matrix factorization using gradient descent

matrix_factorization.py

import numpy as np

# Frobenius norm (X) = Tr(X.X_T)  X_T = Transpose of X
# d(Frobenius norm)/dX = 2X


# M ~ L*R 
# R = l*r - M         
# Loss_fuction = NORM(R) to be minimized
# Loss_fuction = NORM(R) 
# d(Loss_fuction)/dl = d(NORM(R))/dl =  d(NORM(R))/dR * dR/dl = 2R.r_T
# d(Loss_fuction)/dr = d(NORM(R))/dr =  dR/dl * d(NORM(R))/dR = 2l_t.R

def mat_factor(input_mat,d,epoch=100, lr=1e-2):
    m,n = input_mat.shape
    L = np.random.normal(size=(m,d))  # random initialization of Left Mat
    R = np.random.normal(size=(d,n))  # random initialization of Right Mat
    for i in range(1,epoch+1):        # gradient descent loop
        residual = L.dot(R)-input_mat
        dL = 2*residual.dot(R.T)      # Gradient Calculation
        dR = 2*L.T.dot(residual )     # Gradient Calculation 
        L = L - lr*dL                 # Update L
        R = R - lr*dR                 # Update R
        if i%10 == 0:
            print(f'epoch: {i}, residual: {np.linalg.norm(residual)} ') #Looging
    return L,R