浅谈标签传播算法:LPA

标签传播算法:LPA

1.半监督学习

让学习器不依赖外界交互，自动的利用未标记样本来提升学习性能，这种就是半监督学习，主要用来处理现实中有标记数据少、未标记数据多的问题，要利用未标记的数据，必须要做一些将未标记样本所揭示的数据分布信息与类别标签相联系的假设。它基于三大假设：
a）Smoothness平滑假设：相似的数据具有相同的label。
b）Cluster聚类假设：处于同一个聚类下的数据具有相同label。
c）Manifold流形假设：处于同一流形结构下的数据具有相同label。

2.标签传播算法LPA

标签传播算法（LPA）是基于图的半监督学习算法，我们为所有的数据构建一个图，图的节点就是一个数据点，包含labeled和unlabeled的数据。节点i和节点j的边表示他们的相似度。$Wij$在关系网络中就可以节点i与j之间的亲密度值代替。
标签传播算法是通过节点之间的边进行传播label，边的权重越大，说明更容易传播过去，根据权重$Wij$定义$N\ast N$的概率转移矩阵P：

Pij表示从节点i转移到节点j的概率。
假设有C个类和L个labeled样本，我们定义一个LxC的label矩阵YL，同样，我们也给U个unlabeled样本一个UxC的label矩阵YU，初始时将值都赋值成-1。把他们合并，我们得到一个NxC的soft label矩阵F=[YL;YU]。

算法步骤如下：
（1）执行传播：F=PF
（2）将F中有标签的部分重置成原始值：FL=YL
（3）重复1，2两步，直到收敛

步骤1就是将概率矩阵P和标签矩阵F进行相乘，此时每一个节点都将自己的label以P的概率传播给其他节点，步骤2，本来就有labeled的数据是确定的，每次迭代的时候，都需要回归它本来的label。

3.python代码

因为我这里是基于通话记录来实现LPA算法，这里的$weight$是算的节点之间的亲密度，具体的公式如下：$weight(A,B) = 0.5*(0.5count(A->B)/count(A) + 0.5duration(A->B)/duration(A)) + 0.5*(0.5count(B->A)/count(B) + 0.5duration(B->A)/duration(B)) $ ，进而得到概率矩阵P

# -*- coding: utf-8 -*-
import pandas as pd
import os
import numpy as np


def LPA(max_iter=500, tol=1e-3):
    data = pd.read_csv(os.getcwd() + "/data1.csv", low_memory=False)  # 含概率矩阵P和标签的数据集
    num_label_samples = len(data) - (data["dsc_black_list"].isnull()).sum()
    num_unlabel_samples = (data["dsc_black_list"].isnull()).sum()
    num_samples = len(data)
    num_classes = 2
    clamp_data_label = np.zeros((num_label_samples, num_classes), np.float32)
    labels = list(data[~data["dsc_black_list"].isnull()]["dsc_black_list"].values)
    for i in range(num_label_samples):
        clamp_data_label[i][int(labels[i])] = 1.0
    label_function = np.zeros((num_samples, num_classes), np.float32)
    label_function[0: num_label_samples] = clamp_data_label
    label_function[num_label_samples: num_samples] = -1  # 定义标签矩阵F
    data["weight_sum"] = data.iloc[:, 1:-2].sum(axis=1)
    for i in data.columns[1:-3]:
        data[i] = data[i] / data["weight_sum"]
    affinity_matrix = np.array(data.iloc[:,1:-3])  # 定义概率矩阵P
    iter = 0
    pre_label_function = np.zeros((num_samples, num_classes), np.float32)
    changed = np.abs(pre_label_function - label_function).sum()
    while iter < max_iter and changed > tol:
        if iter % 1 == 0:
            print("---> Iteration %d/%d, changed: %f" % (iter, max_iter, changed))
        pre_label_function = label_function
        iter += 1
        label_function = np.dot(affinity_matrix, label_function)
        label_function[0: num_label_samples] = clamp_data_label  # 每次迭代后都需要将labeled数据的label重置
        changed = np.abs(pre_label_function - label_function).sum()
    unlabel_data_labels = np.zeros(num_unlabel_samples)
    for i in range(num_unlabel_samples):
        unlabel_data_labels[i] = np.argmax(label_function[i + num_label_samples])
    for i in range(len(unlabel_data_labels)):
        if unlabel_data_labels[i] == 1:
            print(i + num_label_samples, "==>", data[data['mobile_iid'] == i + num_label_samples]["mobile"])
    return unlabel_data_labels


if __name__ == '__main__':
    unlabel_data_labels = LPA()

运行结果

/Users/xudong/opt/anaconda3/python.app/Contents/MacOS/python /Users/xudong/PycharmProjects/关系网络/相对亲密度计算/标签传播.py
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