LAPLS算法实现与数据预处理详解

#数据读取-单因变量与多因变量
def loadDataSet01(filename):
    fr = open(filename)
    arrayLines = fr.readlines()
    row = len(arrayLines)
    x = mat(zeros((row, 798)))
    y = mat(zeros((row, 1)))
    index = 0
    for line in arrayLines:
        curLine = line.strip().split('\t')
        x[index,:] = curLine[0:798]
        y[index,:] = curLine[-1]
        index +=1
    return x, y

#数据标准化
def stardantDataSet(x0, y0):
    e0 = preprocessing.scale(x0)
    f0 = preprocessing.scale(y0)
    return e0, f0

#求均值-标准差
def data_Mean_Std(x0, y0):
    mean_x = mean(x0, 0)
    mean_y = mean(y0, 0)
    std_x = std(x0, axis=0, ddof=1)
    std_y = std(y0, axis=0, ddof=1)
    return mean_x, mean_y, std_x, std_y

#PLS核心函数

def PLS(x0, y0):
    e0, f0 = stardantDataSet(x0,y0)
    e0 = mat(e0); f0 = mat(f0); m = shape(x0)[1]; ny=shape(y0)[1]
    w = mat(zeros((m, m))).T; w_star = mat(zeros((m, m))).T
    chg = mat(eye((m)))
    my = shape(x0)[0];ss = mat(zeros((m,1))).T
    t = mat(zeros((my,m))); alpha= mat(zeros((m,m)))
    press_i = mat(zeros((1,my)))
    press = mat(zeros((1, m)))
    Q_h2 = mat(zeros((1, m)))
    beta = mat(zeros((1,m))).T
    for i in range(1,m+1):
        #计算w,w*和t的得分向量
        matrix = e0.T * f0 * (f0.T * e0)
        val, vec = linalg.eig(matrix)#求特征向量和特征值
        sort_val = argsort(val)
        index_vec = sort_val[:-2:-1]
        w[:,i-1] = vec[:,index_vec]#求最大特征值对应的特征向量
        w_star[:,i-1] =  chg * w[:,i-1]
        t[:,i-1] = e0 * w[:,i-1]
        #temp_t[:,i-1] = t[:,i-1]
        alpha[:,i-1] = (e0.T * t[:,i-1]) / (t[:,i-1].T * t[:,i-1])
        chg = chg * mat(eye((m)) - w[:,i-1] * alpha[:,i-1].T)
        e = e0 - t[:,i-1] * alpha[:,i-1].T
        e0 = e
        #计算ss(i)的值
        #beta = linalg.inv(t[:,1:i-1], ones((my, 1))) * f0
        #temp_t = hstack((t[:,i-1], ones((my,1))))
        #beta = f0\linalg.inv(temp_t)
        #beta = nnls(temp_t, f0)