0
$\begingroup$

enter image description here

The updates of the gradients are somehow wrong.

I have implemented the below given algorithm. I have done something wrong

enter image description here

'''
Implementation of PALM- proximal alternating linearisation method
'''
def palm(X,m,niter,lamda):
    X = X.T
    l = X.shape[0]
    n = X.shape[1]
    W = np.random.rand(m,n)
    D = np.random.rand(l,m)
    for i in range(niter):
        '''
        Update dictionary D
        '''
        tau_d = np.linalg.norm(W,2)**-2
        D = D - tau_d * np.matmul((np.matmul(D,W)-X),W.T)

        for j in range(1,m):
            D[:,j] = D[:,j] - (np.ones((l,1)).T*D[:,j])/l    

        for j in range(m):
            D[:,j] = D[:,j]/max(1,np.linalg.norm(D[:,j],2))

        '''
        Update coefficients W
        '''
        tau_w = np.linalg.norm(D,2)**-2
        W = W - tau_w * np.matmul(D.T,(np.matmul(D,W)-X))        
        for j in range(m):
            W[j,:] = np.multiply(np.maximum(np.zeros(W[j,:].shape[0]),np.absolute(W[j,:])-lamda),np.sign(W[j,:]))  
    return D,W

The updates of D and W are wrong from 2nd row for W and 2nd column for D i believe

$\endgroup$

1 Answer 1

0
$\begingroup$
import numpy as np
def palm(X,m,niter,lamda):
    X = X.T
    l = X.shape[0]
    n = X.shape[1]
    W = np.random.rand(m,n)
    D = np.random.rand(l,m)
    for i in range(niter):
        '''
        Update dictionary D
        '''
        tau_d = np.linalg.norm(W,2)**-2
        D = D - tau_d * np.matmul((np.matmul(D,W)-X),W.T)

        for j in range(1,m):
            D[:,j] = D[:,j] - (np.ones((l,1)).T*D[:,j])/l    

        for j in range(1,m):
            D[:,j] = D[:,j] - D[:,j]/max(1,np.linalg.norm(D[:,j],2))

        '''
        Update coefficients W
        '''
        tau_w = np.linalg.norm(D,2)**-2
        W = W - tau_w * np.matmul(D.T,(np.matmul(D,W)-X))        
        for j in range(1,m):
            W[j,:] = W[j,:] - np.multiply(np.maximum(np.zeros(W[j,:].shape[0]),np.absolute(W[j,:])-lamda),np.sign(W[j,:]))  
    return D,W
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.