Related papers: When do CF-approximation spaces capture sL-domains
We propose Ordered Subspace Clustering (OSC) to segment data drawn from a sequentially ordered union of subspaces. Similar to Sparse Subspace Clustering (SSC) we formulate the problem as one of finding a sparse representation but include an…
In this paper, we give a topological version of Scott convergence theorem for locally hypercompact spaces. We introduce the notion of $\mathcal{S}^*_X$-convergence on a $T_0$ topological space $X$, and define the notion of finitely…
With a complete residuated lattice $L$ as the truth value table, we extend the definition of sobriety of classical convex spaces to the framework of $L$-convex spaces. We provide a specific construction for the sobrification of an…
Subspace clustering assumes that the data is sepa-rable into separate subspaces. Such a simple as-sumption, does not always hold. We assume that, even if the raw data is not separable into subspac-es, one can learn a representation…
We propose a novel continual self-supervised learning method (CSSL) considering medical domain knowledge in chest CT images. Our approach addresses the challenge of sequential learning by effectively capturing the relationship between…
The inf-sup constant for the divergence, or LBB constant, is explicitly known for only few domains. For other domains, upper and lower estimates are known. If more precise values are required, one can try to compute a numerical…
In this paper, we shall present a topological approach for the computation of some supremal sublanguages, often specified by language equations, which arise from the study of the supervisory control theory. The basic idea is to identify the…
Recently, J. D. Lawson encouraged the domain theory community to consider the scientific program of developing domain theory in the wider context of $T_0$-spaces instead of restricting to posets. In this paper, we respond to this calling by…
In this paper, we give the first constant approximation algorithm for the lower bounded facility location (LBFL) problem with general lower bounds. Prior to our work, such algorithms were only known for the special case where all facilities…
Submodular optimization is a fundamental problem with many applications in machine learning, often involving decision-making over datasets with sensitive attributes such as gender or age. In such settings, it is often desirable to produce a…
This paper studies the problem of approximating a function $f$ in a Banach space $X$ from measurements $l_j(f)$, $j=1,\dots,m$, where the $l_j$ are linear functionals from $X^*$. Most results study this problem for classical Banach spaces…
Proximity maps and regions are defined based on the relative allocation of points from two or more classes in an area of interest and are used to construct random graphs called proximity catch digraphs (PCDs) which have applications in…
We propose a subgradient-based method for finding the maximum feasible subsystem in a collection of closed sets with respect to a given closed set $C$ (MFS$_C$). In this method, we reformulate the MFS$_C$ problem as an $\ell_0$ optimization…
Continuous monitoring with an ever-increasing number of sensors has become ubiquitous across many application domains. However, acquired time series are typically high-dimensional and difficult to interpret. Expressive deep learning (DL)…
We study $G_\delta$ subspaces of continuous dcpos, which we call domain-complete spaces, and $G_\delta$ subspaces of locally compact sober spaces, which we call LCS-complete spaces. Those include all locally compact sober spaces-in…
In-context learning (ICL) and supervised fine-tuning (SFT) are two common strategies for improving the performance of modern large language models (LLMs) on specific tasks. Despite their different natures, these strategies often lead to…
Efficiently capturing the complex spatiotemporal representations from large-scale unlabeled traffic data remains to be a challenging task. In considering of the dilemma, this work employs the advanced contrastive learning and proposes a…
Subspace clustering discovers the clusters embedded in multiple, overlapping subspaces of high dimensional data. Many significant subspace clustering algorithms exist, each having different characteristics caused by the use of different…
This paper investigates a novel structure of stratified L-convex groups, defined as groups possessing stratified L-convex structures, in which the group operations are L-convexity-preserving mappings. It is verified that stratified L-convex…
Finite Lorentz groups acting on 4-dimensional vector spaces coordinatized by finite fields with a prime number of elements are represented as homomorphic images of countable, rational subgroups of the Lorentz group acting on real…