Related papers: Learning Rank Reduced Interpolation with Principal…
Intelligent systems possess a crucial characteristic of breaking complicated problems into smaller reusable components or parts and adjusting to new tasks using these part representations. However, current part-learners encounter…
Sparse principal component analysis (PCA) improves interpretability of the classic PCA by introducing sparsity into the dimension-reduction process. Optimization models for sparse PCA, however, are generally non-convex, non-smooth and more…
Principal Component Analysis (PCA) is a well known procedure to reduce intrinsic complexity of a dataset, essentially through simplifying the covariance structure or the correlation structure. We introduce a novel algebraic, model-based…
We consider the following multi-component sparse PCA problem: given a set of data points, we seek to extract a small number of sparse components with disjoint supports that jointly capture the maximum possible variance. These components can…
In high-dimensional prediction problems, where the number of features may greatly exceed the number of training instances, fully Bayesian approach with a sparsifying prior is known to produce good results but is computationally challenging.…
This article aims to provide a comprehensive overview of sparse optimization, with a focus on both sparse signal recovery and sparse regularization techniques. We will begin by exploring the foundations of sparse optimization, delving into…
We present a novel approach for adaptive, differentiable parameterization of large-scale random fields. If the approach is coupled with any gradient-based optimization algorithm, it can be applied to a variety of optimization problems,…
Principal component analysis (PCA) is widely used for feature extraction and dimensionality reduction, with documented merits in diverse tasks involving high-dimensional data. Standard PCA copes with one dataset at a time, but it is…
This paper is concerned with the problem of low rank plus sparse matrix decomposition for big data. Conventional algorithms for matrix decomposition use the entire data to extract the low-rank and sparse components, and are based on…
The performance of the Self-Organizing Map (SOM) algorithm is dependent on the initial weights of the map. The different initialization methods can broadly be classified into random and data analysis based initialization approach. In this…
The robust principal component analysis (RPCA) decomposes a data matrix into a low-rank part and a sparse part. There are mainly two types of algorithms for RPCA. The first type of algorithm applies regularization terms on the singular…
Hyperspectral optical imaging provides rich spectral information for estimating continuous environmental and material parameters; however, its high dimensionality and strong feature correlation pose significant challenges for machine…
Principal component analysis (PCA) is a widely used dimension reduction tool in the analysis of many kind of high-dimensional data. It is used in signal processing, mechanical engineering, psychometrics, and other fields under different…
The segmentation of animals from camera-trap images is a difficult task. To illustrate, there are various challenges due to environmental conditions and hardware limitation in these images. We proposed a multi-layer robust principal…
Online or recursive robust PCA can be posed as a problem of recovering a sparse vector, $S_t$, and a dense vector, $L_t$, which lies in a slowly changing low-dimensional subspace, from $M_t:= S_t + L_t$ on-the-fly as new data comes in. For…
Principal component analysis (PCA) is a well-known linear dimension-reduction method that has been widely used in data analysis and modeling. It is an unsupervised learning technique that identifies a suitable linear subspace for the input…
We introduce a novel visual tokenization framework that embeds a provable PCA-like structure into the latent token space. While existing visual tokenizers primarily optimize for reconstruction fidelity, they often neglect the structural…
Exiting deep-learning based dense stereo matching methods often rely on ground-truth disparity maps as the training signals, which are however not always available in many situations. In this paper, we design a simple convolutional neural…
Adaptive sparse coding methods learn a possibly overcomplete set of basis functions, such that natural image patches can be reconstructed by linearly combining a small subset of these bases. The applicability of these methods to visual…
We propose to modify the common training protocols of optical flow, leading to sizable accuracy improvements without adding to the computational complexity of the training process. The improvement is based on observing the bias in sampling…