def display_pca_projection_dim2(X3, X5):
X = np.concatenate((X3, X5), axis=1)
m, B, Y = pca.decompose(X)
line3, = plt.plot(Y[0][:20], Y[1][:20], 'o')
line5, = plt.plot(Y[0][20:], Y[1][20:], '+')
plt.legend([line3, line5], ['3', '5'])
plt.show()
def showPcaProjection(X0, X1, legendStr): cat = np.concatenate((X0, X1), axis=1) Y = pca.decompose(cat)[2] print Y.shape line1, = plt.plot(Y[0, :X0.shape[1]], Y[1, :X0.shape[1]], '+') line2, = plt.plot(Y[0, X0.shape[1]:], Y[1, X0.shape[1]:], '*') plt.legend([line1, line2], legendStr) plt.show()
def ldaDemo_Random():
N1, N2 = 10, 10
x1 = [random.gauss(0.0, 3.0) for i in range(N1)]
y1 = [random.gauss(0.0, 1.0) for i in range(N1)]
x2 = [random.gauss(3.0, 3.0) for i in range(N2)]
y2 = [random.gauss(4.0, 1.0) for i in range(N2)]
# pca
X = np.array([x1 + x2, y1 + y2])
m, B, Y = pca.decompose(X)
pcaX = m[0] + B[0, 0] * Y[0, :]
pcaY = m[1] + B[1, 0] * Y[0, :]
# Fisher's lda
X1, X2 = np.array([x1, y1]), np.array([x2, y2])
m1, m2 = rowMean(X1), rowMean(X2)
S1, S2 = np.cov(X1), np.cov(X2)
B = (N1 / float(N1 + N2)) * S1 + (N2 / float(N1 + N2)) * S2
# One may use the Moore-Penrose inverse, la.pinv(), if B is not full rank
w = np.matmul(la.inv(B), m1 - m2)
w /= la.norm(w)
coef = np.matmul(w.T, X)
# w is 2 x 1 matrix
# coef is 1 x (N1 + N2) matrix
projX, projY = w[0][0] * coef[0], w[1][0] * coef[0]
line1, = plt.plot(x1, y1, 'o')
line2, = plt.plot(x2, y2, '+')
line3, = plt.plot(pcaX, pcaY, 'x')
line4, = plt.plot(projX, projY, '.')
plt.legend([line1, line2, line3, line4],
['class 1', 'class 2', 'pca projection', 'lsa projection'])
plt.gca().set_aspect('equal')
plt.show()