Search Results for author: Baba C. Vemuri

Found 24 papers, 5 papers with code

Nested Hyperbolic Spaces for Dimensionality Reduction and Hyperbolic NN Design

no code implementations3 Dec 2021 Xiran Fan, Chun-Hao Yang, Baba C. Vemuri

In this paper, we present a novel fully hyperbolic neural network which uses the concept of projections (embeddings) followed by an intrinsic aggregation and a nonlinearity all within the hyperbolic space.

Dimensionality Reduction

VolterraNet: A higher order convolutional network with group equivariance for homogeneous manifolds

1 code implementation5 Jun 2021 Monami Banerjee, Rudrasis Chakraborty, Jose Bouza, Baba C. Vemuri

In this paper, we present a novel higher order Volterra convolutional neural network (VolterraNet) for data defined as samples of functions on Riemannian homogeneous spaces.

Translation

Nested Grassmannians for Dimensionality Reduction with Applications

1 code implementation27 Oct 2020 Chun-Hao Yang, Baba C. Vemuri

With the proposed NG structure, we develop algorithms for the supervised and unsupervised dimensionality reduction problems respectively.

Action Recognition Dimensionality Reduction +2

MVC-Net: A Convolutional Neural Network Architecture for Manifold-Valued Images With Applications

no code implementations2 Mar 2020 Jose J. Bouza, Chun-Hao Yang, David Vaillancourt, Baba C. Vemuri

Our goal in this paper is to generalize convolutional neural networks (CNN) to the manifold-valued image case which arises commonly in medical imaging and computer vision applications.

MANIFOLDNET: A DEEP NEURAL NETWORK FOR MANIFOLD-VALUED DATA

no code implementations ICLR 2019 Rudrasis Chakraborty, Jose Bouza, Jonathan Manton, Baba C. Vemuri

To this end, we present a provably convergent recursive computation of the wFM of the given data, where the weights makeup the convolution mask, to be learned.

General Classification Image Reconstruction +1

ManifoldNet: A Deep Network Framework for Manifold-valued Data

1 code implementation11 Sep 2018 Rudrasis Chakraborty, Jose Bouza, Jonathan Manton, Baba C. Vemuri

Thus, there is need to generalize the deep neural networks to cope with input data that reside on curved manifolds where vector space operations are not naturally admissible.

Dimensionality Reduction

A mixture model for aggregation of multiple pre-trained weak classifiers

no code implementations31 May 2018 Rudrasis Chakraborty, Chun-Hao Yang, Baba C. Vemuri

The other alternative to increase the performance is to learn multiple weak classifiers and boost their performance using a boosting algorithm or a variant thereof.

General Classification

A CNN for homogneous Riemannian manifolds with applications to Neuroimaging

no code implementations14 May 2018 Rudrasis Chakraborty, Monami Banerjee, Baba C. Vemuri

(ii) As a corrolary, we prove the equivariance of the correlation operation to group actions admitted by the input domains which are Riemannian homogeneous manifolds.

Dictionary Learning and Sparse Coding on Statistical Manifolds

no code implementations3 May 2018 Rudrasis Chakraborty, Monami Banerjee, Baba C. Vemuri

In this paper, we propose a novel information theoretic framework for dictionary learning (DL) and sparse coding (SC) on a statistical manifold (the manifold of probability distributions).

Dictionary Learning General Classification

Sparse Exact PGA on Riemannian Manifolds

no code implementations ICCV 2017 Monami Banerjee, Rudrasis Chakraborty, Baba C. Vemuri

In this paper, we present a novel generalization of SPCA, called sparse exact PGA (SEPGA) that can cope with manifold-valued input data and respect the intrinsic geometry of the underlying manifold.

Dimensionality Reduction

A Geometric Framework for Statistical Analysis of Trajectories With Distinct Temporal Spans

no code implementations ICCV 2017 Rudrasis Chakraborty, Vikas Singh, Nagesh Adluru, Baba C. Vemuri

Finally, by using existing algorithms for recursive Frechet mean and exact principal geodesic analysis on the hypersphere, we present several experiments on synthetic and real (vision and medical) data sets showing how group testing on such diversely sampled longitudinal data is possible by analyzing the reconstructed data in the subspace spanned by the first few PGs.

