arXiv subjects

Adway Mitra

Publications and source records attributed to Adway Mitra.

21 records · Page 2Linked to original sources

arXiv2015

Exploring Bayesian Models for Multi-level Clustering of Hierarchically Grouped Sequential Data

A wide range of Bayesian models have been proposed for data that is divided hierarchically into groups. These models aim to cluster the data at different levels of grouping, by assigning a mixture component to each datapoint, and a mixture distribution to each group. Multi-level clustering is facilitated by the sharing of these components and distributions by the groups. In this paper, we introduce the concept of Degree of Sharing (DoS) for the mixture components and distributions, with an aim to analyze and classify various existing models. Next we introduce a generalized hierarchical Bayesian model, of which the existing models can be shown to be special cases. Unlike most of these models, our model takes into account the sequential nature of the data, and various other temporal structures at different levels while assigning mixture components and distributions. We show one specialization of this model aimed at hierarchical segmentation of news transcripts, and present a Gibbs Sampling based inference algorithm for it. We also show experimentally that the proposed model outperforms existing models for the same task.

cs.LG↗

arXiv2015

Temporally Coherent Bayesian Models for Entity Discovery in Videos by Tracklet Clustering

A video can be represented as a sequence of tracklets, each spanning 10-20 frames, and associated with one entity (eg. a person). The task of \emph{Entity Discovery} in videos can be naturally posed as tracklet clustering. We approach this task by leveraging \emph{Temporal Coherence}(TC): the fundamental property of videos that each tracklet is likely to be associated with the same entity as its temporal neighbors. Our major contributions are the first Bayesian nonparametric models for TC at tracklet-level. We extend Chinese Restaurant Process (CRP) to propose TC-CRP, and further to Temporally Coherent Chinese Restaurant Franchise (TC-CRF) to jointly model short temporal segments. On the task of discovering persons in TV serial videos without meta-data like scripts, these methods show considerable improvement in cluster purity and person coverage compared to state-of-the-art approaches to tracklet clustering. We represent entities with mixture components, and tracklets with vectors of very generic features, which can work for any type of entity (not necessarily person). The proposed methods can perform online tracklet clustering on streaming videos with little performance deterioration unlike existing approaches, and can automatically reject tracklets resulting from false detections. Finally we discuss entity-driven video summarization- where some temporal segments of the video are selected automatically based on the discovered entities.

cs.CV↗

arXiv2009

Some Conjectures on the Number of Primes in Certain Intervals

In this paper, we make some conjectures on prime numbers that are sharper than those found in the current literature. First we describe our studies on Legendre's Conjecture which is still unsolved. Next, we show that Brocard's Conjecture can be proved assuming our improved version of Legendre's Conjecture. Finally, we sharpen the Bertrand's Postulate for prime numbers. Our results are backed by extensive empirical investigation.

math.NT↗