svd, nmf methods

Phase 2/dim_reduction_methods.py

@@ -0,0 +1,51 @@
+import numpy as np
+
+def svd(matrix, k):
+    # Step 1: Compute the covariance matrix
+    cov_matrix = np.dot(matrix.T, matrix)
+
+    # Step 2: Compute the eigenvalues and eigenvectors of the covariance matrix
+    eigenvalues, eigenvectors = np.linalg.eig(cov_matrix)
+
+    # Step 3: Sort the eigenvalues and corresponding eigenvectors
+    sort_indices = eigenvalues.argsort()[::-1]
+    eigenvalues = eigenvalues[sort_indices]
+    eigenvectors = eigenvectors[:, sort_indices]
+
+    # Step 4: Compute the singular values and the left and right singular vectors
+    singular_values = np.sqrt(eigenvalues)
+    left_singular_vectors = np.dot(matrix, eigenvectors)
+    right_singular_vectors = eigenvectors
+
+    # Step 5: Normalize the singular vectors
+    for i in range(left_singular_vectors.shape[1]):
+        left_singular_vectors[:, i] /= singular_values[i]
+
+    for i in range(right_singular_vectors.shape[1]):
+        right_singular_vectors[:, i] /= singular_values[i]
+
+    # Keep only the top k singular values and their corresponding vectors
+    singular_values = singular_values[:k]
+    left_singular_vectors = left_singular_vectors[:, :k]
+    right_singular_vectors = right_singular_vectors[:, :k]
+
+    return left_singular_vectors, np.diag(singular_values), right_singular_vectors.T
+
+def nmf(matrix, k, num_iterations = 100):
+    d1, d2 = matrix.shape
+    # Initialize W and H matrices with random non-negative values
+    W = np.random.rand(d1, k)
+    H = np.random.rand(k, d2)
+
+    for iteration in range(num_iterations):
+        # Update H matrix
+        numerator_h = np.dot(W.T, matrix)
+        denominator_h = np.dot(np.dot(W.T, W), H)
+        H *= numerator_h / denominator_h
+
+        # Update W matrix
+        numerator_w = np.dot(matrix, H.T)
+        denominator_w = np.dot(W, np.dot(H, H.T))
+        W *= numerator_w / denominator_w
+
+    return W, H