Panagiotis A. Traganitis

Sketch and Validate for Big Data Clustering

In response to the need for learning tools tuned to big data analytics, the present paper introduces a framework for efficient clustering of huge sets of (possibly high-dimensional) data. Building on random sampling and consensus (RANSAC) ideas pursued earlier in a different (computer vision) context for robust regression, a suite of novel dimensionality- and set-reduction algorithms is developed. The advocated sketch-and-validate (SkeVa) family includes two algorithms that rely on K-means clustering per iteration on reduced number of dimensions and/or feature vectors: The first operates in a batch fashion, while the second sequential one offers computational efficiency and suitability with streaming modes of operation. For clustering even nonlinearly separable vectors, the SkeVa family offers also a member based on user-selected kernel functions. Further trading off performance for reduced complexity, a fourth member of the SkeVa family is based on a divergence criterion for selecting proper minimal subsets of feature variables and vectors, thus bypassing the need for K-means clustering per iteration. Extensive numerical tests on synthetic and real data sets highlight the potential of the proposed algorithms, and demonstrate their competitive performance relative to state-of-the-art random projection alternatives.

Efficient subspace clustering of large-scale data streams with misses

As the amount of data generated and communicated continuously increases, clustering algorithms that are not able to handle this enormous amount of data have to be redesigned. Recent subspace clustering advances, while powerful, are computationally and memory demanding. The present paper introduces an online algorithm that broadens high-performance batch subspace clustering methods, and is able to perform subspace clustering on data arriving sequentially and possibly with misses. Numerical tests on synthetic and real data demonstrate the potential of the proposed approach.

Sketched Subspace Clustering

The immense amount of daily generated and communicated data presents unique challenges in their processing. Clustering, the grouping of data without the presence of ground-truth labels, is an important tool for drawing inferences from data. Subspace clustering (SC) is a relatively recent method that is able to successfully classify nonlinearly separable data in a multitude of settings. In spite of their high clustering accuracy, SC methods incur prohibitively high computational complexity when processing large volumes of high-dimensional data. Inspired by random sketching approaches for dimensionality reduction, the present paper introduces a randomized scheme for SC, termed Sketch-SC, tailored for large volumes of high-dimensional data. Sketch-SC accelerates the computationally heavy parts of state-of-the-art SC approaches by compressing the data matrix across both dimensions using random projections, thus enabling fast and accurate large-scale SC. Performance analysis as well as extensive numerical tests on real data corroborate the potential of Sketch-SC and its competitive performance relative to state-of-the-art scalable SC approaches.

Topology inference of multilayer networks

Linear structural equation models (SEMs) have been very successful in identifying the topology of complex graphs, such as those representing tactical, social and brain networks. The rising popularity of multilayer networks, presents the need for tools that are tailored to leverage the layered structure of the underlying network. To this end, a multilayer SEM is put forth, to infer causal relations between nodes belonging to multilayer networks. An efficient algorithm based on the alternating direction method of multipliers (ADMM) is developed, and preliminary tests on synthetic as well as real data demonstrate the effectiveness of the proposed approach.

A randomized approach to large-scale subspace clustering

Subspace clustering has become a popular tool for clustering high-dimensional non-linearly separable data. However, state-of-the-art subspace clustering algorithms do not scale well as the number of data increases. The present paper puts forth a novel randomized subspace clustering scheme for high-volume data based on random projections. Performance of the proposed method is assessed via numerical tests, and is compared with state-of-the-art subspace clustering and large-scale subspace clustering methods.

Spectral clustering of large-scale communities via random sketching and validation

In our era of data deluge, clustering algorithms that do not scale well with the dramatically increasing number of data have to be reconsidered. Spectral clustering, while powerful, is computationally and memory demanding, even for high performance computers. Capitalizing on the relationship between spectral clustering and kernel k-means, the present paper introduces a randomized algorithm for identifying communities in large-scale graphs based on a random sketching and validation approach, that enjoys reduced complexity compared to the clairvoyant spectral clustering. Numerical tests on synthetic and real data demonstrate the potential of the proposed approach.

Large-scale subspace clustering using random sketching and validation

While successful in clustering multiple types of high-dimensional data, subspace clustering algorithms do not scale well as the number of data increases. The present paper puts forth a novel randomized subspace clustering algorithm for high-dimensional data based on a random sketching and validation approach. Utilizing a data-driven random sketching technique to estimate the underlying probability density function of the data, the performance of the proposed method is assessed via simulations, and is compared with state-of-the-art sparse subspace clustering methods.

Clustering high-dimensional data via random sampling and consensus

In response to the urgent need for learning tools tuned to big data analytics, the present paper introduces a feature selection approach to efficient clustering of high-dimensional vectors. The resultant method leverages random sampling and consensus (RANSAC) arguments, originally developed for robust regression tasks in computer vision, to yield novel dimensionality reduction schemes. The advocated random sampling and consensus K-means (RSC-Kmeans) algorithm can operate in either batch or sequential modes, with the latter being able to afford lower computational footprint than the former. Extensive numerical tests on synthetic and real datasets highlight the potential of the proposed algorithms, and demonstrate their competitive performance relative to state-of-the-art random projection alternatives.

Big data clustering via random sketching and validation

As the number and dimensionality of data increases, development of new efficient processing tools has become a necessity. The present paper introduces a novel dimensionality reduction approach for fast and efficient clustering of high-dimensional data. The new methods extend random sampling and consensus (RANSAC) arguments, originally developed for robust regression tasks in computer vision, to the dimensionality reduction problem. The advocated random sketching and validation K-means (SkeVa K-means) and Divergence SkeVa algorithms can achieve high performance, with the latter being able to afford lower computational footprint than the former. Extensive numerical tests on synthetic and real datasets highlight the potential of the proposed algorithms, and demonstrate their competitive performance relative to state-of-the-art random projection alternatives.

Network topology inference via elastic net structural equation models

Linear structural equation models (SEMs) have been very successful in identifying the topology of complex graphs, such as those representing social and brain networks. In many cases however, the presence of highly correlated nodes hinders performance of the available SEM estimators that rely on the least-absolute shrinkage and selection operator (LASSO). To this end, an elastic net based SEM is put forth, to infer causal relations between nodes belonging to networks, in the presence of highly correlated data. An efficient algorithm based on the alternating direction method of multipliers (ADMM) is developed, and preliminary tests on synthetic as well as real data demonstrate the effectiveness of the proposed approach.