DOC unsupervised init

doc/conf.py

@@ -42,6 +42,7 @@
     "sphinx.ext.intersphinx",
     "sphinx_gallery.gen_gallery",
     "sphinx_design",
+    "matplotlib.sphinxext.plot_directive",
 ]
 
 # List of patterns, relative to source directory, that match files and

doc/unsupervised.rst

@@ -6,4 +6,76 @@
 Unsupervised feature selection
 ==============================
 
-We can use :class:`FastCan` to do unsupervised feature selection.
+We can use :class:`FastCan` to do unsupervised feature selection.
+The unsupervised application of :class:`FastCan` tries to select features, which
+maximize the sum of the squared canonical correlation (SSC) with the principal
+components (PCs) acquired from PCA (principal component analysis) of the feature
+matrix :math:`X`.
+
+    >>> from sklearn.decomposition import PCA
+    >>> from sklearn import datasets
+    >>> from fastcan import FastCan
+    >>> iris = datasets.load_iris()
+    >>> X = iris["data"]
+    >>> y = iris["target"]
+    >>> f_names = iris["feature_names"]
+    >>> t_names = iris["target_names"]
+    >>> pca = PCA(n_components=2)
+    >>> X_pcs = pca.fit_transform(X)
+    >>> selector = FastCan(n_features_to_select=2, verbose=0)
+    >>> selector.fit(X, X_pcs[:, :2])
+    >>> selector.indices_
+    array([2, 1], dtype=int32)
+
+.. note::
+    There is no guarantee that this unsupervised :class:`FastCan` will select
+    the optimal subset of the features, which has the highest SSC with PCs.
+    Because :class:`FastCan` selects features in a greedy manner, which may lead to
+    suboptimal results. See the following plots.
+
+.. plot::
+    :context: close-figs
+    :align: center
+
+    from itertools import combinations
+    import matplotlib.pyplot as plt
+    from sklearn.cross_decomposition import CCA
+
+    def ssc(X, y):
+        """Sum of the squared canonical correlation coefficients.
+        Parameters
+        ----------
+        X : array-like of shape (n_samples, n_features)
+            Feature matrix.
+
+        y : array-like of shape (n_samples, n_outputs)
+            Target matrix.
+
+        Returns
+        -------
+        ssc : float
+            Sum of the squared canonical correlation coefficients.
+        """
+        n_components = min(X.shape[1], y.shape[1])
+        cca = CCA(n_components=n_components)
+        X_c, y_c = cca.fit_transform(X, y)
+        corrcoef = np.diagonal(
+            np.corrcoef(X_c, y_c, rowvar=False),
+            offset=n_components
+        )
+        return sum(corrcoef**2)
+
+    comb = list(combinations([0, 1, 2, 3], 2))
+    fig, axs = plt.subplots(ncols=3, nrows=2, figsize=(8, 6), layout="constrained")
+    for i in range(2):
+        for j in range(3):
+            f1_idx = comb[i*3+j][0]
+            f2_idx = comb[i*3+j][1]
+            score = ssc(X[:, [f1_idx, f2_idx]], X_pcs)
+            scatter = axs[i, j].scatter(X[:, f1_idx], X[:, f2_idx], c=y)
+            axs[i, j].set(xlabel=f_names[f1_idx], ylabel=f_names[f2_idx])
+            axs[i, j].set_title(f"SSC: {score:.3f}")
+    for spine in axs[1, 0].spines.values():
+            spine.set_edgecolor('red')
+    _ = axs[1, 2].legend(scatter.legend_elements()[0], t_names, loc="lower right")
+

examples/plot_speed.py

@@ -39,6 +39,30 @@
 
 from sklearn.cross_decomposition import CCA
 
+def ssc(X, y):
+    """Sum of the squared canonical correlation coefficients.
+    Parameters
+    ----------
+    X : array-like of shape (n_samples, n_features)
+        Feature matrix.
+
+    y : array-like of shape (n_samples, n_outputs)
+        Target matrix.
+
+    Returns
+    -------
+    ssc : float
+        Sum of the squared canonical correlation coefficients.
+    """
+    n_components = min(X.shape[1], y.shape[1])
+    cca = CCA(n_components=n_components)
+    X_c, y_c = cca.fit_transform(X, y)
+    corrcoef = np.diagonal(
+        np.corrcoef(X_c, y_c, rowvar=False),
+        offset=n_components
+    )
+    return sum(corrcoef**2)
+
 
 def baseline(X, y, t):
     """Baseline method using CCA from sklearn.
@@ -64,24 +88,16 @@ def baseline(X, y, t):
         the scores is corresponding to the feature selection process.
     """
     n_samples, n_features = X.shape
-    n_targets = y.shape[1]
     mask = np.zeros(n_features, dtype=bool)
     r2 = np.zeros(n_features, dtype=float)
     indices  = np.zeros(t, dtype=int)
     scores = np.zeros(t, dtype=float)
     X_selected = np.zeros((n_samples, 0), dtype=float)
     for i in range(t):
-        n_components = min(i+1, n_targets)
-        cca = CCA(n_components=n_components)
         for j in range(n_features):
             if not mask[j]:
                 X_candidate = np.column_stack((X_selected, X[:, j]))
-                X_c, y_c = cca.fit_transform(X_candidate, y)
-                corrcoef = np.diagonal(
-                    np.corrcoef(X_c, y_c, rowvar=False),
-                    offset=n_components
-                )
-                r2[j] = sum(corrcoef**2)
+                r2[j] = ssc(X_candidate, y)
         d = np.argmax(r2)
         indices[i] = d
         scores[i] = r2[d]