Related papers: Low-Rank Discriminative Least Squares Regression f…
Sufficient dimension reduction (SDR) methods, which often rely on class precision matrices, are widely used in supervised statistical classification problems. However, when class-specific sample sizes are small relative to the original…
In this paper, the estimation problem for sparse reduced rank regression (SRRR) model is considered. The SRRR model is widely used for dimension reduction and variable selection with applications in signal processing, econometrics, etc. The…
We propose regression networks for the problem of few-shot classification, where a classifier must generalize to new classes not seen in the training set, given only a small number of examples of each class. In high dimensional embedding…
Reduced-rank linear discriminant analysis (RRLDA) is a foundational method of dimension reduction for classification that has been useful in a wide range of applications. The goal is to identify an optimal subspace to project the…
The objective learning formulation is essential for the success of convolutional neural networks. In this work, we analyse thoroughly the standard learning objective functions for multi-class classification CNNs: softmax regression (SR) for…
Dimensionality reduction (DR) methods have been commonly used as a principled way to understand the high-dimensional data such as facial images. In this paper, we propose a new supervised DR method called Optimized Projection for Sparse…
We present a novel adaptive random subspace learning algorithm (RSSL) for prediction purpose. This new framework is flexible where it can be adapted with any learning technique. In this paper, we tested the algorithm for regression and…
In this paper, we propose a novel classification scheme for the remotely sensed hyperspectral image (HSI), namely SP-DLRR, by comprehensively exploring its unique characteristics, including the local spatial information and low-rankness.…
The reduced-rank method exploits the distortion-variance tradeoff to yield superior solutions for classic problems in statistical signal processing such as parameter estimation and filtering. The central idea is to reduce the variance of…
Images suffer from heavy spatial redundancy because pixels in neighboring regions are spatially correlated. Existing approaches strive to overcome this limitation by reducing less meaningful image regions. However, current leading methods…
Sparse linear regression (SLR) is a well-studied problem in statistics where one is given a design matrix $X\in\mathbb{R}^{m\times n}$ and a response vector $y=X\theta^*+w$ for a $k$-sparse vector $\theta^*$ (that is, $\|\theta^*\|_0\leq…
We prove rates of convergence in the statistical sense for kernel-based least squares regression using a conjugate gradient algorithm, where regularization against overfitting is obtained by early stopping. This method is directly related…
The spatial linear mixed model (SLMM) consists of fixed and spatial random effects that may be linearly dependent. Partially motivated as a means to address potential issues with confounding, the Restricted spatial regression (RSR) model…
A low-rank transformation learning framework for subspace clustering and classification is here proposed. Many high-dimensional data, such as face images and motion sequences, approximately lie in a union of low-dimensional subspaces. The…
We settle the complexity of dynamic least-squares regression (LSR), where rows and labels $(\mathbf{A}^{(t)}, \mathbf{b}^{(t)})$ can be adaptively inserted and/or deleted, and the goal is to efficiently maintain an $\epsilon$-approximate…
Low-rank matrix approximation (LRMA) is a powerful technique for signal processing and pattern analysis. However, its potential for data compression has not yet been fully investigated in the literature. In this paper, we propose sparse…
Unsupervised domain adaptation leverages rich information from a labeled source domain to model an unlabeled target domain. Existing methods attempt to align the cross-domain distributions. However, the statistical representations of the…
The recent development of more sophisticated spectroscopic methods allows acqui- sition of high dimensional datasets from which valuable information may be extracted using multivariate statistical analyses, such as dimensionality reduction…
Few-shot class incremental learning -- the problem of updating a trained classifier to discriminate among an expanded set of classes with limited labeled data -- is a key challenge for machine learning systems deployed in non-stationary…
Unsupervised learning with generative adversarial networks (GANs) has proven hugely successful. Regular GANs hypothesize the discriminator as a classifier with the sigmoid cross entropy loss function. However, we found that this loss…