MDS算法python实现

import numpy as np

def MDS(D,d):
    D = np.asarray(D)
    DSquare = D ** 2
    totalMean = np.mean(DSquare)
    columnMean = np.mean(DSquare, axis = 0)
    rowMean = np.mean(DSquare, axis = 1)
    B = np.zeros(DSquare.shape)
    for i in range(B.shape[0]):
        for j in range(B.shape[1]):
            B[i][j] = -0.5 * (DSquare[i][j] - rowMean[i] - columnMean[j] + totalMean)
    eigVal, eigVec = np.linalg.eig(B)#求特征值及特征向量
    #对特征值进行排序，得到排序索引
    eigValSorted_indices = np.argsort(eigVal)
    #提取d个最大特征向量
    topd_eigVec = eigVec[:,eigValSorted_indices[:-d-1:-1]] #-d-1前加:才能向左切
    X = np.dot(topd_eigVec, np.sqrt(np.diag(eigVal[:-d-1:-1])))
    return X


D = [[0,587,1212,701,1936,604,748,2139,2182,543],
[587,0,920,940,1745,1188,713,1858,1737,597],
[1212,920,0,879,831,1726,1631,949,1021,1494],
[701,940,879,0,1374,968,1420,1645,1891,1220],
[1936,1745,831,1374,0,2339,2451,347,959,2300],
[604,1188,1726,968,2339,0,1092,2594,2734,923],
[748,713,1631,1420,2451,1092,0,2571,2408,205],
[2139,1858,949,1645,347,2594,2571,0,678,2442],
[2182,1737,1021,1891,959,2734,2408,678,0,2329],
[543,597,1494,1220,2300,923,205,2442,2329,0]]

X = MDS(D,2)
print(X)

参考：https://blog.csdn.net/Dark_Scope/article/details/53229427