def cca_projection(self, X, Y, k=2):
'''
Return U_K^T, \Simgma_{XX}^{-1/2}
'''
###SCALE AN IDENTITY MATRIX BY THIS TERM AND ADD TO COMPUTED COVARIANCE MATRIX TO PREVENT IT BEING SINGULAR ###
reg = 1e-5
Y = create_one_hot_label(Y, self.NUM_CLASSES)
X, Y = subtract_mean_from_data(X, Y)
cov_XX = compute_covariance_matrix(X, X)
cov_XX = cov_XX + reg * np.identity(len(cov_XX))
cov_XY = compute_covariance_matrix(X, Y)
cov_YY = compute_covariance_matrix(Y, Y)
cov_YY = cov_YY + reg * np.identity(len(cov_YY))
left = sqrtm(inv(cov_XX))
middle = cov_XY
right = sqrtm(inv(cov_YY))
m = left.dot(middle.dot(right))
U, D, V = svd(m)
return (U.T)[0:k], left
def cca_projection(self, X, Y, k=2):
'''
Return U_K^T, \Simgma_{XX}^{-1/2}
'''
###SCALE AN IDENTITY MATRIX BY THIS TERM AND ADD TO COMPUTED COVARIANCE MATRIX TO PREVENT IT BEING SINGULAR ###
reg = 1e-5
#number of classes for this part is 3
y_one_hot = create_one_hot_label(Y, 3)
#perform mean subtraction
X_new, Y_new = subtract_mean_from_data(X, y_one_hot)
m = X_new.shape[1]
n = Y_new.shape[1]
XX = compute_covariance_matrix(X_new, X_new)
YY = compute_covariance_matrix(Y_new, Y_new)
#compute the trace of each matrix
XX += np.trace(XX)**reg**np.eye(m)
YY += np.trace(YY)**reg**np.eye(n)
#compute the inverses
XX_inverse = inv(sqrtm(XX)).T
YY_inverse = inv(sqrtm(YY)).T
#correlation X and Y
correlation_XY = np.dot(
np.dot(X_new, XX_inverse).T, np.dot(Y_new, YY_inverse))
#finally svd decomposition
U, sigma, V = svd(correlation_XY)
#first two columns only
U = U[:, :3]
return U.T, XX_inverse
def cca_projection(self,X,Y,k=2):
'''
Return U_K^T, \Simgma_{XX}^{-1/2}
'''
Y = create_one_hot_label(Y,self.NUM_CLASSES)
X,Y = subtract_mean_from_data(X,Y)
C_XY = compute_covariance_matrix(X,Y)
C_XX = compute_covariance_matrix(X,X)
C_YY = compute_covariance_matrix(Y,Y)
dim_x = C_XX.shape[0]
dim_y = C_YY.shape[0]
A = inv(sqrtm(C_XX+1e-5*np.eye(dim_x)))
B = inv(sqrtm(C_YY+1e-5*np.eye(dim_y)))
C = np.matmul(A,np.matmul(C_XY,B))
u,s,d = svd(C)
return u[:,0:k].T, A
def cca_projection(self, X, Y, k=2):
reg = 1e-5
Y = np.array(Y)
one_hot_y = create_one_hot_label(Y, self.NUM_CLASSES)
X_bar = subtract_mean_from_data(X, Y)
Y_bar = subtract_mean_from_data(one_hot_y, X)
cov_XX = compute_covariance_matrix(X_bar[0], X_bar[0])
cov_XX += np.identity(729) * (reg)
cov_YY = compute_covariance_matrix(Y_bar[0], Y_bar[0])
cov_XY = compute_covariance_matrix(X_bar[0], Y_bar[0])
cov_XX_inv = inv(sqrtm(cov_XX))
cov_YY_inv = inv(sqrtm(cov_YY))
ccm = cov_XX_inv.dot(cov_XY).dot(cov_YY_inv)
U, s, V = svd(ccm)
return U.T[:k], cov_XX_inv
def pca_projection(self, X, Y):
'''
Return U_2^T
'''
X, Y = subtract_mean_from_data(X, Y)
cov_X = compute_covariance_matrix(X, X)
U, D, V = svd(cov_X)
want = (U.T)[0:2]
return want
def pca_projection(self, X, Y):
'''
Return U_2^T
'''
X, Y = subtract_mean_from_data(X, Y)
C_XX = compute_covariance_matrix(X, X)
u, s, d = svd(C_XX)
return u[:, 0:2].T
def pca_projection(self, X, Y):
'''
Return U_2^T
'''
Y = create_one_hot_label(Y, self.NUM_CLASSES)
X, Y = subtract_mean_from_data(X, Y)
