Related papers: Incremental and Decremental Fuzzy Bounded Twin Sup…

In the domain of Computing with words (CW), fuzzy linguistic approaches are known to be relevant in many decision-making problems. Indeed, they allow us to model the human reasoning in replacing words, assessments, preferences, choices,…

We propose an incremental strategy for learning hash functions with kernels for large-scale image search. Our method is based on a two-stage classification framework that treats binary codes as intermediate variables between the feature…

Considering the classification problem, we summarize the nonparallel support vector machines with the nonparallel hyperplanes to two types of frameworks. The first type constructs the hyperplanes separately. It solves a series of small…

In any learning framework, an expert knowledge always plays a crucial role. But, in the field of machine learning, the knowledge offered by an expert is rarely used. Moreover, machine learning algorithms (SVM based) generally use hinge loss…

Support Vector Machines (SVM) have gathered significant acclaim as classifiers due to their successful implementation of Statistical Learning Theory. However, in the context of multiclass and multilabel settings, the reliance on…

Numeric modeling of electromagnetics and acoustics frequently entails matrix-vector multiplication with block Toeplitz structure. When the corresponding block Toeplitz matrix is not highly sparse, e.g. when considering the electromagnetic…

We introduce a generalization of the linearized Alternating Direction Method of Multipliers to optimize a real-valued function $f$ of multiple arguments with potentially multiple constraints $g_\circ$ on each of them. The function $f$ may…

In the field of image clustering, the widely used contrastive learning networks improve clustering performance by maximizing the similarity between positive pairs and the dissimilarity of negative pairs of the inputs. Extant contrastive…

We introduce a new class of multilevel, adaptive, dual-space methods for computing fast convolutional transforms. These methods can be applied to a broad class of kernels, from the Green's functions for classical partial differential…

A deep convolutional fuzzy system (DCFS) on a high-dimensional input space is a multi-layer connection of many low-dimensional fuzzy systems, where the input variables to the low-dimensional fuzzy systems are selected through a moving…

We introduce a cutting-plane framework for nonconvex quadratic programs (QPs) that progressively tightens convex relaxations. Our approach leverages the doubly nonnegative (DNN) relaxation to compute strong lower bounds and generate…

Multitask learning (MTL) can utilize the relatedness between multiple tasks for performance improvement. The advent of multimodal data allows tasks to be referenced by multiple indices. High-order tensors are capable of providing efficient…

Backward stochastic differential equation (BSDE) provides probabilistic solutions for a class of parabolic partial differential equations (PDEs). DeepBSDE and FBSNN are two deep learning approaches for solving high-dimensional PDEs through…

In the conventional Takagi-Sugeno-Kang (TSK)-type fuzzy models, constant or linear functions are usually utilized as the consequent parts of the fuzzy rules, but they cannot effectively describe the behavior within local regions defined by…

We re-examine a practical aspect of combinatorial fuzzy problems of various types, including search, counting, optimization, and decision problems. We are focused only on those fuzzy problems that take series of fuzzy input objects and…

This study develops a graph search algorithm to find the optimal discrimination path for the binary classification problem. The objective function is defined as the difference of variations between the true positive (TP) and false positive…

We establish the first global convergence result of neural networks for two stage least squares (2SLS) approach in nonparametric instrumental variable regression (NPIV). This is achieved by adopting a lifted perspective through mean-field…

Fine-grained visual classification (FGVC) is much more challenging than traditional classification tasks due to the inherently subtle intra-class object variations. Recent works mainly tackle this problem by focusing on how to locate the…

We consider convex-concave saddle point problems with a separable structure and non-strongly convex functions. We propose an efficient stochastic block coordinate descent method using adaptive primal-dual updates, which enables flexible…

The support vector machine (SVM) and deep learning (e.g., convolutional neural networks (CNNs)) are the two most famous algorithms in small and big data, respectively. Nonetheless, smaller datasets may be very important, costly, and not…