12,572 research outputs found
Tensor Spectral Clustering for Partitioning Higher-order Network Structures
Spectral graph theory-based methods represent an important class of tools for
studying the structure of networks. Spectral methods are based on a first-order
Markov chain derived from a random walk on the graph and thus they cannot take
advantage of important higher-order network substructures such as triangles,
cycles, and feed-forward loops. Here we propose a Tensor Spectral Clustering
(TSC) algorithm that allows for modeling higher-order network structures in a
graph partitioning framework. Our TSC algorithm allows the user to specify
which higher-order network structures (cycles, feed-forward loops, etc.) should
be preserved by the network clustering. Higher-order network structures of
interest are represented using a tensor, which we then partition by developing
a multilinear spectral method. Our framework can be applied to discovering
layered flows in networks as well as graph anomaly detection, which we
illustrate on synthetic networks. In directed networks, a higher-order
structure of particular interest is the directed 3-cycle, which captures
feedback loops in networks. We demonstrate that our TSC algorithm produces
large partitions that cut fewer directed 3-cycles than standard spectral
clustering algorithms.Comment: SDM 201
Multilinear Subspace Clustering
In this paper we present a new model and an algorithm for unsupervised
clustering of 2-D data such as images. We assume that the data comes from a
union of multilinear subspaces (UOMS) model, which is a specific structured
case of the much studied union of subspaces (UOS) model. For segmentation under
this model, we develop Multilinear Subspace Clustering (MSC) algorithm and
evaluate its performance on the YaleB and Olivietti image data sets. We show
that MSC is highly competitive with existing algorithms employing the UOS model
in terms of clustering performance while enjoying improvement in computational
complexity
Clustering Patients with Tensor Decomposition
In this paper we present a method for the unsupervised clustering of
high-dimensional binary data, with a special focus on electronic healthcare
records. We present a robust and efficient heuristic to face this problem using
tensor decomposition. We present the reasons why this approach is preferable
for tasks such as clustering patient records, to more commonly used
distance-based methods. We run the algorithm on two datasets of healthcare
records, obtaining clinically meaningful results.Comment: Presented at 2017 Machine Learning for Healthcare Conference (MLHC
2017). Boston, M
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