python - Python 中的马尔可夫聚类

Question

正如标题所说，我正在尝试让马尔可夫聚类算法在 Python 中工作，即 Python 3.7

不幸的是，它没有做任何事情，而且它让我在试图修复它时遇到困难。

编辑:首先，我对主代码进行了调整，使每列的总和为 100，即使它不是完全平衡的。我将尝试在最终答案中说明这一点。

需要明确的是，最大的问题是数字逐渐失控，变成了 5.56268465e-309 这样容易理解的数字，我不知道如何将其转换成可以理解的数字。

这是目前的代码:

import numpy as np
import math
## How far you'd like your random-walkers to go (bigger number -> more walking)
EXPANSION_POWER = 2
## How tightly clustered you'd like your final picture to be (bigger number -> more clusters)
INFLATION_POWER = 2
ITERATION_COUNT = 10
def normalize(matrix):
    return matrix/np.sum(matrix, axis=0)

def expand(matrix, power):
    return np.linalg.matrix_power(matrix, power)

def inflate(matrix, power):
    for entry in np.nditer(transition_matrix, op_flags=['readwrite']):
        entry[...] = math.pow(entry, power)
    return matrix

def run(matrix):
    #np.fill_diagonal(matrix, 1)
    #print(matrix)
    matrix = normalize(matrix)
    print(matrix)
    for _ in range(ITERATION_COUNT):
        matrix = normalize(inflate(expand(matrix, EXPANSION_POWER), INFLATION_POWER))
    return matrix

transition_matrix = np.array ([[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
                                [0.5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
                                [0.5,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
                                [0,0,0.34,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
                                [0,0,0.33,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
                                [0,0,0.33,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
                                [0,0,0,0.34,0,0,0,0,0,0,0,0,0,0,0,0,0.125,0],
                                [0,0,0,0.33,0,0,0.5,0,0,0,0,0,0,0,0,0,0.125,1],
                                [0,0,0,0.33,0,0,0.5,1,1,0,0,0,0,0,0,0,0.125,0],
                                [0,0,0,0,0.166,0,0,0,0,0,0,0,0,0,0,0,0.125,0],
                                [0,0,0,0,0.166,0,0,0,0,0.2,0,0,0,0,0,0,0.125,0],
                                [0,0,0,0,0.167,0,0,0,0,0.2,0.25,0,0,0,0,0,0.125,0],
                                [0,0,0,0,0.167,0,0,0,0,0.2,0.25,0.5,0,0,0,0,0,0],
                                [0,0,0,0,0.167,0,0,0,0,0.2,0.25,0.5,0,1,0,0,0.125,0],
                                [0,0,0,0,0.167,0,0,0,0,0.2,0.25,0,1,0,1,0,0.125,0],
                                [0,0,0,0,0,0.34,0,0,0,0,0,0,0,0,0,0,0,0],
                                [0,0,0,0,0,0.33,0,0,0,0,0,0,0,0,0,0.5,0,0],
                                [0,0,0,0,0,0.33,0,0,0,0,0,0,0,0,0,0.5,0,0]])
run(transition_matrix)
print(transition_matrix)

这是 uni 作业的一部分 - 我需要对这个数组进行加权和未加权处理(尽管加权部分可以等到我让这该死的东西开始工作)有什么提示或建议吗？

Answer 1

您的转换矩阵无效。

>>> transition_matrix.sum(axis=0)
>>> matrix([[1.  , 1.  , 0.99, 0.99, 0.96, 0.99, 1.  , 1.  , 0.  , 1.  ,
         1.  , 1.  , 1.  , 0.  , 0.  , 1.  , 0.88, 1.  ]])

不仅有些列的总和不为 1，有些列的总和为 0。

这意味着当您尝试对矩阵进行归一化时，您最终会得到 nan，因为您除以 0。

最后，您使用 Numpy 矩阵而不是仅使用 Numpy 数组(这是此类数据的推荐容器)是否有原因？因为使用 Numpy 数组会简化一些操作，例如将每个条目提高一次幂。此外，Numpy 矩阵和 Numpy 数组之间存在一些差异，这可能会导致细微的错误。