线性判别分析LDA的多个python实现

在这里就不说明LDA的原理了，不懂的同学可以百度找相关资料学。这里直接给出楼主的python实现，以及搜索到的其他实现。

楼主实现：

#实现线性判别分析算法#二类n维降至一维#传入的data,target都是array,target分别是0和1def lda(data,target):    target=target.flatten()  #将target变成意味数组    print(target.shape)    df1=data[target==0]  #第0类    df2=data[target==1]  #第1类    n=data.shape[1]    u1=df1.mean(0).reshape((1,n))    u2=df2.mean(0).reshape((1,n))    print(u2.shape)    data_mean_1=df1-u1  #应用numpy的广播机制    data_mean_2=df2-u2    print(data_mean_1.T.dot(data_mean_1))    Sw=data_mean_1.T.dot(data_mean_1)+data_mean_2.T.dot(data_mean_2)    w=np.mat((u1-u2))*np.mat(Sw).I    return w

#多类别降至K维的实现def lda_muliti_class(data,target,K):    #within_class scatter matrix    clusters=unique(target)    if K>len(clusters)-1:        print("K is too much")        print("please input again")        exit(0)    Sw=np.zeros((data.shape[1],data.shape[1]))    for i in clusters:        datai=data[target==i]        datai=datai-datai.mean(0)        Swi=np.mat(datai).T*np.mat(datai)        Sw+=Swi    #between_class scatter matrix    SB=np.zeros((data.shape[1],data.shape[1]))    u=data.mean(0)  #所有样本的平均值    for i in clusters:        Ni=data[target==i].shape[0]        ui=data[target==i].mean(0)  #某个类别的平均值        SBi=Ni*np.mat(ui-u).T*np.mat(ui-u)        SB+=SBi    S=np.linalg.inv(Sw)*SB    eigVals,eigVects=np.linalg.eig(S)  #求特征值，特征向量    eigValInd=argsort(eigVals)    eigValInd=eigValInd[:(-K-1):-1]    w=eigVects[:,eigValInd]    return ww=lda_muliti_class(data_iris,target_iris,2)    w    

搜索到的其他实现：

#二类n维降至一维def calulate_w(df):        df1=df[df.label==1]        df2=df[df.label==0]        X1=df1.values[:,1:3]        X0=df2.values[:,1:3]        mean1=np.array([mean(X1[:,0]),mean(X1[:,1])])        mean0=np.array([mean(X0[:,0]),mean(X0[:,1])])        m1=shape(X1)[0]        sw=zeros(shape=(2,2))        for i in range(m1):            xsmean=mat(X1[i,:]-mean1)            sw+=xsmean.transpose()*xsmean        m0=shape(X0)[0]        for i in range(m0):            xsmean=mat(X0[i,:]-mean0)            sw+=xsmean.transpose()*xsmean        w=(mean0-mean1)*(mat(sw).I)        return w    w=calulate_w(df)w

#多类降至二维，注意是二维而已def read_iris():   #导入iris数据集，作为例子    from sklearn.datasets import load_iris    from sklearn import preprocessing    data_set = load_iris()    data_x = data_set.data     label = data_set.target + 1    #preprocessing.scale(data_x, axis=0, with_mean=True, with_std=True, copy=False)     return data_x,label    # 特征均值,计算每类的均值，返回一个向量def class_mean(data,label,clusters):    mean_vectors = []     for cl in range(1,clusters+1):        mean_vectors.append(np.mean(data[label==cl,],axis=0))    #print mean_vectors    return mean_vectors    # 计算类内散度def within_class_SW(data,label,clusters):    m = data.shape[1]    S_W = np.zeros((m,m))    mean_vectors = class_mean(data,label,clusters)    for cl ,mv in zip(range(1,clusters+1),mean_vectors):        class_sc_mat = np.zeros((m,m))        # 对每个样本数据进行矩阵乘法         for row  in data[label == cl]:            row ,mv =row.reshape(4,1),mv.reshape(4,1)            class_sc_mat += (row-mv).dot((row-mv).T)        S_W +=class_sc_mat    #print S_W     return S_Wdef between_class_SB(data,label,clusters):    m = data.shape[1]    all_mean =np.mean(data,axis = 0)    S_B = np.zeros((m,m))    mean_vectors = class_mean(data,label,clusters)    for cl ,mean_vec in enumerate(mean_vectors):        n = data[label==cl+1,:].shape[0]        mean_vec = mean_vec.reshape(4,1) # make column vector        all_mean = all_mean.reshape(4,1)# make column vector        S_B += n * (mean_vec - all_mean).dot((mean_vec - all_mean).T)    #print S_B     return S_Bdef lda():    data,label=read_iris();    clusters = 3    S_W = within_class_SW(data,label,clusters)    S_B = between_class_SB(data,label,clusters)    eig_vals, eig_vecs = np.linalg.eig(np.linalg.inv(S_W)*S_B)    #print S_W     #print S_B     for i in range(len(eig_vals)):        eigvec_sc = eig_vecs[:,i].reshape(4,1)        #print('\nEigenvector {}: \n{}'.format(i+1, eigvec_sc.real))        #print('Eigenvalue {:}: {:.2e}'.format(i+1, eig_vals[i].real))    eig_pairs = [(np.abs(eig_vals[i]), eig_vecs[:,i]) for i in range(len(eig_vals))]    eig_pairs = sorted(eig_pairs, key=lambda k: k[0], reverse=True)    W = np.hstack((eig_pairs[0][1].reshape(4,1), eig_pairs[1][1].reshape(4,1)))    #print 'Matrix W:\n', W.real    #print data.dot(W)    return W data,labels = read_iris()W = lda()Y = data.dot(W)print(W)

参考博客：
1. http://blog.csdn.net/qunxingvip/article/details/47283293
2. http://blog.csdn.net/wzmsltw/article/details/51037725