10 accepted papers
Hyperbolic spaces have been quite popular in the recent past for representing hierarchically organized data. Further, several classification algorithms for data in these spaces have been proposed in the literature. These algorithms mainly use either hyperplanes or geodesics for decision boundaries i…
Hyperbolic neural networks have been popular in the recent past due to their ability to represent hierarchical data sets effectively and efficiently. The challenge in developing these networks lies in the nonlinearity of the embedding space namely, the Hyperbolic space. Hyperbolic space is a homogen…
Analyzing data representing multifarious trajectories is central to the many fields in Science and Engineering; for example, trajectories representing a tennis serve, a gymnast's parallel bar routine, progression/remission of disease and so on. We present a novel geometric algorithm for performing s…
Principal Component Analysis (PCA) is a fundamental method for estimating a linear subspace approximation to high-dimensional data. Many algorithms exist in literature to achieve a statistically robust version of PCA called RPCA. In this paper, we present a geometric framework for computing the pri…
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. While non-parametric methods have been relatively well studied in the literature, efficient formu…
Principal Component Analysis (PCA) is a widely popular dimensionality reduction technique for vector-valued inputs. In the past decade, a nonlinear generalization of PCA, called the Principal Geodesic Analysis (PGA) was developed to tackle data that lie on a smooth manifold. PGA suffers from the sam…
Regression is an essential tool in Statistical analysis of data with many applications in Computer Vision, Machine Learning, Medical Imaging and various disciplines of Science and Engineering. Linear and nonlinear regression in a vector space setting has been well studied in literature. However, gen…
Manifold-valued datasets are widely encountered in many computer vision tasks. A non-linear analog of the PCA algorithm, called the Principal Geodesic Analysis (PGA) algorithm suited for data lying on Riemannian manifolds was reported in literature a decade ago. Since the objective function in the P…
Probability density functions (PDFs) are fundamental "objects" in mathematics with numerous applications in computer vision, machine learning and medical imaging. The feasibility of basic operations such as computing the distance between two PDFs and estimating a mean of a set of PDFs is a direct fu…
In the past decade, Grassmann manifolds (Grassmannian) have been commonly used in mathematical formulations of many Computer Vision tasks. Averaging points on a Grassmann manifold is a very common operation in many applications including but not limited to, tracking, action recognition, video-face r…