models.py 文件源码

def train(self):
        super().train()
        W = self.Sigma_hat
        # prior probabilities (K, 1)
        Pi = self.Pi
        # class centroids (K, p)
        Mu = self.Mu
        p = self.p
        # the number of class
        K = self.n_class
        # the dimension you want
        L = self.L

        # Mu is (K, p) matrix, Pi is (K, 1)
        mu = np.sum(Pi * Mu, axis=0)
        B = np.zeros((p, p))

        for k in range(K):
            # vector @ vector equal scalar, use vector[:, None] to transform to matrix
            # vec[:, None] equal to vec.reshape((1, vec.shape[0]))
            B = B + Pi[k]*((Mu[k] - mu)[:, None] @ ((Mu[k] - mu)[None, :]))

        # Be careful, the `eigh` method get the eigenvalues in ascending , which is opposite to R.
        Dw, Uw = LA.eigh(W)
        # reverse the Dw_ and Uw
        Dw = Dw[::-1]
        Uw = np.fliplr(Uw)

        W_half = self.math.pinv(np.diagflat(Dw**0.5) @ Uw.T)
        B_star = W_half.T @ B @ W_half
        D_, V = LA.eigh(B_star)

        # reverse V
        V = np.fliplr(V)

        # overwrite `self.A` so that we can reuse `predict` method define in parent class
        self.A = np.zeros((L, p))
        for l in range(L):
            self.A[l, :] = W_half @ V[:, l]