def toyExample():
mat = scipy.io.loadmat('../data/toy_data.mat')
data = mat['toy_data']
# TODO: Train PCA
pca = PCA(-1)
pca.train(data)
print("Variance of the data")
# TODO 1.2: Compute data variance to the S vector computed by the PCA
data_variance = np.var(data, axis=1)
print(data_variance)
print(np.power(pca.S, 2) / data.shape[1])
# TODO 1.3: Compute data variance for the projected data (into 1D) to the S vector computed by the PCA
Xout = pca.project(data, 1)
print("Variance of the projected data")
data_variance = np.var(Xout, axis=1)
print(data_variance)
print(np.power(pca.S[0], 2) / data.shape[1])
plt.figure()
plt.title('PCA plot')
plt.subplot(1, 2, 1) # Visualize given data and principal components
# TODO 1.1: Plot original data (hint, use the plot_pca function
pca.plot_pca(data)
plt.subplot(1, 2, 2)
# TODO 1.3: Plot data projected into 1 dimension
pca.S[1] = 0
pca.plot_pca(Xout)
plt.show()
def toyExample() -> None:
## Toy Data Set
mat = scipy.io.loadmat('../data/toy_data.mat')
data = mat['toy_data']
data = importGallery()
## limit datafor testing purposes
data = data[:, :144].T
print(data.shape)
## Iris dataset. Just for testing purposes
#iris = datasets.load_iris()
#data = iris['data'].astype(np.float32) # a 150x4 matrix with features
#data = data.T
# TODO: Train PCA
nComponents = 25
pca = PCA(nComponents)
## 1.1 Calculate PCA manuelly. SVD is following
#pca.pca_manuel(data)
## 1.2 Calculate PCA via SVD
mu, U, C, dataCenter = pca.train(data)
## 2. Transform RAW data using first n principal components
alpha = pca.to_pca(dataCenter)
## 3. Backtransform alpha to Raw data
Xout = pca.from_pca(alpha)
print("Variance")
# TODO 1.2: Compute data variance to the eigenvalue vector computed by the PCA
print(f'Total Variance: {np.var(data)}')
print(f'Eigenvalues: {C} \n')
# TODO 1.3: Compute data variance for the projected data (into 1D) to the S vector computed by the PCA
print(f'Total Variance Transform: {np.var(alpha)}')
print(f'Mean Eigenvalues: {np.mean(C)}')
## Plot only if fewer than 2 components
if nComponents == 2:
plt.figure()
plt.title('PCA plot')
plt.subplot(1, 2, 1) # Visualize given data and principal components
# TODO 1.1: Plot original data (hint, use the plot_pca function
pca.plot_pca(data)
plt.subplot(1, 2, 2)
# TODO 1.3: Plot data projected into 1 dimension
pca.plot_pca(Xout)
plt.show()
## Plot variances
else:
x = np.arange(1, len(C) + 1)
plt.bar(x, C)
plt.show()