Related papers: A Computational Approach to Classifying Low Rank M…
The latent class model is a powerful tool for identifying latent classes within populations that share common characteristics for categorical data in social, psychological, and behavioral sciences. In this article, we propose two new…
Let $R$ be a graded ring. We introduce a class of graded $R$-modules called Gr\"obner-coherent modules. Roughly, these are graded $R$-modules that are coherent as ungraded modules because they admit an adequate theory of Gr\"obner bases.…
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…
For a commutative ring $R$ and a weakly proregular ideal $I$, we prove a simple universal property of the category of $L_0$-complete $R$-modules: it is the smallest replete exact abelian subcategory of the category of $R$-modules which…
This study proposes a low-complexity interpretable classification system. The proposed system contains three main modules including feature extraction, feature reduction, and classification. All of them are linear. Thanks to the linear…
A group of matrices $G$ with entries in a number field $K$ is defined to be numerical if $G$ has a finite index subgroup of matrices whose entries are algebraic integers. It is shown that an irreducible or completely reducible subgroup of…
A class of rational functions characterized by some wonderful properties is studied. The properties that identify this class include simple algebra (their inverses can be expressed in radicals), simple topology (the total space of the…
A wide range of Bayesian models have been proposed for data that is divided hierarchically into groups. These models aim to cluster the data at different levels of grouping, by assigning a mixture component to each datapoint, and a mixture…
It has been argued that in supervised classification tasks, in practice it may be more sensible to perform model selection with respect to some more focused model selection score, like the supervised (conditional) marginal likelihood, than…
We provide a foundation for working with homological and homotopical methods in categorical algebra. This involves two mutually complementary components, namely (a) the strategic selection of suitable axiomatic frameworks, some well known…
We study certain monoidal subcategories (introduced by David Hernandez and Bernard Leclerc) of finite--dimensional representations of a quantum affine algebra of type $A$. We classify the set of prime representations in these subcategories…
In the context of protomodular categories, several additional conditions have been considered in order to obtain a closer group-like behavior. Among them are locally algebraic cartesian closedness and algebraic coherence. The recent notion…
In the framework of supervised classification (discrimination) for functional data, it is shown that the optimal classification rule can be explicitly obtained for a class of Gaussian processes with "triangular" covariance functions. This…
In this paper, a novel approach for coding nominal data is proposed. For the given nominal data, a rank in a form of complex number is assigned. The proposed method does not lose any information about the attribute and brings other…
We study properties of relative modular categories and derive sufficient conditions for their existence. In particular, we derive sufficient conditions for relative pre-modular categories to be non-degenerate and relative modular, and for…
Standard Bayesian inference can build models that combine information from various sources, but this inference may not be reliable if components of a model are misspecified. Cut inference, as a particular type of modularized Bayesian…
We develop abstract nonsense for module categories over monoidal categories (this is a straightforward categorification of modules over rings). As applications we show that any semisimple monoidal category with finitely many simple objects…
Modular Decomposition focuses on repeatedly identifying a module M (a collection of vertices that shares exactly the same neighbourhood outside of M) and collapsing it into a single vertex. This notion of exactitude of neighbourhood is very…
For a given abelian group G, we classify the isomorphism classes of G-gradings on the simple restricted Lie algebras of types W(m;1) and S(m;1) (m>=2), in terms of numerical and group-theoretical invariants. Our main tool is automorphism…
Associated to an abelian variety over a number field are several interesting and related groups: the motivic Galois group, the Mumford-Tate group, $\ell$-adic monodromy groups, and the Sato-Tate group. Assuming the Mumford-Tate conjecture,…