随机行走获得不良结果 [英] Get bad result for random walk
问题描述
我想实现随机游走并计算稳态.
I want to implement random walk and compute the steady state.
假设我的图形如下图所示:
Suppose my graph is given as in the following image:
上面的图在文件中定义如下:
The graph above is defined in a file as follows:
1 2 0.9
1 3 0.1
2 1 0.8
2 2 0.1
2 4 0.1
etc
要阅读并构建此图,我使用以下方法:
To read and build this graph, I use the following method:
def _build_og(self, original_ppi):
""" Build the original graph, without any nodes removed. """
try:
graph_fp = open(original_ppi, 'r')
except IOError:
sys.exit("Could not open file: {}".format(original_ppi))
G = nx.DiGraph()
edge_list = []
# parse network input
for line in graph_fp.readlines():
split_line = line.rstrip().split('\t')
# assume input graph is a simple edgelist with weights
edge_list.append((split_line[0], split_line[1], float(split_line[2])))
G.add_weighted_edges_from(edge_list)
graph_fp.close()
print edge_list
return G
在上面的函数中,我需要将图形定义为DiGraph还是simpy Graph?
In the function above do I need to define the graph as DiGraph or simpy Graph?
我们构建过渡矩阵如下:
We build the transition matrix as following:
def _build_matrices(self, original_ppi, low_list, remove_nodes):
""" Build column-normalized adjacency matrix for each graph.
NOTE: these are column-normalized adjacency matrices (not nx
graphs), used to compute each p-vector
"""
original_graph = self._build_og(original_ppi)
self.OG = original_graph
og_not_normalized = nx.to_numpy_matrix(original_graph)
self.og_matrix = self._normalize_cols(og_not_normalized)
然后我使用:
def _normalize_cols(self, matrix):
""" Normalize the columns of the adjacency matrix """
return normalize(matrix, norm='l1', axis=0)
现在要模拟我们定义的随机游走:
now to simulate the random walk we define :
def run_exp(self, source):
CONV_THRESHOLD = 0.000001
# set up the starting probability vector
p_0 = self._set_up_p0(source)
diff_norm = 1
# this needs to be a deep copy, since we're reusing p_0 later
p_t = np.copy(p_0)
while (diff_norm > CONV_THRESHOLD):
# first, calculate p^(t + 1) from p^(t)
p_t_1 = self._calculate_next_p(p_t, p_0)
# calculate L1 norm of difference between p^(t + 1) and p^(t),
# for checking the convergence condition
diff_norm = np.linalg.norm(np.subtract(p_t_1, p_t), 1)
# then, set p^(t) = p^(t + 1), and loop again if necessary
# no deep copy necessary here, we're just renaming p
p_t = p_t_1
我们使用以下方法定义初始状态(p_0):
We define the initial state (p_0) by using the following method:
def _set_up_p0(self, source):
""" Set up and return the 0th probability vector. """
p_0 = [0] * self.OG.number_of_nodes()
# convert self.OG.number_of_nodes() to list
l = list(self.OG.nodes())
#nx.draw(self.OG, with_labels=True)
#plt.show()
for source_id in source:
try:
# matrix columns are in the same order as nodes in original nx
# graph, so we can get the index of the source node from the OG
source_index = l.index(source_id)
p_0[source_index] = 1 / float(len(source))
except ValueError:
sys.exit("Source node {} is not in original graph. Source: {}. Exiting.".format(source_id, source))
return np.array(p_0)
要生成下一个状态,我们使用以下函数
To generate the next state, we use the following function
和功率迭代策略:
def _calculate_next_p(self, p_t, p_0):
""" Calculate the next probability vector. """
print 'p_0\t{}'.format(p_0)
print 'p_t\t{}'.format(p_t)
epsilon = np.squeeze(np.asarray(np.dot(self.og_matrix, p_t)))
print 'epsilon\t{}'.format(epsilon)
print 10*"*"
return np.array(epsilon)
假设随机游走可以从任何节点(1、2、3或4)开始.
Suppose the random walk can start from any node (1, 2, 3 or 4).
运行代码时,我得到以下结果:
When runing the code i get the following result:
2 0.32
3 0.31
1 0.25
4 0.11
结果必须是:
(0.28, 0.30, 0.04, 0.38).
那么有人可以帮助我发现我的错误在哪里吗?
So can someone help me to detect where my mistake is?
我不知道问题是否出在我的转换矩阵中.
I don't know if the problem is in my transition matrix.
推荐答案
这里是矩阵(应该是过渡矩阵从左边乘以状态向量,这是一个左随机矩阵 >,其中列加起来为1,(i, j)
项是从j
到i
的概率.
Here is what the matrix should be (given than your transition matrix multiplies the state vector from the left, it is a left stochastic matrix, where the columns add up to 1, and the (i, j)
entry is the probability of going from j
to i
).
import numpy as np
transition = np.array([[0, 0.8, 0, 0.1], [0.9, 0.1, 0.5, 0], [0.1, 0, 0.3, 0], [0, 0.1, 0.2, 0.9]])
state = np.array([1, 0, 0, 0]) # could be any other initial position
diff = tol = 0.001
while diff >= tol:
next_state = transition.dot(state)
diff = np.linalg.norm(next_state - state, ord=np.inf)
state = next_state
print(np.around(state, 3))
这将打印[0.279 0.302 0.04 0.378]
.
我无法确定您是错误地加载数据还是其他原因. 列归一化"步骤是一个警告信号:如果给定的转换概率不等于1,则应报告错误数据,而不是对列进行归一化.而且我不知道为什么当数据已经以矩阵形式呈现时,为什么根本不使用NetworkX:给定的表可以读为
I can't tell if you are loading the data incorrectly, or something else. The step with "column normalization" is a warning sign: if the given transition probabilities don't add up to 1, you should report bad data, not normalize the columns. And I don't know why you use NetworkX at all when the data is already presented as a matrix: the table you are given can be read as
column row entry
这个矩阵是计算所需要的.
and this matrix is what is needed for calculations.
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