流形學習——MDS多維縮放算法

from sklearn import metrics
import matplotlib.pyplot as plt
import numpy as np
from mpl_toolkits import mplot3d

def loadDataSet(fileName,delim='\t'):
    fr = open(fileName)
    stringArr = [line.strip().split(delim) for line in fr.readlines()]
    datArr = [list(map(float,line)) for line in stringArr]
    return np.mat(datArr)

#計算任意兩個樣本點之間的距離
def calDist(x, y):
    d = metrics.pairwise_distances(x, y)
    return d

def cal_B(d):
    m, n = np.shape(d)
    dij2 = np.square(d)                   # 計算dist(ij)^2
    di = np.sum(dij2, axis=1) / m         # 計算dist(i.)^2
    dj = np.sum(dij2, axis=0) / m         # 計算dist(.j)^2
    dij = np.sum(dij2) / (m ** 2)         # 計算dist(..)^2
    b = np.zeros((m, m))
    for i in range(m):
        for j in range(n):
            b[i, j] = (dij2[i, j] - di[i] - dj[j] + dij) / (-2)
    return b

def MDS(data, n=2):
    d = calDist(data, data)
    b = cal_B(d)
    bVals, bVects = np.linalg.eig(b)   # 計算矩陣B的特徵值和特徵向量
    bValInd = np.argsort(bVals)        # 特徵值排序
    bValInd = bValInd[:-(n+1):-1]      # 取前n個
    bValdiag = np.diag(bVals[bValInd])
    bVectSele = bVects[:, bValInd]
    z = np.dot(np.sqrt(bValdiag), bVectSele.T).T    # 得到降維後的樣本矩陣z
    return z

if __name__=="__main__":
    data = loadDataSet("testSet3.txt")
    Z = MDS(data)
    ax = plt.axes(projection="3d")
    ax.scatter3D(data[:, 0], data[:, 1], data[:, 2], edgecolors='r')
    ax.scatter(Z[:, 0], Z[:, 1])
    plt.show()

參考：
機器學習-降維算法(MDS算法)
《機器學習》周志華著