Anup Bhattacharya

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The k-means++ seeding algorithm is one of the most popular algorithms that is used for finding the initial k centers when using the k-means heuristic. The algorithm is a simple sampling procedure and can be described as follows: Pick the first center randomly from the given points. For i > 1, pick a point to be the i th center with probability proportional(More)
Space efficient algorithms play a central role in dealing with large amount of data. In such settings, one would like to analyse the large data using small amount of " working space ". One of the key steps in many algorithms for analysing large data is to maintain a (or a small number) random sample from the data points. In this paper, we consider two space(More)
Eta pairing on a supersingular elliptic curve over the binary field F 2 1223 used to offer 128-bit security, and has been studied extensively for efficient implementations. In this paper, we report our GPU-based implementations of this algorithm on an NVIDIA Tesla C2050 platform. We propose efficient parallel implementation strategies for multiplication,(More)
The classical center based clustering problems such as k-means/median/center assume that the optimal clusters satisfy the locality property that the points in the same cluster are close to each other. A number of clustering problems arise in machine learning where the optimal clusters do not follow such a locality property. For instance, consider the(More)
Privacy and authenticity are two essential security attributes of secure Vehicle-to-Vehicle communications. Pseudonymous Public Key Infrastructure (PPKI), an extension of standard PKI, has been proposed to achieve these security attributes. In Pseudonymous PKI, a user needs certificates or pseudonyms periodically from the Certificate Authority (CA) to(More)
In this work, we study the k-means cost function. The (Euclidean) k-means problem can be described as follows: given a dataset X ⊆ R d and a positive integer k, find a set of k centers C ⊆ R d such that Φ(C, X) def = x∈X minc∈C ||x − c|| 2 is minimized. Let ∆ k (X) def = min C⊆R d Φ(C, X) denote the cost of the optimal k-means solution. It is simple to(More)
Ashtiani et al. proposed a Semi-Supervised Active Clustering framework (SSAC), where the learner is allowed to make adaptive queries to a domain expert. The queries are of the kind " do two given points belong to the same optimal cluster? " , and the answers to these queries are assumed to be consistent with a unique optimal solution. There are many(More)
Eta pairing on supersingular elliptic curves defined over fields of characteristics two and three is a popular and practical variant of pairing used in many cryptographic protocols. In this paper, we study SIMD-based implementations of eta pairing over these fields. Our implementations use standard SIMD-based vectorization techniques which we call(More)
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