• An Algorithmic Characterization Of Polynomial Functions Over Zpn 

      Guha, Ashwin (2014-07-04)
      The problem of polynomial representability of functions is central to many branches of mathematics. If the underlying set is a finite field, every function can be represented as a polynomial. In this thesis we consider ...
    • Consistency of Spectral Algorithms for Hypergraphs under Planted Partition Model 

      Ghoshdastidar, Debarghya (2018-01-01)
      Hypergraph partitioning lies at the heart of a number of problems in machine learning as well as other engineering disciplines. While partitioning uniform hypergraphs is often required in computer vision problems that ...
    • Deep Learning Models for Few-shot and Metric Learning 

      Mehrotra, Akshay
      Deep neural network-based models have achieved unprecedented performance levels over many tasks in the traditional supervised setting and scale well with large quantities of data. On the other hand, improving performance ...
    • Deep Learning with Minimal Supervision 

      Pandey, Gaurav
      Abstract In recent years, deep neural networks have achieved extraordinary performance on supervised learning tasks. Convolutional neural networks (CNN) have vastly improved the state of the art for most computer vision ...
    • A GPU Accelerated Tensor Spectral Method for Subspace Clustering 

      Pai, Nithish (2017-11-30)
      In this thesis we consider the problem of clustering the data lying in a union of subspaces using spectral methods. Though the data generated may have high dimensionality, in many of the applications, such as motion ...
    • Grobuer Basis Algorithms for Polynomial Ideal Theory over Noetherian Commutative Rings 

      Francis, Maria (2018-05-14)
      One of the fundamental problems in commutative algebra and algebraic geometry is to understand the nature of the solution space of a system of multivariate polynomial equations over a field k, such as real or complex ...
    • Module Grobner Bases Over Fields With Valuation 

      Sen, Aritra (2017-07-12)
      Tropical geometry is an area of mathematics that interfaces algebraic geometry and combinatorics. The main object of study in tropical geometry is the tropical variety, which is the combinatorial counterpart of a classical ...
    • Multimodal Deep Learning for Multi-Label Classification and Ranking Problems 

      Dubey, Abhishek (2018-06-11)
      In recent years, deep neural network models have shown to outperform many state of the art algorithms. The reason for this is, unsupervised pretraining with multi-layered deep neural networks have shown to learn better ...
    • On The Complexity Of Grobner Basis And Border Basis Detection 

      Prabhanjan, V A (2013-06-14)
      The theory of Grobner bases has garnered the interests of a large number of researchers in computational algebra due to its applications not only in mathematics but also in areas like control systems, robotics, cryptography ...