Intrinsic Grassmann Averages for Online Linear and Robust Subspace Learning

no code implementations CVPR 2017 Rudrasis Chakraborty, Soren Hauberg, Baba C. Vemuri

We have demonstrated competitive performance of our proposed online subspace algorithm method on one synthetic and two real data sets.

Riemannian Nonlinear Mixed Effects Models: Analyzing Longitudinal Deformations in Neuroimaging

no code implementations CVPR 2017 Hyunwoo J. Kim, Nagesh Adluru, Heemanshu Suri, Baba C. Vemuri, Sterling C. Johnson, Vikas Singh

Statistical machine learning models that operate on manifold-valued data are being extensively studied in vision, motivated by applications in activity recognition, feature tracking and medical imaging.

Activity Recognition

Intrinsic Grassmann Averages for Online Linear, Robust and Nonlinear Subspace Learning

no code implementations3 Feb 2017 Rudrasis Chakraborty, Søren Hauberg, Baba C. Vemuri

In this paper, we present a geometric framework for computing the principal linear subspaces in both situations as well as for the robust PCA case, that amounts to computing the intrinsic average on the space of all subspaces: the Grassmann manifold.

Dimensionality Reduction

A Nonlinear Regression Technique for Manifold Valued Data With Applications to Medical Image Analysis

no code implementations CVPR 2016 Monami Banerjee, Rudrasis Chakraborty, Edward Ofori, Michael S. Okun, David E. Viallancourt, Baba C. Vemuri

With the exception of a few, most existing methods of regression for manifold valued data are limited to geodesic regression which is a generalization of the linear regression in vector-spaces.

An information theoretic formulation of the Dictionary Learning and Sparse Coding Problems on Statistical Manifolds

no code implementations23 Apr 2016 Rudrasis Chakraborty, Monami Banerjee, Victoria Crawford, Baba C. Vemuri

In this work, we propose a novel information theoretic framework for dictionary learning (DL) and sparse coding (SC) on a statistical manifold (the manifold of probability distributions).

Dictionary Learning General Classification

An efficient Exact-PGA algorithm for constant curvature manifolds

no code implementations CVPR 2016 Rudrasis Chakraborty, Dohyung Seo, Baba C. Vemuri

Recently, an alternative called exact PGA was proposed which tries to solve the optimization without any linearization.

Interpolation on the Manifold of K Component GMMs

no code implementations ICCV 2015 Hyunwoo J. Kim, Nagesh Adluru, Monami Banerjee, Baba C. Vemuri, Vikas Singh

Probability density functions (PDFs) are fundamental "objects" in mathematics with numerous applications in computer vision, machine learning and medical imaging.

Recursive Frechet Mean Computation on the Grassmannian and its Applications to Computer Vision

no code implementations ICCV 2015 Rudrasis Chakraborty, Baba C. Vemuri

In the limit as the number of samples tends to infinity, we prove that GiFME converges to the FM (this is called the weak consistency result on the Grassmann manifold).

Action Recognition Face Recognition

A Riemannian Framework for Matching Point Clouds Represented by the Schrodinger Distance Transform

no code implementations CVPR 2014 Yan Deng, Anand Rangarajan, Stephan Eisenschenk, Baba C. Vemuri

In this paper, we use the well known Riemannian framework never before used for point cloud matching, and present a novel matching algorithm.

set matching

Computing Diffeomorphic Paths for Large Motion Interpolation

no code implementations CVPR 2013 Dohyung Seo, Jeffrey Ho, Baba C. Vemuri

In this paper, we introduce a novel framework for computing a path of diffeomorphisms between a pair of input diffeomorphisms.

MOTION INTERPOLATION

Robust Point Set Registration Using Gaussian Mixture Models

1 code implementation IEEE Transactions on Pattern Analysis and Machine Intelligence 2010 Bing Jian, Baba C. Vemuri

Then, the problem of point set registration is reformulated as the problem of aligning two Gaussian mixtures such that a statistical discrepancy measure between the two corresponding mixtures is minimized.

3D Point Cloud Matching Point Cloud Registration

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