相关论文: The Label Algorithm For Irreducible Decomposition …

Given an ideal $I$ in a polynomial ring $K[x_1,\dots,x_n]$ over a field $K$, we present a complete algorithm to compute the binomial part of $I$, i.e., the subideal ${\rm Bin}(I)$ of $I$ generated by all monomials and binomials in $I$. This…

Multimodal multilabel classification (MMC) is a challenging task that aims to design a learning algorithm to handle two data sources, the image and text, and learn a comprehensive semantic feature presentation across the modalities. In this…

Deep ConvNets have shown great performance for single-label image classification (e.g. ImageNet), but it is necessary to move beyond the single-label classification task because pictures of everyday life are inherently multi-label.…

Extreme multi-label learning (XML) or classification has been a practical and important problem since the boom of big data. The main challenge lies in the exponential label space which involves $2^L$ possible label sets especially when the…

Label distribution (LD) uses the description degree to describe instances, which provides more fine-grained supervision information when learning with label ambiguity. Nevertheless, LD is unavailable in many real-world applications. To…

When a monomial ideal has linear quotients with respect to an admissible order of increasing support-degree, we provide two proofs of different flavors to show that it is componentwise support-linear. We also introduce the variable…

We present a neural semi-supervised learning model termed Self-Pretraining. Our model is inspired by the classic self-training algorithm. However, as opposed to self-training, Self-Pretraining is threshold-free, it can potentially update…

We present an alternative method for computing primary decomposition of zero-dimensional ideals over finite fields. Based upon the further decomposition of the invariant subspace of the Frobenius map acting on the quotient algebra in the…

The rapid development of deep learning has made a great progress in image segmentation, one of the fundamental tasks of computer vision. However, the current segmentation algorithms mostly rely on the availability of pixel-level…

Extreme multi-label classification (XML) is becoming increasingly relevant in the era of big data. Yet, there is no method for effectively generating stratified partitions of XML datasets. Instead, researchers typically rely on provided…

In this paper, we propose an online learning algorithm PRIL for learning ranking classifiers using interval labeled data and show its correctness. We show its convergence in finite number of steps if there exists an ideal classifier such…

In this paper, a progressive learning algorithm for multi-label classification to learn new labels while retaining the knowledge of previous labels is designed. New output neurons corresponding to new labels are added and the neural network…

We develop a probabilistic algorithm for computing elimination ideals of likelihood equations, which is for larger models by far more efficient than directly computing Groebner bases or the interpolation method proposed in the first…

We find an explicit expression of the associated primes of monomial ideals as a colon by an element $v$, using the unique irredundant irreducible decomposition whose irreducible components are monomial ideals (Theorem 3.1). An algorithm to…

Data efficiency, or the ability to generalize from a few labeled data, remains a major challenge in deep learning. Semi-supervised learning has thrived in traditional recognition tasks alleviating the need for large amounts of labeled data,…

Dense semantic 3D reconstruction is typically formulated as a discrete or continuous problem over label assignments in a voxel grid, combining semantic and depth likelihoods in a Markov Random Field framework. The depth and semantic…

This paper proposes a novel and efficient method for Learning from Label Proportions (LLP), whose goal is to train a classifier only by using the class label proportions of instance sets, called bags. We propose a novel LLP method based on…

This paper has been withdrawn due to a critical error discovered in Theorem 4.21. Anyone with a historical or pragamatic interest in prior "negative results", however - e.g., failed proof attempts relating to the (in)consistency of ZF or…

In this article, we study the primary decomposition of some binomial ideals. In particular, we introduce the concept of polyocollection, a combinatorial object that generalizes the definitions of collection of cells and polyomino, that can…

The aim of this paper is to propose an ``elementary" approach to Coleman's theory of p-adic abelian integrals. Our main tool is a theory of commutative p-adic Lie groups (the logarithm map); we use neither dagger analysis nor…