《模式识别与智能计算》基于二值数据的贝叶斯分类实现

算法流程

1. 将数据二值化
2. 计算每类数字的先验概率
3. 计算条件概率
4. 计算后验概率
   (具体计算过程请见书上77页）

算法实现

贝叶斯算法

def bayeserzhi(x_train,y_train,sample):
    """
    :function 基于二值数据的贝叶斯分类器
    :param x_train: 训练集 M*N  M为样本个数 N为特征个数
    :param y_train: 训练集标签 1*M
    :param sample: 待识别样品
    :return: 返回判断类别
    """
    #后验概率
    pwx = []

    target = np.unique(y_train)

    spit = 0.5 * (np.max(x_train) - np.min(x_train))
    train = np.where(x_train > spit, 1, 0)
    sample = np.where(sample > spit, 1, 0)

    for i in target:
        trainIndex = (([j for j, y in enumerate(y_train) if y == i]))
        trainNum = len(trainIndex)
        # 计算先验概率
        pw = trainNum/x_train.shape[0]
        # 计算类条件概率
        p = (np.sum(train[trainIndex],axis=0)+1)/(trainNum+2)
        pxw = 1
        for j in range(train.shape[1]):
            if sample[j]:
                pxw *= p[j]
            else:
                pxw *= (1-p[j])
        #计算pxw*pw
        pwx.append(pxw*pw)
    pwx = pwx/np.sum(pwx)
    maxId = np.argmax(pwx)
    label = target[maxId]
    return label

划分数据集

def train_test_split(x,y,ratio = 3):
    """
    :function: 对数据集划分为训练集、测试集
    :param x: m*n维 m表示数据个数 n表示特征个数
    :param y: 标签
    :param ratio: 产生比例 train:test = 3:1(默认比例)
    :return: x_train y_train  x_test y_test
    """
    n_samples , n_train = x.shape[0] , int(x.shape[0]*(ratio)/(1+ratio))
    train_id = random.sample(range(0,n_samples),n_train)
    x_train = x[train_id,:]
    y_train = y[train_id]
    x_test = np.delete(x,train_id,axis = 0)
    y_test = np.delete(y,train_id,axis = 0)
    return x_train,y_train,x_test,y_test

测试代码

from sklearn import datasets
from Include.chapter4 import function
import numpy as np

#读取数据
digits = datasets.load_digits()
x , y = digits.data,digits.target

#划分数据集
x_train, y_train, x_test, y_test = function.train_test_split(x,y)
testId = np.random.randint(0, x_test.shape[0])
sample = x_test[testId, :]

#模板匹配
ans = function.bayeserzhi(x_train,y_train,sample)
y_test[testId]
print("预测的数字类型",ans)
print("真实的数字类型",y_test[testId])

算法结果

预测的数字类型 0
真实的数字类型 0