65 lines
1.8 KiB
Python
65 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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from . import _ncut_cy
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def DW_matrices(graph):
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"""Returns the diagonal and weight matrices 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
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all edges incident on `i`. All other entries 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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# sparse.eighsh is most efficient with CSC-formatted input
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W = nx.to_scipy_sparse_matrix(graph, format='csc')
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entries = W.sum(axis=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(cut, 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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cut : ndarray
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The mask for the nodes in the graph. Nodes corresponding 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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References
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----------
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.. [1] Normalized Cuts and Image Segmentation, Jianbo Shi and
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Jitendra Malik, IEEE Transactions on Pattern Analysis and Machine
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Intelligence, Page 889, Equation 2.
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"""
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cut = np.array(cut)
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cut_cost = _ncut_cy.cut_cost(cut, W)
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# D has elements only along the diagonal, one per node, so we can directly
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# index the data attribute with cut.
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assoc_a = D.data[cut].sum()
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assoc_b = D.data[~cut].sum()
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return (cut_cost / assoc_a) + (cut_cost / assoc_b)
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