Gunjan Gupta

Robust one-class clustering using hybrid global and local search

Unsupervised learning methods often involve summarizing the data using a small number of parameters. In certain domains, only a small subset of the available data is relevant for the problem. One-Class Classification or One-Class Clustering attempts to find a useful subset by locating a dense region in the data. In particular, a recently proposed algorithm called One-Class Information Ball (OC-IB) shows the advantage of modeling a small set of highly coherent points as opposed to pruning outliers. We present several modifications to OC-IB and integrate it with a global search that results in several improvements such as deterministic results, optimality guarantees, control over cluster size and extension to other cost functions. Empirical studies yield significantly better results on various real and artificial data.

Automated Hierarchical Density Shaving: A Robust Automated Clustering and Visualization Framework for Large Biological Data Sets

A key application of clustering data obtained from sources such as microarrays, protein mass spectroscopy, and phylogenetic profiles is the detection of functionally related genes. Typically, only a small number of functionally related genes cluster into one or more groups, and the rest need to be ignored. For such situations, we present Automated Hierarchical Density Shaving (Auto-HDS), a framework that consists of a fast hierarchical density-based clustering algorithm and an unsupervised model selection strategy. Auto-HDS can automatically select clusters of different densities, present them in a compact hierarchy, and rank individual clusters using an innovative stability criteria. Our framework also provides a simple yet powerful 2D visualization of the hierarchy of clusters that is useful for further interactive exploration. We present results on Gasch and Lee microarray data sets to show the effectiveness of our methods. Additional results on other biological data are included in the supplemental material.

Bregman Bubble Clustering: A Robust, Scalable Framework for Locating Multiple, Dense Regions in Data

In traditional clustering, every data point is assigned to at least one cluster. On the other extreme, one class clustering algorithms proposed recently identify a single dense cluster and consider the rest of the data as irrelevant. However, in many problems, the relevant data forms multiple natural clusters. In this paper, we introduce the notion of Bregman bubbles and propose Bregman bubble clustering (BBC) that seeks k dense Bregman bubbles in the data. We also present a corresponding generative model, soft BBC, and show several connections with Bregman clustering, and with a one class clustering algorithm. Empirical results on various datasets show the effectiveness of our method.

Value-balanced agglomerative connectivity clustering

In this paper we propose a new clustering framework for transactional data-sets involving large numbers of customers and products. Such transactional data pose particular issues such as very high dimensionality (greater than 10,000), and sparse categorical entries, that have been dealt with more effectively using a graph-based approach to clustering such as ROCK. But large transactional data raises certain other issues such as how to compare diverse products (e.g. milk vs. cars) cluster balancing and outlier removal, that need to be addressed. We first propose a new similarity measure that takes the value of the goods purchased into account, and form a value-based graph representation based on this similarity measure. A novel value-based balancing criterion that allows the user to control the balancing of clusters, is then defined. This balancing criterion is integrated with a value-based goodness measure for merging two clusters in an agglomerative clustering routine. Since graph-based clustering algorithms are very sensitive to outliers, we also propose a fast, effective and simple outlier detection and removal method based on under-clustering or over- partitioning. The performance of the proposed clustering framework is compared with leading graph-theoretic approaches such as ROCK and METIS.

Bregman bubble clustering: A robust framework for mining dense clusters

In classical clustering, each data point is assigned to at least one cluster. However, in many applications only a small subset of the available data is relevant for the problem and the rest needs to be ignored in order to obtain good clusters. Certain nonparametric density-based clustering methods find the most relevant data as multiple dense regions, but such methods are generally limited to low-dimensional data and do not scale well to large, high-dimensional datasets. Also, they use a specific notion of “distance”, typically Euclidean or Mahalanobis distance, which further limits their applicability. On the other hand, the recent One Class Information Bottleneck (OC-IB) method is fast and works on a large class of distortion measures known as Bregman Divergences, but can only find a single dense region. This article presents a broad framework for finding k dense clusters while ignoring the rest of the data. It includes a seeding algorithm that can automatically determine a suitable value for k. When k is forced to 1, our method gives rise to an improved version of OC-IB with optimality guarantees. We provide a generative model that yields the proposed iterative algorithm for finding k dense regions as a special case. Our analysis reveals an interesting and novel connection between the problem of finding dense regions and exponential mixture models; a hard model corresponding to k exponential mixtures with a uniform background results in a set of k dense clusters. The proposed method describes a highly scalable algorithm for finding multiple dense regions that works with any Bregman Divergence, thus extending density based clustering to a variety of non-Euclidean problems not addressable by earlier methods. We present empirical results on three artificial, two microarray and one text dataset to show the relevance and effectiveness of our methods.

Hierarchical Density Shaving: A clustering and visualization framework for large biological datasets

In many clustering applications for bioinformatics, only part of the data clusters into one or more groups while the rest needs to be pruned. For such situations, we present hierarchical density shaving (HDS), a framework that consists of a fast, hierarchical, density-based clustering algorithm. Our framework also provides a simple yet powerful 2D visualization of the hierarchy of clusters that can be very useful for further exploration. We present results to show the effectiveness of our methods

Distributed, Scalable Clustering for Detecting Halos in Terascale Astronomy Datasets

Terascale astronomical datasets have the potential to provide unprecedented insights into the origins of our universe. However, automated techniques for determining regions of interest are a must if domain experts are to cope with the intractable amounts of simulation data. This paper addresses the important problem of locating and tracking high density regions in space that generally correspond to halos and sub-halos and host galaxies. A density based, mode following clustering method called Automated Hierarchical Density Shaving (Auto-HDS) is adapted for this application. Auto-HDS can detect clusters of different densities while discarding the vast majority of background data. Two alternative parallel implementations of the algorithm, based respectively on the dataflow computational model and on Hadoop/ MapReduce functional programming constructs, are realized and compared. Based on runtime performance, scalability across compute cores and across increasing data volumes, we demonstrate the benefits of fine grain parallelism. The proposed distributed and multithreaded AutoHDS clustering algorithm is shown to produce high quality clusters, be computationally efficient, and scalable from 1 through 1024 compute-cores.