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75 lines
1.8 KiB
Python
75 lines
1.8 KiB
Python
import networkx as nx
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import numpy as np
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from scipy import sparse
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def DW_matrix(graph):
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"""Returns the diagonal and weight matrix of a graph.
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Parameters
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----------
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graph : RAG
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A Region Adjacency Graph.
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Returns
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-------
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D : csc_matrix
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The diagonal matrix of the graph. `D[i,i]` is the sum of weights of all
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edges incident on `i`. All other enteries are `0`.
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W : csc_matrix
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The weight matrix of the graph. `W[i,j]` is the weight of the edge
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joining `i` to `j`.
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"""
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#Cause sparse.eigsh prefers CSC format
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W = nx.to_scipy_sparse_matrix(graph, format='csc')
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entries = W.sum(0)
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D = sparse.dia_matrix((entries, 0), shape=W.shape).tocsc()
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return D, W
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def ncut_cost(mask, D, W):
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"""Returns the N-cut cost of a bi-partition of a graph.
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Parameters
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----------
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mask : ndarray
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The mask for the nodes in the graph. Nodes corrsesponding to a `True`
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value are in one set.
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D : csc_matrix
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The diagonal matrix of the graph.
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W : csc_matrix
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The weight matrix of the graph.
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Returns
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-------
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cost : float
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The cost of performing the N-cut.
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"""
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mask = np.array(mask)
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mask_list = [np.logical_xor(mask[i], mask) for i in range(mask.shape[0])]
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mask_array = np.array(mask_list)
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cut = float(W[mask_array].sum() / 2.0)
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assoc_a = D.data[mask].sum()
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assoc_b = D.data[np.logical_not(mask)].sum()
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return (cut / assoc_a) + (cut / assoc_b)
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def normalize(a):
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"""Normalize values in an array between `0` and `1`.
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Parameters
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----------
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a : ndarray
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The array to be normalized.
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Returns
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-------
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out : ndarray
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The normalized array.
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"""
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mi = a.min()
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mx = a.max()
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return (a - mi) / (mx - mi)
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