FM算法python实现

我们需要注意以下四点：

1. 初始化参数，包括对偏置项权值w0、一次项权值w以及交叉项辅助向量的初始化；

2. 定义FM算法；

3. 损失函数梯度的定义；

4. 利用梯度下降更新参数。

下面的代码片段是以上四点的描述，其中的loss并不是二分类的损失loss，而是分类loss的梯度中的一部分：

loss = self.sigmoid(classLabels[x] * p[0, 0]) -1

实际上，二分类的损失loss的梯度可以表示为：

gradient = (self.sigmoid(classLabels[x] * p[0, 0]) -1)*classLabels[x]*p_derivative

其中 p_derivative 代表常数项、一次项、交叉项的导数

[code]# -*- coding: utf-8 -*-

from __future__ import division
from math import exp
from numpy import *
from random import normalvariate  # 正态分布
from sklearn import preprocessing
import numpy as np

'''
data : 数据的路径
feature_potenital : 潜在分解维度数
alpha ： 学习速率
iter ： 迭代次数
_w,_w_0,_v ： 拆分子矩阵的weight
with_col : 是否带有columns_name
first_col : 首列有价值的feature的index
'''

class fm(object):
def __init__(self):
self.data = None
self.feature_potential = None
self.alpha = None
self.iter = None
self._w = None
self._w_0 = None
self.v = None
self.with_col = None
self.first_col = None

def min_max(self, data):
self.data = data
min_max_scaler = preprocessing.MinMaxScaler()
return min_max_scaler.fit_transform(self.data)

def loadDataSet(self, data, with_col=True, first_col=2):
# 我就是闲的蛋疼，明明pd.read_table()可以直接度，非要搞这样的，显得代码很长，小数据下完全可以直接读嘛，唉～
self.first_col = first_col
dataMat = []
labelMat = []
fr = open(data)
self.with_col = with_col
if self.with_col:
N = 0
for line in fr.readlines():
# N=1时干掉列表名
if N > 0:
currLine = line.strip().split()
lineArr = []
featureNum = len(currLine)
for i in range(self.first_col, featureNum):
lineArr.append(float(currLine[i]))
dataMat.append(lineArr)
labelMat.append(float(currLine[1]) * 2 - 1)
N = N + 1
else:
for line in fr.readlines():
currLine = line.strip().split()
lineArr = []
featureNum = len(currLine)
for i in range(2, featureNum):
lineArr.append(float(currLine[i]))
dataMat.append(lineArr)
labelMat.append(float(currLine[1]) * 2 - 1)
return mat(self.min_max(dataMat)), labelMat

def sigmoid(self, inx):
# return 1.0/(1+exp(min(max(-inx,-10),10)))
return 1.0 / (1 + exp(-inx))

# 得到对应的特征weight的矩阵
def fit(self, data, feature_potential=8, alpha=0.01, iter=100):
# alpha是学习速率
self.alpha = alpha
self.feature_potential = feature_potential
self.iter = iter
# dataMatrix用的是mat, classLabels是列表
dataMatrix, classLabels = self.loadDataSet(data)
print('dataMatrix:',dataMatrix.shape)
print('classLabels:',classLabels)
k = self.feature_potential
m, n = shape(dataMatrix)
# 初始化参数
w = zeros((n, 1))  # 其中n是特征的个数
w_0 = 0.
v = normalvariate(0, 0.2) * ones((n, k))
for it in range(self.iter): # 迭代次数
# 对每一个样本，优化
for x in range(m):
# 这边注意一个数学知识：对应点积的地方通常会有sum，对应位置积的地方通常都没有，详细参见矩阵运算规则，本处计算逻辑在：http://blog.csdn.net/google19890102/article/details/45532745
# xi·vi,xi与vi的矩阵点积
inter_1 = dataMatrix[x] * v
# xi与xi的对应位置乘积   与   xi^2与vi^2对应位置的乘积    的点积
inter_2 = multiply(dataMatrix[x], dataMatrix[x]) * multiply(v, v)  # multiply对应元素相乘
# 完成交叉项,xi*vi*xi*vi - xi^2*vi^2
interaction = sum(multiply(inter_1, inter_1) - inter_2) / 2.
# 计算预测的输出
p = w_0 + dataMatrix[x] * w + interaction
print('classLabels[x]:',classLabels[x])
print('预测的输出p:', p)
# 计算sigmoid(y*pred_y)-1
loss = self.sigmoid(classLabels[x] * p[0, 0]) - 1
if loss >= -1:
loss_res = '正方向 '
else:
loss_res = '反方向'
# 更新参数
w_0 = w_0 - self.alpha * loss * classLabels[x]
for i in range(n):
if dataMatrix[x, i] != 0:
w[i, 0] = w[i, 0] - self.alpha * loss * classLabels[x] * dataMatrix[x, i]
for j in range(k):
v[i, j] = v[i, j] - self.alpha * loss * classLabels[x] * (
dataMatrix[x, i] * inter_1[0, j] - v[i, j] * dataMatrix[x, i] * dataMatrix[x, i])
print('the no %s times, the loss arrach %s' % (it, loss_res))
self._w_0, self._w, self._v = w_0, w, v

def predict(self, X):
if (self._w_0 == None) or (self._w == None).any() or (self._v == None).any():
raise NotFittedError("Estimator not fitted, call `fit` first")
# 类型检查
if isinstance(X, np.ndarray):
pass
else:
try:
X = np.array(X)
except:
raise TypeError("numpy.ndarray required for X")
w_0 = self._w_0
w = self._w
v = self._v
m, n = shape(X)
result = []
for x in range(m):
inter_1 = mat(X[x]) * v
inter_2 = mat(multiply(X[x], X[x])) * multiply(v, v)  # multiply对应元素相乘
# 完成交叉项
interaction = sum(multiply(inter_1, inter_1) - inter_2) / 2.
p = w_0 + X[x] * w + interaction  # 计算预测的输出
pre = self.sigmoid(p[0, 0])
result.append(pre)
return result

def getAccuracy(self, data):
dataMatrix, classLabels = self.loadDataSet(data)
w_0 = self._w_0
w = self._w
v = self._v
m, n = shape(dataMatrix)
allItem = 0
error = 0
result = []
for x in range(m):
allItem += 1
inter_1 = dataMatrix[x] * v
inter_2 = multiply(dataMatrix[x], dataMatrix[x]) * multiply(v, v)  # multiply对应元素相乘
# 完成交叉项
interaction = sum(multiply(inter_1, inter_1) - inter_2) / 2.
p = w_0 + dataMatrix[x] * w + interaction  # 计算预测的输出
pre = self.sigmoid(p[0, 0])
result.append(pre)
if pre < 0.5 and classLabels[x] == 1.0:
error += 1
elif pre >= 0.5 and classLabels[x] == -1.0:
error += 1
else:
continue
# print(result)
value = 1 - float(error) / allItem
return value

class NotFittedError(Exception):
"""
Exception class to raise if estimator is used before fitting
"""
pass

if __name__ == '__main__':
fm()