# Learning on Manifolds

@inproceedings{Porikli2010LearningOM, title={Learning on Manifolds}, author={Fatih Murat Porikli}, booktitle={SSPR/SPR}, year={2010} }

Mathematical formulation of certain natural phenomena exhibits group structure on topological spaces that resemble the Euclidean space only on a small enough scale, which prevents incorporation of conventional inference methods that require global vector norms. More specifically in computer vision, such underlying notions emerge in differentiable parameter spaces. Here, two Riemannian manifolds including the set of affine transformations and covariance matrices are elaborated and their…

## 6 Citations

### Large-Margin Classification in Hyperbolic Space

- Computer Science, MathematicsAISTATS
- 2019

Hyperbolic SVM, a hyperbolic formulation of support vector machine classifiers, is introduced and its theoretical connection to the Euclidean counterpart is described, allowing end-to-end analyses based on the inherenthyperbolic geometry of the data without resorting to ill-fitting tools developed for Euclidan space.

### Tensor Sparse Coding for Positive Definite Matrices

- Computer ScienceIEEE Transactions on Pattern Analysis and Machine Intelligence
- 2014

This paper proposes a novel sparse coding technique for positive definite matrices, which respects the structure of the Riemannian manifold and preserves the positivity of their eigenvalues, without resorting to vectorization.

### Coherence algorithm with a high‐resolution time–time transform and feature matrix for seismic data

- GeologyGeophysical Prospecting
- 2020

Traditional coherence algorithms are often based on the assumption that seismic traces are stationary and Gaussian. However, seismic traces are actually non‐stationary and non‐Gaussian. A constant…

### Count on Me: Learning to Count on a Single Image

- Computer ScienceIEEE Transactions on Circuits and Systems for Video Technology
- 2018

An iterative algorithm to locate patches similar to the seeds working in three steps, operating on Lie algebra, and exploiting a mixture of templates to process heterogeneous unstructured images with multiple visual motifs and extremely crowded scenarios with high precision and recall.

### A Novel Dynamic System in the Space of SPD Matrices with Applications to Appearance Tracking

- Computer Science, MathematicsSIAM J. Imaging Sci.
- 2013

A novel probabilistic dynamic model in $P_n$ based on Riemannian geometry and probability theory is presented in conjunction with a geometric (intrinsic) recursive filter for tracking a time sequence of SPD matrix measurements in a Bayesian framework.

### Algorithms for tracking on the manifold of symmetric positive definite matrices

- Computer Science
- 2012

A novel probabilistic dynamic model is proposed in conjunction with an intrinsic recursive filter for tracking a time sequence of SPD matrix measurements in a Bayesian framework and this newly developed filtering method can then be used for the covariance.

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