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scikit-learn 1.3.2
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# Putting it all together

## Pipelining

We have seen that some estimators can transform data and that some estimators can predict variables. We can also create combined estimators:

    from sklearn.linear_model import LogisticRegression
    from sklearn.model_selection import GridSearchCV
    from sklearn.pipeline import Pipeline
    from sklearn.preprocessing import StandardScaler

    # Define a pipeline to search for the best combination of PCA truncation
    # and classifier regularization.
    pca = PCA()
    # Define a Standard Scaler to normalize inputs
    scaler = StandardScaler()

    # set the tolerance to a large value to make the example faster
    logistic = LogisticRegression(max_iter=10000, tol=0.1)
    pipe = Pipeline(steps=[("scaler", scaler), ("pca", pca), ("logistic", logistic)])

    X_digits, y_digits = datasets.load_digits(return_X_y=True)
    # Parameters of pipelines can be set using '__' separated parameter names:
    param_grid = {
        "pca__n_components": [5, 15, 30, 45, 60],
        "logistic__C": np.logspace(-4, 4, 4),
    }
    search = GridSearchCV(pipe, param_grid, n_jobs=2)
    search.fit(X_digits, y_digits)
    print("Best parameter (CV score=%0.3f):" % search.best_score_)
    print(search.best_params_)

    # Plot the PCA spectrum
    pca.fit(X_digits)

    fig, (ax0, ax1) = plt.subplots(nrows=2, sharex=True, figsize=(6, 6))
    ax0.plot(
        np.arange(1, pca.n_components_ + 1), pca.explained_variance_ratio_, "+", linewidth=2
    )
    ax0.set_ylabel("PCA explained variance ratio")

    ax0.axvline(
        search.best_estimator_.named_steps["pca"].n_components,
        linestyle=":",
        label="n_components chosen",
    )
    ax0.legend(prop=dict(size=12))

## Face recognition with eigenfaces

The dataset used in this example is a preprocessed excerpt of the “Labeled Faces in the Wild”, also known as LFW:

> http://vis-www.cs.umass.edu/lfw/lfw-funneled.tgz (233MB)

    """
    ===================================================
    Faces recognition example using eigenfaces and SVMs
    ===================================================

    The dataset used in this example is a preprocessed excerpt of the
    "Labeled Faces in the Wild", aka LFW_:

      http://vis-www.cs.umass.edu/lfw/lfw-funneled.tgz (233MB)

    .. _LFW: http://vis-www.cs.umass.edu/lfw/

    """
    # %%
    from time import time

    import matplotlib.pyplot as plt
    from scipy.stats import loguniform

    from sklearn.datasets import fetch_lfw_people
    from sklearn.decomposition import PCA
    from sklearn.metrics import ConfusionMatrixDisplay, classification_report
    from sklearn.model_selection import RandomizedSearchCV, train_test_split
    from sklearn.preprocessing import StandardScaler
    from sklearn.svm import SVC

    # %%
    # Download the data, if not already on disk and load it as numpy arrays

    lfw_people = fetch_lfw_people(min_faces_per_person=70, resize=0.4)

    # introspect the images arrays to find the shapes (for plotting)
    n_samples, h, w = lfw_people.images.shape

    # for machine learning we use the 2 data directly (as relative pixel
    # positions info is ignored by this model)
    X = lfw_people.data
    n_features = X.shape[1]

    # the label to predict is the id of the person
    y = lfw_people.target
    target_names = lfw_people.target_names
    n_classes = target_names.shape[0]

    print("Total dataset size:")
    print("n_samples: %d" % n_samples)
    print("n_features: %d" % n_features)
    print("n_classes: %d" % n_classes)

    # %%
    # Split into a training set and a test and keep 25% of the data for testing.

    X_train, X_test, y_train, y_test = train_test_split(
        X, y, test_size=0.25, random_state=42
    )

    scaler = StandardScaler()
    X_train = scaler.fit_transform(X_train)
    X_test = scaler.transform(X_test)

