匿名打分还原模型

记录一次数据建模的过程：背景是根据5名评委的匿名打分的加权结果反推出各自打分情况。

数据集： $Y = \alpha X$

数据集详细描述： $y_i = \alpha_{ij}x_{ij}, i \in [1,12], j \in [1,5]$

建模：

1、令同一评委的打分方差最小： $f_1(X) = \sum_j^m \sum_i^n \frac{(x_{ij} - \overline {x_j})^2}{n} \rightarrow min, n = 12, m = 5$

2、令所有评委对同一对象的打分方差最小： $f_2(X) = \sum_i^n \sum_j^m \frac{(x_{ij} - \overline{x_i})^2}{m} \rightarrow min, n = 12, m = 5$

3、加权求最优解： $F(X) = \alpha f_1(X) + \beta f_2(X) \rightarrow min$

# coding:utf-8
import numpy as np
from sklearn import tree

p = [100,97,94,91]
score = [97.6, 97.6, 97.3, 99.4, 96.1, 97.6, 99.4, 96.7, 97.6, 96.1, 98.2, 96.55]
# [hong,xiong,zhuang,wang,zhang]
alpha = [[0.4, 0.1, 0.1, 0.3, 0.1],# MM
   [0.4, 0.1, 0.3, 0.1, 0.1],# RCS
   [0.4, 0.1, 0.1, 0.3, 0.1],# Cloud
   [0.4, 0.1, 0.3, 0.1, 0.1],# Platform
   [0.4, 0.1, 0.1, 0.3, 0.1],# Market
   [0.4, 0.3, 0.1, 0.1, 0.1],# RD
   [0.4, 0.1, 0.3, 0.1, 0.1],# System
   [0.4, 0.3, 0.1, 0.1, 0.1],# Quality
   [0.4, 0.1, 0.1, 0.3, 0.1],# General
   [0.4, 0.3, 0.1, 0.1, 0.1],# Finance
   [0.4, 0.15, 0.15, 0.15, 0.15],# HR
   [0.4, 0.15, 0.15, 0.15, 0.15]# Party
]

get_raw_scores = lambda p,score,alpha: [[i+1,score[i],[x for x in [[x1,x2,x3,x4,x5] 
    for x1 in p for x2 in p for x3 in p for x4 in p for x5 in p] 
    if score[i] == np.dot(alpha[i],x)]] 
    for i in range(len(score))]

def make_X(X, x, raw_scores, i):
    x_i = raw_scores[i][2]
    if i == len(raw_scores) - 1:
        for x_i_j in x_i:
            new_x = x + [x_i_j]
            X.append(new_x)
    else:
        for x_i_j in x_i:
            new_x = x + [x_i_j]
            make_X(X, new_x, raw_scores, i+1)

def get_y1(raw_scores,X_set):
    y1_set = []
    for X in X_set:
        X1 = np.array(X)
        XT = X1.T
        x_j = []
        y1 = 0
        for XT_j in XT:
            x_j.append(np.average(XT_j))
        for j in range(5):
            y1_j = 0
            for i in range(12):
                y1_j += np.power((X[i][j] - x_j[j]),2) / 12
            y1 += y1_j
    y1_set.append(y1)
    return y1_set

def get_y2(raw_scores,X_set):
    y2_set = []
    for X in X_set:
        y2 = 0
        for i in range(12):
            y2_i = 0
            x_i = np.average(X[i])
            for j in range(5):
                y2_i += np.power((X[i][j] - x_i,2) / 5
            y2 += y2_i
    y2_set.append(y2)
    return y2_set

raw_scores = get_raw_scores(p, score, alpha)
# X_set = []
# make_X(X_set, [], raw_scores, 0)

最后编辑于：2019.06.06 11:46:24