15,451 research outputs found
Laplacian Mixture Modeling for Network Analysis and Unsupervised Learning on Graphs
Laplacian mixture models identify overlapping regions of influence in
unlabeled graph and network data in a scalable and computationally efficient
way, yielding useful low-dimensional representations. By combining Laplacian
eigenspace and finite mixture modeling methods, they provide probabilistic or
fuzzy dimensionality reductions or domain decompositions for a variety of input
data types, including mixture distributions, feature vectors, and graphs or
networks. Provable optimal recovery using the algorithm is analytically shown
for a nontrivial class of cluster graphs. Heuristic approximations for scalable
high-performance implementations are described and empirically tested.
Connections to PageRank and community detection in network analysis demonstrate
the wide applicability of this approach. The origins of fuzzy spectral methods,
beginning with generalized heat or diffusion equations in physics, are reviewed
and summarized. Comparisons to other dimensionality reduction and clustering
methods for challenging unsupervised machine learning problems are also
discussed.Comment: 13 figures, 35 reference
Batch kernel SOM and related Laplacian methods for social network analysis
Large graphs are natural mathematical models for describing the structure of
the data in a wide variety of fields, such as web mining, social networks,
information retrieval, biological networks, etc. For all these applications,
automatic tools are required to get a synthetic view of the graph and to reach
a good understanding of the underlying problem. In particular, discovering
groups of tightly connected vertices and understanding the relations between
those groups is very important in practice. This paper shows how a kernel
version of the batch Self Organizing Map can be used to achieve these goals via
kernels derived from the Laplacian matrix of the graph, especially when it is
used in conjunction with more classical methods based on the spectral analysis
of the graph. The proposed method is used to explore the structure of a
medieval social network modeled through a weighted graph that has been directly
built from a large corpus of agrarian contracts
Optimal Clustering Framework for Hyperspectral Band Selection
Band selection, by choosing a set of representative bands in hyperspectral
image (HSI), is an effective method to reduce the redundant information without
compromising the original contents. Recently, various unsupervised band
selection methods have been proposed, but most of them are based on
approximation algorithms which can only obtain suboptimal solutions toward a
specific objective function. This paper focuses on clustering-based band
selection, and proposes a new framework to solve the above dilemma, claiming
the following contributions: 1) An optimal clustering framework (OCF), which
can obtain the optimal clustering result for a particular form of objective
function under a reasonable constraint. 2) A rank on clusters strategy (RCS),
which provides an effective criterion to select bands on existing clustering
structure. 3) An automatic method to determine the number of the required
bands, which can better evaluate the distinctive information produced by
certain number of bands. In experiments, the proposed algorithm is compared to
some state-of-the-art competitors. According to the experimental results, the
proposed algorithm is robust and significantly outperform the other methods on
various data sets
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