wehub-resource-sync
81 lines
2.1 KiB
Python
Executable File
81 lines
2.1 KiB
Python
Executable File
import numpy as np
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from prml.linear.classifier import Classifier
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from prml.rv.gaussian import Gaussian
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class FishersLinearDiscriminant(Classifier):
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"""
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Fisher's Linear discriminant model
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"""
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def __init__(self, w:np.ndarray=None, threshold:float=None):
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self.w = w
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self.threshold = threshold
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def fit(self, X:np.ndarray, t:np.ndarray):
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"""
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estimate parameter given training dataset
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Parameters
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----------
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X : (N, D) np.ndarray
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training dataset independent variable
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t : (N,) np.ndarray
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training dataset dependent variable
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binary 0 or 1
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"""
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X0 = X[t == 0]
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X1 = X[t == 1]
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m0 = np.mean(X0, axis=0)
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m1 = np.mean(X1, axis=0)
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cov_inclass = np.cov(X0, rowvar=False) + np.cov(X1, rowvar=False)
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self.w = np.linalg.solve(cov_inclass, m1 - m0)
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self.w /= np.linalg.norm(self.w).clip(min=1e-10)
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g0 = Gaussian()
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g0.fit((X0 @ self.w))
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g1 = Gaussian()
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g1.fit((X1 @ self.w))
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root = np.roots([
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g1.var - g0.var,
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2 * (g0.var * g1.mu - g1.var * g0.mu),
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g1.var * g0.mu ** 2 - g0.var * g1.mu ** 2
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- g1.var * g0.var * np.log(g1.var / g0.var)
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])
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if g0.mu < root[0] < g1.mu or g1.mu < root[0] < g0.mu:
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self.threshold = root[0]
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else:
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self.threshold = root[1]
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def transform(self, X:np.ndarray):
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"""
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project data
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Parameters
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----------
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X : (N, D) np.ndarray
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independent variable
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Returns
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-------
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y : (N,) np.ndarray
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projected data
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"""
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return X @ self.w
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def classify(self, X:np.ndarray):
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"""
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classify input data
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Parameters
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----------
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X : (N, D) np.ndarray
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independent variable to be classified
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Returns
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-------
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(N,) np.ndarray
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binary class for each input
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"""
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return (X @ self.w > self.threshold).astype(np.int)
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