C_XX = compute_covariance_matrix(X, X)
u, s, d = svd(C_XX)
return u[:, 0:2].T
def train_model(self,X,Y): '''' FILL IN CODE TO TRAIN MODEL MAKE SURE TO ADD HYPERPARAMTER TO MODEL ''' X = np.array(X) Y = np.array(Y) self.mu = [] for i in range(self.NUM_CLASSES) : index = Y == i n = sum(index) Xi = X[index,:] mean = np.mean(Xi, axis = 0) self.mu.append(mean) Xi_minus_mean = Xi - mean if i == 0 : self.cov = n * compute_covariance_matrix(Xi_minus_mean, Xi_minus_mean) else : self.cov += n * compute_covariance_matrix(Xi_minus_mean, Xi_minus_mean) self.cov = self.cov / X.shape[0]
def pca_projection(self, X, Y):
'''
Return U_2^T
'''
Y_one_hot = create_one_hot_label(Y, 729)
#perform mean subtraction
X_new, Y_new = subtract_mean_from_data(X, Y_one_hot)
#compute covariance matrix
cov_matrix = compute_covariance_matrix(X_new, Y_new)
#svd decomposition
U, sigma, V_transpose = LA.svd(cov_matrix, full_matrices=False)
return np.dot(U, np.dot(np.diag(sigma), V_transpose.T))
def train_model(self,X,Y):
"""
self.muj = []
self.cov_XX = []
X0 = X[:324]
mu0 = np.mean(X0,axis=0)
X1 = X[325:633]
mu1 = np.mean(X1,axis=0)
X2 = X[634:]
mu2 = np.mean(X2,axis=0)
self.muj.append(mu0)
self.muj.append(mu1)
self.muj.append(mu2)
X_bar_0 = subtract_mean_from_data(X0, Y)
X_bar_1 = subtract_mean_from_data(X1, Y)
X_bar_2 = subtract_mean_from_data(X2, Y)
self.cov_XX.append(compute_covariance_matrix(X_bar_0[0],X_bar_0[0])+np.identity(len(np.array(X0).T))*self.reg_cov)
self.cov_XX.append(compute_covariance_matrix(X_bar_1[0],X_bar_1[0])+np.identity(len(np.array(X0).T))*self.reg_cov)
self.cov_XX.append(compute_covariance_matrix(X_bar_2[0],X_bar_2[0])+np.identity(len(np.array(X0).T))*self.reg_cov)
"""
self.muj = []
self.cov_XX = []
j = 0
k = 0
val = Y[0]
for i in range(self.NUM_CLASSES):
while(j<len(Y)-1 and val==Y[j]):
j = j + 1
X0 = X[k:j-1]
mu0 = np.mean(X0,axis=0)
self.muj.append(mu0)
X_bar_0 = subtract_mean_from_data(X0,Y)
cov_XX_0 = compute_covariance_matrix(X_bar_0[0],X_bar_0[0]) + np.identity(len(np.array(X0).T))*self.reg_cov
self.cov_XX.append(cov_XX_0)
k = j
val = Y[j]
def train_model(self, X, Y):
"""
X_bar = subtract_mean_from_data(X,Y)
cov_XX = compute_covariance_matrix(X_bar[0],X_bar[0])
cov_XX += np.identity(len(np.array(X_bar).T)) * self.reg_cov
self.cov_XX = cov_XX
self.muj = []
X0 = X[:324]
mu0 = np.mean(X0,axis=0)
print(mu0)
X1 = X[325:633]
mu1 = np.mean(X1,axis=0)
X2 = X[634:]
mu2 = np.mean(X2,axis=0)
self.muj.append(mu0)
self.muj.append(mu1)
self.muj.append(mu2)
"""
X_bar = subtract_mean_from_data(X, Y)
cov_XX = compute_covariance_matrix(X_bar[0], X_bar[0])
cov_XX += np.identity(len(np.array(X).T)) * self.reg_cov
self.cov_XX = cov_XX
self.muj = []
j = 0
k = 0
val = Y[0]
for i in range(self.NUM_CLASSES):
print(i)
while (j < len(Y) - 1 and val == Y[j]):
j = j + 1
X0 = X[k:j - 1]
mu0 = np.mean(X0, axis=0)
self.muj.append(mu0)
k = j
val = Y[j]
def pca_projection(self, X, Y):
#mux = np.mean(X,axis=0)
X_bar = subtract_mean_from_data(X, Y)
cov_XX = compute_covariance_matrix(X_bar[0], X_bar[0])
U, s, V = svd(cov_XX)
return U.T[:2]