SVD算法的原理网络上也有很多,不再细说了,关键是我们得到的数据是不完整的数据,所以要算SVD就必须做一次矩阵补全。补全的方式有很多,这里推荐使用均值补全的方法(用每一行均值和每一列均值的平均来代替空白处)，然后可以计算SVD,作PCA分析,然后就可以得到预测结果。

但是我们这里有一个极为关键的思路,迭代是SVD,我们用第一次预测得到的SVD的值来原来的均值预测,然后继续做SVD分解,直到收敛。这里的方法非常有效,最后得到的效果也不错(RMSE在0.87左右，第一次迭代的RMSE接近0.98)

同样将中间结果保存到文本文件里面,使得程序可以中断之后继续计算。

import numpy as np
from queue import PriorityQueue
from collections import Iterable,Counter,namedtuple,ChainMap,defaultdict
from functools import reduce
from itertools import groupby,chain,compress
from statistics import mean
from code import read_file
from PCA import get_train

def get_mean(train):
    mean_u,mean_i,cnt = {},defaultdict(lambda:0),defaultdict(lambda:0)
    for u,user_items in train.items():
        mean_u[u] = mean(user_items.values())
        for item,r in user_items.items():
            mean_i[item]+=r
            cnt[item]+=1
    sum = 0
    for each,mean_r in mean_i.items():
        mean_i[each] = mean_r/cnt[each]
        sum+=mean_i[each]
    return mean_u,mean_i,sum/len(mean_i)

def construct_matrix(train=get_train(path=r'smaller_train.txt')):#get train data from smaller data set
    row = max(train)
    col = 0
    mean_u,mean_i,all_mean = get_mean(train)
    for u,i in train.items():
        col = max(col,max(i))
    matrix = np.zeros((row,col))
    for u,user_items in train.items():
        for i in range(col):
            mean_r = (mean_u[u]+mean_i[i+1])/2
            if (i+1) in user_items:
                matrix[u-1][i] = round(user_items[i+1]-all_mean,3)
            else:
                matrix[u-1][i] = round(mean_r-all_mean,3)
    return matrix


def save_svd_predict(k):
    initial = construct_matrix()
    n = get_svd_predict(index=k)#get last result
    print('svd start')
    train = get_train(path = r'smaller_train.txt')
    mean_u,mean_i,all_mean = get_mean(train)

    u,s,v = None,None,None
    for step in range(10):
        print(step)
        u,s,v = np.linalg.svd(n)
        u = u[:,:k]
        s = s[:k]
        v = v[:k,:]
        S = np.diag(s)
        n = np.dot(u,np.dot(S,v))
        np.savetxt('u{}.txt'.format(k),u)
        np.savetxt('s{}.txt'.format(k),S)
        np.savetxt('v{}.txt'.format(k),v)
        RMES(get_svd_predict(index=k),all_mean)
        for row_index in range(len(n)):
            user = train[row_index+1]
            row_ini = initial[row_index]
            row_iter = n[row_index]
            for col in range(len(n[0])):
                if col+1 in user:#recover value rated
                    row_iter[col] = row_ini[col]
    print('svd finished')


def get_svd_predict(index):
    u = np.loadtxt('u{0}.txt'.format(index))
    s = np.loadtxt('s{0}.txt'.format(index))
    v = np.loadtxt('v{0}.txt'.format(index))
    return np.dot(u,np.dot(s,v))
def svd_predict(u,i,predictions):
    try:
        x = predictions[u-1][i-1]
        return x
    except:
        return None
def write_ans(w_path,data):
    with open(w_path,'w'):
        pass
    with open(w_path,'a') as file:
            for r in data:
                file.write('{0:.3f}\n'.format(r))