Source code for graspy.embed.lse

# ase.py
# Created by Ben Pedigo on 2018-09-26.
# Email: bpedigo@jhu.edu
import warnings

from .base import BaseEmbed
from .svd import selectSVD
from ..utils import import_graph, to_laplace, get_lcc, is_fully_connected


[docs]class LaplacianSpectralEmbed(BaseEmbed): r""" Class for computing the laplacian spectral embedding of a graph The laplacian spectral embedding (LSE) is a k-dimensional Euclidean representation of the graph based on its Laplacian matrix [1]_. It relies on an SVD to reduce the dimensionality to the specified k, or if k is unspecified, can find a number of dimensions automatically. Parameters ---------- form : {'DAD' (default), 'I-DAD'}, optional Specifies the type of Laplacian normalization to use. n_components : int or None, default = None Desired dimensionality of output data. If "full", n_components must be <= min(X.shape). Otherwise, n_components must be < min(X.shape). If None, then optimal dimensions will be chosen by ``select_dimension`` using ``n_elbows`` argument. n_elbows : int, optional, default: 2 If `n_compoents=None`, then compute the optimal embedding dimension using `select_dimension`. Otherwise, ignored. algorithm : {'full', 'truncated' (default), 'randomized'}, optional SVD solver to use: - 'full' Computes full svd using ``scipy.linalg.svd`` - 'truncated' Computes truncated svd using ``scipy.sparse.linalg.svd`` - 'randomized' Computes randomized svd using ``sklearn.utils.extmath.randomized_svd`` n_iter : int, optional (default = 5) Number of iterations for randomized SVD solver. Not used by 'full' or 'truncated'. The default is larger than the default in randomized_svd to handle sparse matrices that may have large slowly decaying spectrum. Attributes ---------- latent_left_ : array, shape (n_samples, n_components) Estimated left latent positions of the graph. latent_right_ : array, shape (n_samples, n_components), or None Only computed when the graph is directed, or adjacency matrix is assymetric. Estimated right latent positions of the graph. Otherwise, None. singular_values_ : array, shape (n_components) Singular values associated with the latent position matrices. indices_ : array, or None If ``lcc`` is True, these are the indices of the vertices that were kept. See Also -------- graspy.embed.selectSVD graspy.embed.select_dimension graspy.utils.to_laplace Notes ----- The singular value decomposition: .. math:: A = U \Sigma V^T is used to find an orthonormal basis for a matrix, which in our case is the Laplacian matrix of the graph. These basis vectors (in the matrices U or V) are ordered according to the amount of variance they explain in the original matrix. By selecting a subset of these basis vectors (through our choice of dimensionality reduction) we can find a lower dimensional space in which to represent the graph References ---------- .. [1] Sussman, D.L., Tang, M., Fishkind, D.E., Priebe, C.E. "A Consistent Adjacency Spectral Embedding for Stochastic Blockmodel Graphs," Journal of the American Statistical Association, Vol. 107(499), 2012 """ def __init__( self, form="DAD", n_components=None, n_elbows=2, algorithm="randomized", n_iter=5, ): super().__init__( n_components=n_components, n_elbows=n_elbows, algorithm=algorithm, n_iter=n_iter, ) self.form = form
[docs] def fit(self, graph, y=None): """ Fit LSE model to input graph By default, uses the Laplacian normalization of the form: .. math:: L = D^{-1/2} A D^{-1/2} Parameters ---------- graph : array_like or networkx.Graph Input graph to embed. see graphstats.utils.import_graph y : Ignored Returns ------- self : returns an instance of self. """ A = import_graph(graph) L_norm = to_laplace(A, form=self.form) self._reduce_dim(L_norm) return self