97,434 research outputs found
Temporal Ordered Clustering in Dynamic Networks: Unsupervised and Semi-supervised Learning Algorithms
In temporal ordered clustering, given a single snapshot of a dynamic network
in which nodes arrive at distinct time instants, we aim at partitioning its
nodes into ordered clusters such that for , nodes in cluster arrived
before nodes in cluster , with being a data-driven parameter
and not known upfront. Such a problem is of considerable significance in many
applications ranging from tracking the expansion of fake news to mapping the
spread of information. We first formulate our problem for a general dynamic
graph, and propose an integer programming framework that finds the optimal
clustering, represented as a strict partial order set, achieving the best
precision (i.e., fraction of successfully ordered node pairs) for a fixed
density (i.e., fraction of comparable node pairs). We then develop a sequential
importance procedure and design unsupervised and semi-supervised algorithms to
find temporal ordered clusters that efficiently approximate the optimal
solution. To illustrate the techniques, we apply our methods to the vertex
copying (duplication-divergence) model which exhibits some edge-case challenges
in inferring the clusters as compared to other network models. Finally, we
validate the performance of the proposed algorithms on synthetic and real-world
networks.Comment: 14 pages, 9 figures, and 3 tables. This version is submitted to a
journal. A shorter version of this work is published in the proceedings of
IEEE International Symposium on Information Theory (ISIT), 2020. The first
two authors contributed equall
Semi-Supervised Learning of Hidden Markov Models via a Homotopy Method
Hidden Markov model (HMM) classifier design is considered for analysis of sequential data,
incorporating both labeled and unlabeled data for training; the balance between labeled and unlabeled
data is controlled by an allocation parameter lambda in [0, 1), where lambda = 0 corresponds to purely supervised
HMM learning (based only on the labeled data) and lambda = 1 corresponds to unsupervised HMM-based
clustering (based only on the unlabeled data). The associated estimation problem can typically be reduced
to solving a set of fixed point equations in the form of a “natural-parameter homotopy”. This paper
applies a homotopy method to track a continuous path of solutions, starting from a local supervised
solution (lambda = 0) to a local unsupervised solution (lambda = 1). The homotopy method is guaranteed to track
with probability one from lambda = 0 to lambda = 1 if the lambda = 0 solution is unique; this condition is not satisfied
for the HMM, since the maximum likelihood supervised solution (lambda = 0) is characterized by many local
optimal solutions. A modified form of the homotopy map for HMMs assures a track from lambda = 0 to
lambda = 1. Following this track leads to a formulation for selecting lambda in [0, 1) for a semi-supervised solution,
and it also provides a tool for selection from among multiple (local optimal) supervised solutions. The
results of applying the proposed method to measured and synthetic sequential data verify its robustness
and feasibility compared to the conventional EM approach for semi-supervised HMM training
Natural clustering: the modularity approach
We show that modularity, a quantity introduced in the study of networked
systems, can be generalized and used in the clustering problem as an indicator
for the quality of the solution. The introduction of this measure arises very
naturally in the case of clustering algorithms that are rooted in Statistical
Mechanics and use the analogy with a physical system.Comment: 11 pages, 5 figure enlarged versio
Solving k-center Clustering (with Outliers) in MapReduce and Streaming, almost as Accurately as Sequentially.
Center-based clustering is a fundamental primitive for data analysis and becomes very challenging for large datasets. In this paper, we focus on the popular k-center variant which, given a set S of points from some metric space and a parameter k0, the algorithms yield solutions whose approximation ratios are a mere additive term \u3f5 away from those achievable by the best known polynomial-time sequential algorithms, a result that substantially improves upon the state of the art. Our algorithms are rather simple and adapt to the intrinsic complexity of the dataset, captured by the doubling dimension D of the metric space. Specifically, our analysis shows that the algorithms become very space-efficient for the important case of small (constant) D. These theoretical results are complemented with a set of experiments on real-world and synthetic datasets of up to over a billion points, which show that our algorithms yield better quality solutions over the state of the art while featuring excellent scalability, and that they also lend themselves to sequential implementations much faster than existing ones
Bayesian Agglomerative Clustering with Coalescents
We introduce a new Bayesian model for hierarchical clustering based on a
prior over trees called Kingman's coalescent. We develop novel greedy and
sequential Monte Carlo inferences which operate in a bottom-up agglomerative
fashion. We show experimentally the superiority of our algorithms over others,
and demonstrate our approach in document clustering and phylolinguistics.Comment: NIPS 200
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