Grassmannian Discriminant Maps (GDM) for Manifold Dimensionality Reduction with Application to Image Set Classification
In image set classification, a considerable progress has been made by representing original image sets on Grassmann manifolds. In order to extend the advantages of the Euclidean based dimensionality reduction methods to the Grassmann Manifold, several methods have been suggested recently which jointly perform dimensionality reduction and metric learning on Grassmann manifold to improve performance. Nevertheless, when applied to complex datasets, the learned features do not exhibit enough discriminatory power. To overcome this problem, we propose a new method named Grassmannian Discriminant Maps (GDM) for manifold dimensionality reduction problems. The core of the method is a new discriminant function for metric learning and dimensionality reduction. For comparison and better understanding, we also study a simple variations to GDM. The key difference between them is the discriminant function. We experiment on data sets corresponding to three tasks: face recognition, object categorization, and hand gesture recognition to evaluate the proposed method and its simple extensions. Compared with the state of the art, the results achieved show the effectiveness of the proposed algorithm.
Code (0)
등록된 구현이 없습니다.
Tasks
Dimensionality ReductionFace RecognitionGeneral ClassificationGesture RecognitionHand Gesture RecognitionHand-Gesture RecognitionMetric LearningObject CategorizationSimilar Papers 제목 키워드 기반
Grassmannian diffusion maps based dimension reduction and classification for high-dimensional data
This work introduces the Grassmannian Diffusion Maps, a novel nonlinear dimensionality reduction technique that defines the affinity between points through their representation as low-dimensional subspaces corresponding …
ClusteringDimensionality ReductionFace RecognitionGeneral Classification+1Nested Grassmannians for Dimensionality Reduction with Applications
In the recent past, nested structures in Riemannian manifolds has been studied in the context of dimensionality reduction as an alternative to the popular principal geodesic analysis (PGA) technique, for example, the pri…
Action RecognitionClusteringDimensionality ReductionFace Recognition+1Bayesian Inference on Matrix Manifolds for Linear Dimensionality Reduction
We reframe linear dimensionality reduction as a problem of Bayesian inference on matrix manifolds. This natural paradigm extends the Bayesian framework to dimensionality reduction tasks in higher dimensions with simpler …
Bayesian InferenceDimensionality Reduction$O(k)$-Equivariant Dimensionality Reduction on Stiefel Manifolds
Many real-world datasets live on high-dimensional Stiefel and Grassmannian manifolds, $V_k(\mathbb{R}^N)$ and $Gr(k, \mathbb{R}^N)$ respectively, and benefit from projection onto lower-dimensional Stiefel and Grassmannia…
Dimensionality ReductionDimensionality Reduction on Grassmannian via Riemannian Optimization: A Generalized Perspective
This paper proposes a generalized framework with joint normalization which learns lower-dimensional subspaces with maximum discriminative power by making use of the Riemannian geometry. In particular, we model the simila…
Dimensionality ReductionRiemannian optimization