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 representation and the trace quotient criterion, to disentangle underlying factors of variation in high dimensional images. Specifically, we aim to learn simple representations of low dimensional, discriminant factors by applying the trace quotient criterion to well-engineered sparse representations. We construct a unified cost function, coined as the SPARse LOW dimensional representation (SparLow) function, for jointly learning both a sparsifying dictionary and a dimensionality reduction transformation. The SparLow function is widely applicable for developing various algorithms in three classic machine learning scenarios, namely, unsupervised, supervised, and semi-supervised learning. In order to develop efficient joint learning algorithms for maximizing the SparLow function, we deploy a framework of sparse coding with appropriate convex priors to ensure the sparse representations to be locally differentiable. Moreover, we develop an efficient geometric conjugate gradient algorithm to maximize the SparLow function on its underlying Riemannian manifold. Performance of the proposed SparLow algorithmic framework is investigated on several image processing tasks, such as 3D data visualization, face/digit recognition, and object/scene categorization.

This code is just for LDA Sparlow.

Impact of the regularizers to the recognition rate on the USPS digits:

Trace of performance over optimization process initialized with different sparse coding methods on 15-Scenes dataset:

Averaged classification Rate (%) comparison on 15-Scenes dataset.The classifier is 1NN for the third column if not specified:

You can load dataset from here.

You can load paper for detail.

if this repo helps your research, Please cite:

@article{wei2019trace,
title={Trace Quotient with Sparsity Priors for Learning Low Dimensional Image Representations},
author={Wei, Xian and Shen, Hao and Kleinsteuber, Martin},
journal={IEEE transactions on pattern analysis and machine intelligence},
year={2019},
publisher={IEEE}
}