Related papers: Ellipsoidal Subspace Support Vector Data Descripti…
This paper introduces a novel framework for dynamic classification in high dimensional spaces, addressing the evolving nature of class distributions over time or other index variables. Traditional discriminant analysis techniques are…
Tabular data is the most commonly used form of data in industry. Gradient Boosting Trees, Support Vector Machine, Random Forest, and Logistic Regression are typically used for classification tasks on tabular data. DNN models using…
Subspace optimization methods have the attractive property of reducing large-scale optimization problems to a sequence of low-dimensional subspace optimization problems. However, existing subspace optimization frameworks adopt a fixed…
We introduce a supervised dimensionality reduction methodology for categorical (and discretized mixed-type) data based on a density-matrix construction induced by class-conditional frequencies. Given a labeled dataset encoded in a one-hot…
The visualization of multi-dimensional data with interpretable methods remains limited by capabilities for both high-dimensional lossless visualizations that do not suffer from occlusion and that are computationally capable by parameterized…
In this paper, we introduce a new domain adaptation (DA) algorithm where the source and target domains are represented by subspaces spanned by eigenvectors. Our method seeks a domain invariant feature space by learning a mapping function…
Modeling the dynamic behavior of deformable objects is crucial for creating realistic digital worlds. While conventional simulations produce high-quality motions, their computational costs are often prohibitive. Subspace simulation…
Data representation is usually a natural form with their attribute values. On this basis, data processing is an attribute-centered calculation. However, there are three limitations in the attribute-centered calculation, saying, inflexible…
Data compression techniques are characterized by four key performance indices which are (i) associated accuracy, (ii) compression ratio, (iii) computational work, and (iv) degree of freedom. The method of data compression developed in this…
We propose new small-sphere distributional families for modeling multivariate directional data on $(\mathbb{S}^{p-1})^K$ for $p \ge 3$ and $K \ge 1$. In a special case of univariate directions in $\Re^3$, the new densities model random…
In this work we address the subspace recovery problem. Given a set of data samples (vectors) approximately drawn from a union of multiple subspaces, our goal is to segment the samples into their respective subspaces and correct the possible…
The performance of a machine learning model degrades when it is applied to data from a similar but different domain than the data it has initially been trained on. To mitigate this domain shift problem, domain adaptation (DA) techniques…
We consider the problem of optimal recovery of an element $u$ of a Hilbert space $\mathcal{H}$ from $m$ measurements obtained through known linear functionals on $\mathcal{H}$. Problems of this type are well studied \cite{MRW} under an…
This paper presents a method for the approximation of harmonic potentials that combines downward continuation of globally available data on a sphere $\Omega_R$ of radius $R$ (e.g., a satellite's orbit) with locally available data on a…
A method based on one class support vector machine (OCSVM) is proposed for class incremental learning. Several OCSVM models divide the input space into several parts. Then, the 1VS1 classifiers are constructed for the confuse part by using…
This paper introduces {\em fusion subspace clustering}, a novel method to learn low-dimensional structures that approximate large scale yet highly incomplete data. The main idea is to assign each datum to a subspace of its own, and minimize…
Datasets with non-trivial large scale topology can be hard to embed in low-dimensional Euclidean space with existing dimensionality reduction algorithms. We propose to model topologically complex datasets using vector bundles, in such a way…
Unsupervised Domain Adaptation (UDA) addresses the problem of performance degradation due to domain shift between training and testing sets, which is common in computer vision applications. Most existing UDA approaches are based on…
Hyperspherical Prototypical Learning (HPL) is a supervised approach to representation learning that designs class prototypes on the unit hypersphere. The prototypes bias the representations to class separation in a scale invariant and known…
Hierarchical and tree-like data sets arise in many applications, including language processing, graph data mining, phylogeny and genomics. It is known that tree-like data cannot be embedded into Euclidean spaces of finite dimension with…