Related papers: The Label Algorithm For Irreducible Decomposition …
Irreducible decomposition of monomial ideals has an increasing number of applications from biology to pure math. This paper presents the Slice Algorithm for computing irreducible decompositions, Alexander duals and socles of monomial…
The paper presents two algorithms for finding irreducible decomposition of monomial ideals. The first one is recursive, derived from staircase structures of monomial ideals. This algorithm has a good performance for highly non-generic…
Irreducible decompositions of monomial ideals in polynomial rings over a field are well-understood. In this paper, we investigate decompositions in the set of monomial ideals in the semigroup ring A[\mathbb{R}_{\geq 0}^d] where A is an…
This report is a reproducibility study of the paper "CDUL: CLIP-Driven Unsupervised Learning for Multi-Label Image Classification" (Abdelfattah et al, ICCV 2023). Our report makes the following contributions: (1) We provide a reproducible,…
This paper is a revised version of a previously posted paper in arxiv. The authors posted it as a new submission by mistake. The latest version of the paper can be found at arXiv:math-ph/0512003v2
The current dominant paradigm when building a machine learning model is to iterate over a dataset over and over until convergence. Such an approach is non-incremental, as it assumes access to all images of all categories at once. However,…
The reduction algorithm is used to compute reduced ideals of a number field. However, there are reduced ideals that can never be obtained from this algorithm. In this paper, we will show that these ideals have inverses of larger norms among…
Among the three main components (data, labels, and models) of any supervised learning system, data and models have been the main subjects of active research. However, studying labels and their properties has received very little attention.…
The assumption that response and predictor belong to the same statistical unit may be violated in practice. Unbiased estimation and recovery of true label ordering based on unlabeled data are challenging tasks and have attracted increasing…
The package Binomials contains implementations of specialized algorithms for binomial ideals, including primary decomposition into binomial ideals. The current implementation works in characteristic zero. Primary decomposition is restricted…
Building on coprincipal mesoprimary decomposition [Kahle and Miller, 2014], we combinatorially construct an irreducible decomposition of any given binomial ideal. In a parallel manner, for congruences in commutative monoids we construct…
preprint withdrawn. A revised version of this paper, with different authors appears in E. Nelson, P. Wolynes, and J. Onuchic, in Optimization in computational chemistry and molecular biology, C. Floudas and P. Pardalos editors, (1999)). The…
The modular decomposition is a technique that applies but is not restricted to graphs. The notion of module naturally appears in the proofs of many graph theoretical theorems. Computing the modular decomposition tree is an important…
The learning from imbalanced data is a deeply studied problem in standard classification and, in recent times, also in multilabel classification. A handful of multilabel resampling methods have been proposed in late years, aiming to balance…
We define a scheme for labelling and ordering integral ideals of number fields, including prime ideals as a special case. The order we define depends only on the choice of a monic irreducible integral defining polynomial for each field $K$,…
In this work, we present an abstract framework for some algebraic error-correcting codes with the aim of capturing codes that are list-decodable to capacity, along with their decoding algorithm. In the polynomial ideal framework, a code is…
Let $I$ be a monomial ideal in a polynomial ring $A=K[x_1,...,x_n]$. We call a monomial ideal $J$ to be a minimal monomial reduction ideal of $I$ if there exists no proper monomial ideal $L \subset J$ such that $L$ is a reduction ideal of…
Cross-modal data matching refers to retrieval of data from one modality, when given a query from another modality. In general, supervised algorithms achieve better retrieval performance compared to their unsupervised counterpart, as they…
Many modern applications deal with multi-label data, such as functional categorizations of genes, image labeling and text categorization. Classification of such data with a large number of labels and latent dependencies among them is a…
Label distribution learning (LDL) is a novel paradigm that describe the samples by label distribution of a sample. However, acquiring LDL dataset is costly and time-consuming, which leads to the birth of incomplete label distribution…