Trace Quotient Meets Sparsity: A Method for Learning Low Dimensional Image Representations
This paper presents an algorithm that allows to learn low dimensional representations of images in an unsupervised manner. The core idea is to combine two criteria that play important roles in unsupervised representation learning, namely sparsity and trace quotient. The former is known to be a convenient tool to identify underlying factors, and the latter is known as a disentanglement of underlying discriminative factors. In this work, we develop a generic cost function for learning jointly a sparsifying dictionary and a dimensionality reduction transformation. It leads to several counterparts of classic low dimensional representation methods, such as Principal Component Analysis, Local Linear Embedding, and Laplacian Eigenmap. Our proposed optimisation algorithm leverages the efficiency of geometric optimisation on Riemannian manifolds and a closed form solution to the elastic net problem.
Code (0)
등록된 구현이 없습니다.
Tasks
Dimensionality ReductionDisentanglementRepresentation LearningSimilar Papers 제목 키워드 기반
Trace Quotient with Sparsity Priors for Learning Low Dimensional Image Representations
This work studies the problem of learning appropriate low dimensional image representations. We propose a generic algorithmic framework, which leverages two classic representation learning paradigms, i.e., sparse represe…
Data VisualizationDimensionality ReductionRepresentation LearningA Trace Lasso Regularized L1-norm Graph Cut for Highly Correlated Noisy Hyperspectral Image
This work proposes an adaptive trace lasso regularized L1-norm based graph cut method for dimensionality reduction of Hyperspectral images, called as `Trace Lasso-L1 Graph Cut' (TL-L1GC). The underlying idea of this meth…
Dimensionality ReductionIsometric Quotient Variational Auto-Encoders for Structure-Preserving Representation Learning
We study structure-preserving low-dimensional representation of a data manifold embedded in a high-dimensional observation space based on variational auto-encoders (VAEs). We approach this by decomposing the data manifol…
Rapidly-Exploring Quotient-Space Trees: Motion Planning using Sequential Simplifications
Motion planning problems can be simplified by admissible projections of the configuration space to sequences of lower-dimensional quotient-spaces, called sequential simplifications. To exploit sequential simplifications,…
Motion PlanningA Benchmark for Sparse Coding: When Group Sparsity Meets Rank Minimization
Sparse coding has achieved a great success in various image processing tasks. However, a benchmark to measure the sparsity of image patch/group is missing since sparse coding is essentially an NP-hard problem. This work …
Dictionary LearningImage InpaintingImage Restoration