    # %%
    # Compute a PCA (eigenfaces) on the face dataset (treated as unlabeled
    # dataset): unsupervised feature extraction / dimensionality reduction

    n_components = 150

    print(
        "Extracting the top %d eigenfaces from %d faces" % (n_components, X_train.shape[0])
    )
    t0 = time()
    pca = PCA(n_components=n_components, svd_solver="randomized", whiten=True).fit(X_train)
    print("done in %0.3fs" % (time() - t0))

    eigenfaces = pca.components_.reshape((n_components, h, w))

    print("Projecting the input data on the eigenfaces orthonormal basis")
    t0 = time()
    X_train_pca = pca.transform(X_train)
    X_test_pca = pca.transform(X_test)
    print("done in %0.3fs" % (time() - t0))

    # %%
    # Train a SVM classification model

    print("Fitting the classifier to the training set")
    t0 = time()
    param_grid = {
        "C": loguniform(1e3, 1e5),
        "gamma": loguniform(1e-4, 1e-1),
    }
    clf = RandomizedSearchCV(
        SVC(kernel="rbf", class_weight="balanced"), param_grid, n_iter=10
    )
    clf = clf.fit(X_train_pca, y_train)
    print("done in %0.3fs" % (time() - t0))
    print("Best estimator found by grid search:")
    print(clf.best_estimator_)

    # %%
    # Quantitative evaluation of the model quality on the test set

    print("Predicting people's names on the test set")
    t0 = time()
    y_pred = clf.predict(X_test_pca)
    print("done in %0.3fs" % (time() - t0))

    print(classification_report(y_test, y_pred, target_names=target_names))
    ConfusionMatrixDisplay.from_estimator(
        clf, X_test_pca, y_test, display_labels=target_names, xticks_rotation="vertical"
    )
    plt.tight_layout()
    plt.show()

    # %%
    # Qualitative evaluation of the predictions using matplotlib

    def plot_gallery(images, titles, h, w, n_row=3, n_col=4):
        """Helper function to plot a gallery of portraits"""
        plt.figure(figsize=(1.8 * n_col, 2.4 * n_row))
        plt.subplots_adjust(bottom=0, left=0.01, right=0.99, top=0.90, hspace=0.35)
        for i in range(n_row * n_col):
            plt.subplot(n_row, n_col, i + 1)
            plt.imshow(images[i].reshape((h, w)), cmap=plt.cm.gray)
            plt.title(titles[i], size=12)
            plt.xticks(())
            plt.yticks(())

    # %%
    # plot the result of the prediction on a portion of the test set

    def title(y_pred, y_test, target_names, i):
        pred_name = target_names[y_pred[i]].rsplit(" ", 1)[-1]
        true_name = target_names[y_test[i]].rsplit(" ", 1)[-1]
        return "predicted: %s\ntrue:      %s" % (pred_name, true_name)

    prediction_titles = [
        title(y_pred, y_test, target_names, i) for i in range(y_pred.shape[0])
    ]

    plot_gallery(X_test, prediction_titles, h, w)
    # %%
    # plot the gallery of the most significative eigenfaces

    eigenface_titles = ["eigenface %d" % i for i in range(eigenfaces.shape[0])]
    plot_gallery(eigenfaces, eigenface_titles, h, w)

    plt.show()

    # %%
    # Face recognition problem would be much more effectively solved by training
    # convolutional neural networks but this family of models is outside of the scope of
    # the scikit-learn library. Interested readers should instead try to use pytorch or
    # tensorflow to implement such models.

Prediction

Eigenfaces

Expected results for the top 5 most represented people in the dataset:

                       precision    recall  f1-score   support

    Gerhard_Schroeder       0.91      0.75      0.82        28
      Donald_Rumsfeld       0.84      0.82      0.83        33
           Tony_Blair       0.65      0.82      0.73        34
         Colin_Powell       0.78      0.88      0.83        58
        George_W_Bush       0.93      0.86      0.90       129

          avg / total       0.86      0.84      0.85       282

## Open problem: Stock Market Structure

Can we predict the variation in stock prices for Google over a given time frame?

Learning a graph structure