chore: import upstream snapshot with attribution

2026-07-13 13:30:25 +08:00
commit f19b2512d7
562 changed files with 38082 additions and 0 deletions
@@ -0,0 +1,80 @@
+import numpy as np
+from prml.linear.classifier import Classifier
+from prml.rv.gaussian import Gaussian
+
+
+class FishersLinearDiscriminant(Classifier):
+    """
+    Fisher's Linear discriminant model
+    """
+
+    def __init__(self, w:np.ndarray=None, threshold:float=None):
+        self.w = w
+        self.threshold = threshold
+
+    def fit(self, X:np.ndarray, t:np.ndarray):
+        """
+        estimate parameter given training dataset
+
+        Parameters
+        ----------
+        X : (N, D) np.ndarray
+            training dataset independent variable
+        t : (N,) np.ndarray
+            training dataset dependent variable
+            binary 0 or 1
+        """
+        X0 = X[t == 0]
+        X1 = X[t == 1]
+        m0 = np.mean(X0, axis=0)
+        m1 = np.mean(X1, axis=0)
+        cov_inclass = np.cov(X0, rowvar=False) + np.cov(X1, rowvar=False)
+        self.w = np.linalg.solve(cov_inclass, m1 - m0)
+        self.w /= np.linalg.norm(self.w).clip(min=1e-10)
+
+        g0 = Gaussian()
+        g0.fit((X0 @ self.w))
+        g1 = Gaussian()
+        g1.fit((X1 @ self.w))
+        root = np.roots([
+            g1.var - g0.var,
+            2 * (g0.var * g1.mu - g1.var * g0.mu),
+            g1.var * g0.mu ** 2 - g0.var * g1.mu ** 2
+            - g1.var * g0.var * np.log(g1.var / g0.var)
+        ])
+        if g0.mu < root[0] < g1.mu or g1.mu < root[0] < g0.mu:
+            self.threshold = root[0]
+        else:
+            self.threshold = root[1]
+
+    def transform(self, X:np.ndarray):
+        """
+        project data
+
+        Parameters
+        ----------
+        X : (N, D) np.ndarray
+            independent variable
+
+        Returns
+        -------
+        y : (N,) np.ndarray
+            projected data
+        """
+        return X @ self.w
+
+    def classify(self, X:np.ndarray):
+        """
+        classify input data
+
+        Parameters
+        ----------
+        X : (N, D) np.ndarray
+            independent variable to be classified
+
+        Returns
+        -------
+        (N,) np.ndarray
+            binary class for each input
+        """
+        return (X @ self.w > self.threshold).astype(np.int)