使用numpy实现机器学习模型

LR:

import numpy as np
import matplotlib.pyplot as plt

def gene_dataset(opt='linear'):
    pos_num , neg_num = 100, 100
    X = np.zeros((2,pos_num+neg_num))
    Y = np.zeros((1,pos_num+neg_num))
    
    if opt == 'linear':
        x1 = np.random.normal(loc=-1,scale=3,size=(1,pos_num)) # 正态分布 均值 方差 样本个数
        
        X[0,:pos_num] = x1
        X[1,:pos_num] = 2*x1+10+0.1*x1**2 + np.random.normal(loc=0,scale=5,size=(1,pos_num)) 
        Y[0,:pos_num] = 1

        x2 = np.random.normal(loc=1,scale=3,size=(1,neg_num)) # 正态分布 均值 方差 样本个数
        
        X[0,pos_num:] = x1
        X[1,pos_num:] = 2*x1-5-0.1*x1**2 + np.random.normal(loc=0,scale=5,size=(1,neg_num)) 
        Y[0,pos_num:] = 0
        
    return X,Y

def plotData(X,Y):
    
    plt.figure()
    pos_idx = (Y==1);
    pos_idx = pos_idx[0,:];
    neg_idx = (Y==0);
    neg_idx = neg_idx[0,:];
    plt.plot(X[0,pos_idx],X[1,pos_idx],'r+')
    plt.plot(X[0,neg_idx],X[1,neg_idx],'bo')
    
X,Y= gene_dataset()
plotData(X,Y)

def sigmoid(X):
    return 1/(1+np.exp(-X))

def loss_function(Y, P):
    return Y*np.log(P) + (1-Y)*np.log(1-P)

def cost_function(Y, P):
    m = Y.shape[1]
    return -np.sum(loss_function(Y,P))/m

'''
dw = αL/αw = (sigmoid(w*x+b)-y)*x
db = αL/αw = sigmoid(w*x+b)-y
'''
def LR(X,Y,alpha,w,b,epoches):
    m = Y.shape[1]
    for epoch in range(epoches):
        Z = sigmoid(np.dot(w.transpose(), X) + b) # sigmoid(wT*X+b) w (n,1) X (n,m) b = (1) => (1, m)
        dw = np.dot(X, (Z-Y).transpose())/m  #   X (n, m) Z-Y (1, m) =>  (n,1)
        db = np.sum(Z-Y)/m
        w = w-alpha*dw
        b = b-alpha*db
        if epoch%10==0:
            print(cost_function(Y, Z))
    return w,b

def pred_func(X, w, b):
    return sigmoid(np.dot(w.transpose(), X) + b)>=0.5

def init_wb(featnum):
    return np.zeros((featnum,1)) , 0

X,Y= gene_dataset()

plotData(X,Y)
w,b = init_wb(X.shape[0])

w,b = LR(X,Y,0.1,w,b,50)

pred = pred_func(X, w, b)

print(pred)
print(w, b)

Kmeans：

import numpy as np
import matplotlib.pyplot as plt
from copy import deepcopy

def distance(v1, v2):
    return np.sum((v1-v2)**2)**0.5

def init(X, k):
    m, n = X.shape[0], X.shape[1]
    center = np.zeros((k,n))
    idx = [i for i in range(m)]
    np.random.shuffle(idx)
    for i in range(k):
        center[i,:] = X[idx[i],:]
    return center
    
def kmeans(X, k):
    center = init(X,k)
    clusterChanged = True
    while clusterChanged:
        clusterChanged = False
        clusterDict = {}
        precenter = deepcopy(center)
        for i in range(len(X)):
            MIN_dist = 1e9
            MIN_INDEX = 0
            for j in range(k):
                if distance(center[j,:] , X[i,:]) < MIN_dist:
                    MIN_dist = distance(center[j,:] , X[i,:])
                    MIN_INDEX = j
            
            if MIN_INDEX not in clusterDict: clusterDict[MIN_INDEX] = []
            clusterDict[MIN_INDEX].append(X[i])
        
        for i in range(k):
            center[i,:] = np.mean(clusterDict[i],axis=0) # axis=0对横轴进行操作
            
        if np.allclose(center, precenter):
            clusterChanged = True
    
    return center

X = np.array([[1,3],[1,4],[2,3],[2,4],[3,1],[3,2],[4,1],[4,2]])*1.0
print(X)
                
print(kmeans(X,2))