gradient_descent.py

def train(lam, num_features, rate = 0.1):
    iter = 0
    P = defaultdict(np.array)
    Q = defaultdict(np.array)
    # initialize P and Q
    for k, v in user_item_rating_train.items():
        P[k[0]] = np.random.uniform(size = num_features)
        Q[k[1]] = np.random.uniform(size = num_features)
    initial_mse = validate(user_item_rating_train, P, Q)
    print ("initial mse", initial_mse)
    while iter < 1:
        # gradient descent 
        # take gradient of matrix Q
        Q_grad = defaultdict(np.array)
        for item in items_train:
            Q_grad[item] = np.zeros(num_features)
        for k, v in user_item_rating_train.items():
            # item vector 
            q = Q[k[1]]
            # user vector  
            p = P[k[0]]
            y = -2 * (v - np.dot(q, p))
            # compute item gradient
            item_grad = np.ones(num_features) * y * p
            # update item gradient 
            Q_grad[k[1]] += item_grad
        for item in items_train:
            Q_grad[item] += 2 * Q[item]
            Q[item] -= Q_grad[item] * rate
            
        # take gradient of matrix P
        P_grad = defaultdict(np.array)
        for user in users_train:
            P_grad[user] = np.zeros(num_features)
            
        for k, v in user_item_rating_train.items():
            # item vector 
            q = Q[k[1]]
            # user vector  
            p = P[k[0]]
            y = -2 * (v - np.dot(q, p))
            # compute user gradient 
            user_grad = np.ones(num_features) * y * q
            P_grad[k[0]] += user_grad 
        
        for user in users_train:
            P[user] -= P_grad[user] * rate
            
        iter+=1
        print (iter, "mse =", mse)
    return P, Q