLiP2017_Specification.pdf

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+from matplotlib.colors import ListedColormap
+
+cm3 = ListedColormap(['#0000aa', '#ff2020', '#50ff50'])
+cm2 = ListedColormap(['#0000aa', '#ff2020'])

nbs/fig_codes/__pycache__/figures.cpython-36.pyc

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+from sklearn.decomposition import PCA
+import matplotlib.pyplot as plt
+import numpy as np
+
+
+def plot_pca_illustration():
+    rnd = np.random.RandomState(5)
+    X_ = rnd.normal(size=(300, 2))
+    X_blob = np.dot(X_, rnd.normal(size=(2, 2))) + rnd.normal(size=2)
+
+    pca = PCA()
+    pca.fit(X_blob)
+    X_pca = pca.transform(X_blob)
+
+    S = X_pca.std(axis=0)
+
+    fig, axes = plt.subplots(2, 2, figsize=(10, 10))
+    axes = axes.ravel()
+
+    axes[0].set_title("Original data")
+    axes[0].scatter(X_blob[:, 0], X_blob[:, 1], c=X_pca[:, 0], linewidths=0,
+                    s=60, cmap='viridis')
+    axes[0].set_xlabel("feature 1")
+    axes[0].set_ylabel("feature 2")
+    axes[0].arrow(pca.mean_[0], pca.mean_[1], S[0] * pca.components_[0, 0],
+                  S[0] * pca.components_[0, 1], width=.1, head_width=.3,
+                  color='k')
+    axes[0].arrow(pca.mean_[0], pca.mean_[1], S[1] * pca.components_[1, 0],
+                  S[1] * pca.components_[1, 1], width=.1, head_width=.3,
+                  color='k')
+    axes[0].text(-1.5, -.5, "Component 2", size=14)
+    axes[0].text(-4, -4, "Component 1", size=14)
+    axes[0].set_aspect('equal')
+
+    axes[1].set_title("Transformed data")
+    axes[1].scatter(X_pca[:, 0], X_pca[:, 1], c=X_pca[:, 0], linewidths=0,
+                    s=60, cmap='viridis')
+    axes[1].set_xlabel("First principal component")
+    axes[1].set_ylabel("Second principal component")
+    axes[1].set_aspect('equal')
+    axes[1].set_ylim(-8, 8)
+
+    pca = PCA(n_components=1)
+    pca.fit(X_blob)
+    X_inverse = pca.inverse_transform(pca.transform(X_blob))
+
+    axes[2].set_title("Transformed data w/ second component dropped")
+    axes[2].scatter(X_pca[:, 0], np.zeros(X_pca.shape[0]), c=X_pca[:, 0],
+                    linewidths=0, s=60, cmap='viridis')
+    axes[2].set_xlabel("First principal component")
+    axes[2].set_aspect('equal')
+    axes[2].set_ylim(-8, 8)
+
+    axes[3].set_title("Back-rotation using only first component")
+    axes[3].scatter(X_inverse[:, 0], X_inverse[:, 1], c=X_pca[:, 0],
+                    linewidths=0, s=60, cmap='viridis')
+    axes[3].set_xlabel("feature 1")
+    axes[3].set_ylabel("feature 2")
+    axes[3].set_aspect('equal')
+    axes[3].set_xlim(-8, 4)
+    axes[3].set_ylim(-8, 4)
+
+
+def plot_pca_whitening():
+    rnd = np.random.RandomState(5)
+    X_ = rnd.normal(size=(300, 2))
+    X_blob = np.dot(X_, rnd.normal(size=(2, 2))) + rnd.normal(size=2)
+
+    pca = PCA(whiten=True)
+    pca.fit(X_blob)
+    X_pca = pca.transform(X_blob)
+
+    fig, axes = plt.subplots(1, 2, figsize=(10, 10))
+    axes = axes.ravel()
+
+    axes[0].set_title("Original data")
+    axes[0].scatter(X_blob[:, 0], X_blob[:, 1], c=X_pca[:, 0], linewidths=0, s=60, cmap='viridis')
+    axes[0].set_xlabel("feature 1")
+    axes[0].set_ylabel("feature 2")
+    axes[0].set_aspect('equal')
+
+    axes[1].set_title("Whitened data")
+    axes[1].scatter(X_pca[:, 0], X_pca[:, 1], c=X_pca[:, 0], linewidths=0, s=60, cmap='viridis')
+    axes[1].set_xlabel("First principal component")
+    axes[1].set_ylabel("Second principal component")
+    axes[1].set_aspect('equal')
+    axes[1].set_xlim(-3, 4)