Matrix_factorization

import numpy as np


class matrix_factorization():
    def __init__(self,data:np.ndarray,numOfFeatures=2) -> None:
        self.data = data
        self.numOfUser = data.shape[0]
        self.numOfItem = data.shape[1]
        self.numOfFeatures = numOfFeatures
        #self.numOfFeatures隐向量的大小
        self.userFeatures = np.ones((self.numOfUser,self.numOfFeatures))
        self.itemFeatures = np.ones((self.numOfFeatures,self.numOfItem))

        self.lr = 0.1

    def prediction(self) -> np.ndarray:
        return np.dot(self.userFeatures,self.itemFeatures)

    def MSE(self,i:int,j:int) -> float:
        user_row = self.userFeatures[i,:] #遍历每一行
        item_col = self.itemFeatures[:,j] #遍历每一列
        return self.data[i][j] - np.sum(user_row * item_col) #(target-prediction)² ？为什么这里没平方，只是算差，

    def loss(self) -> float:
        return sum([self.MSE(i,j) for i in range(self.numOfUser) for j in range(self.numOfItem)])

    def updateUserFeature(self,i:int,k:int,j:int):
        self.userFeatures[i][k] += 2 * self.lr * self.MSE(i,j) * self.itemFeatures[k,j]


    def updateItemFeature(self,i:int,k:int,j:int):
        self.itemFeatures[k][j] += 2 * self.lr * self.MSE(i,j) * self.userFeatures[i,k]

    def updateUser(self,i:int,j:int):
        for k in range(self.numOfFeatures):
            self.updateUserFeature(i,k,j)

    def updateItem(self,i:int,j:int):
        for k in range(self.numOfFeatures):
            self.updateItemFeature(i,k,j)

    def update(self):
        for i in range(self.numOfUser):
            for j in range(self.numOfItem):
                self.updateUser(i,j)
                self.updateItem(i,j)

    def train(self,lr=0.1, iteration=1000):
        self.lr= lr
        for i in range(iteration):
            if(i % 100 == 0):
                print(f"Echo {i},\tMSE={self.loss()}")
            self.update()

if __name__ == '__main__':
    data = np.array([[2,1],[4,2]])
    mode1 = matrix_factorization(data, 1)
    mode1.train(iteration=1000)
    print(mode1.userFeatures,mode1.itemFeatures,sep='\n')
    print(mode1.prediction())
    print(mode1.data)

'''
输出
Echo 0,    MSE=5.0
Echo 100,    MSE=0.0
Echo 200,    MSE=0.0
Echo 300,    MSE=0.0
Echo 400,    MSE=0.0
Echo 500,    MSE=0.0
Echo 600,    MSE=0.0
Echo 700,    MSE=0.0
Echo 800,    MSE=0.0
Echo 900,    MSE=0.0
[[1.02102854]
 [2.04205708]]
 
[[1.9588091  0.97940455]]

[[2. 1.]
 [4. 2.]]
 
[[2 1]
 [4 2]]
'''