In this paper, we propose a new variant of Linear Discriminant Analysis (LDA) to solve multi-label classification tasks. The proposed method is based on a probabilistic model for defining the weights of individual samples in a weighted multi-label LDA approach. Linear Discriminant Analysis is a classical statistical machine learning method, which aims to find a linear data transformation increasing class discrimination in an optimal discriminant subspace. Traditional LDA sets assumptions related to Gaussian class distributions and single-label data annotations. To employ the LDA technique in multi-label classification problems, we exploit intuitions coming from a probabilistic interpretation of class saliency to redefine the between-class and within-class scatter matrices. The saliency-based weights obtained based on various kinds of affinity encoding prior information are used to reveal the probability of each instance to be salient for each of its classes in the multi-label problem at hand. The proposed Saliency-based weighted Multi-label LDA approach is shown to lead to performance improvements in various multi-label classification problems.
Fisher Discriminant Analysis (FDA) is a subspace learning method which minimizes and maximizes the intra- and inter-class scatters of data, respectively. Although, in FDA, all the pairs of classes are treated the same way, some classes are closer than the others. Weighted FDA assigns weights to the pairs of classes to address this shortcoming of FDA. In this paper, we propose a cosine-weighted FDA as well as an automatically weighted FDA in which weights are found automatically. We also propose a weighted FDA in the feature space to establish a weighted kernel FDA for both existing and newly p…
We consider the two-group classification problem and propose a kernel classifier based on the optimal scoring framework. Unlike previous approaches, we provide theoretical guarantees on the expected risk consistency of the method. We also allow for feature selection by imposing structured sparsity using weighted kernels. We propose fully-automated methods for selection of all tuning parameters, and in particular adapt kernel shrinkage ideas for ridge parameter selection. Numerical studies demonstrate the superior classification performance of the proposed approach compared to existing nonparam…
Classical linear discriminant analysis (LDA) is based on squared Frobenious norm and hence is sensitive to outliers and noise. To improve the robustness of LDA, in this paper, we introduce capped l_{2,1}-norm of a matrix, which employs non-squared l_2-norm and "capped" operation, and further propose a novel capped l_{2,1}-norm linear discriminant analysis, called CLDA. Due to the use of capped l_{2,1}-norm, CLDA can effectively remove extreme outliers and suppress the effect of noise data. In fact, CLDA can be also viewed as a weighted LDA. CLDA is solved through a series of generalized eigenv…
A lot of effort is currently made to provide methods to analyze and understand deep neural network impressive performances for tasks such as image or text classification. These methods are mainly based on visualizing the important input features taken into account by the network to build a decision. However these techniques, let us cite LIME, SHAP, Grad-CAM, or TDS, require extra effort to interpret the visualization with respect to expert knowledge. In this paper, we propose a novel approach to inspect the hidden layers of a fitted CNN in order to extract interpretable linguistic objects from…
Recently proposed L2-norm linear discriminant analysis criterion via the Bhattacharyya error bound estimation (L2BLDA) is an effective improvement of linear discriminant analysis (LDA) for feature extraction. However, L2BLDA is only proposed to cope with vector input samples. When facing with two-dimensional (2D) inputs, such as images, it will lose some useful information, since it does not consider intrinsic structure of images. In this paper, we extend L2BLDA to a two-dimensional Bhattacharyya bound linear discriminant analysis (2DBLDA). 2DBLDA maximizes the matrix-based between-class dista…
Zhijiang College, Zhejiang University of Technology（浙江工业大学之江学院）；Hainan University（海南大学）；China Agricultural University（中国农业大学）
In this paper, we propose a novel linear discriminant analysis criterion via the Bhattacharyya error bound estimation based on a novel L1-norm (L1BLDA) and L2-norm (L2BLDA). Both L1BLDA and L2BLDA maximize the between-class scatters which are measured by the weighted pairwise distances of class means and meanwhile minimize the within-class scatters under the L1-norm and L2-norm, respectively. The proposed models can avoid the small sample size (SSS) problem and have no rank limit that may encounter in LDA. It is worth mentioning that, the employment of L1-norm gives a robust performance of L1B…
Chongqing University（重庆大学）；School of Microelectronics and Communication Engineering（微电子与通信工程学院）
Unsupervised domain adaptation (UDA) aims to improve the classification performance on an unlabeled target domain by leveraging information from a fully labeled source domain. Recent approaches explore domain-invariant and class-discriminant representations to tackle this task. These methods, however, ignore the interaction between domain alignment learning and class discrimination learning. As a result, the missing or inadequate tradeoff between domain alignment and class discrimination are prone to the problem of negative transfer. In this paper, we propose Dynamic Weighted Learning (DWL) to…
Linear Discriminant Analysis (LDA) on Electronic Health Records (EHR) data is widely-used for early detection of diseases. Classical LDA for EHR data classification, however, suffers from two handicaps: the ill-posed estimation of LDA parameters (e.g., covariance matrix), and the "linear inseparability" of EHR data. To handle these two issues, in this paper, we propose a novel classifier FWDA -- Fast Wishart Discriminant Analysis, that makes predictions in an ensemble way. Specifically, FWDA first surrogates the distribution of inverse covariance matrices using a Wishart distribution estimated…
This paper proposes a discrimination technique for vertices in a weighted network. We assume that the edge weights and adjacencies in the network are conditionally independent and that both sources of information encode class membership information. In particular, we introduce a edge weight distribution matrix to the standard K-Block Stochastic Block Model to model weighted networks. This allows us to develop simple yet powerful extensions of classification techniques using the spectral embedding of the unweighted adjacency matrix. We consider two assumptions on the edge weight distributions a…
CNR-Institute of Intelligent Industrial Technologies and Systems for Advanced Manufacturing（意大利国家研究委员会智能工业技术与先进制造系统研究所）；Politecnico di Milano（米兰理工大学）
Hybrid system identification is a key tool to achieve reliable models of Cyber-Physical Systems from data. PieceWise Affine models guarantees universal approximation, local linearity and equivalence to other classes of hybrid system. Still, PWA identification is a challenging problem, requiring the concurrent solution of regression and classification tasks. In this work, we focus on the identification of PieceWise Auto Regressive with eXogenous input models with arbitrary regions (NPWARX), thus not restricted to polyhedral domains, and characterized by discontinuous maps. To this end, we propo…
Xi’an Jiaotong University（西安交通大学）；Monash University（莫纳什大学）；Wenzhou University（温州大学）；Qilu University of Technology（齐鲁工业大学）；Shandong Academy of Sciences（山东省科学院）；Northwestern Polytechnical University（西北工业大学）
Linear discriminant analysis (LDA) is a popular technique to learn the most discriminative features for multi-class classification. A vast majority of existing LDA algorithms are prone to be dominated by the class with very large deviation from the others, i.e., edge class, which occurs frequently in multi-class classification. First, the existence of edge classes often makes the total mean biased in the calculation of between-class scatter matrix. Second, the exploitation of l2-norm based between-class distance criterion magnifies the extremely large distance corresponding to edge class. In t…
Bridging visual saliency and large language models for explainable deep learning in medical imaging
Department of Mathematics and Computer science（数学与计算机科学系）；Institute of Cognitive Science（认知科学研究所）；Rhodes University（罗德斯大学）；National Institute for Theoretical and Computational Sciences (NITheCS)（理论与计算科学国家研究所）
Healthcare Technology and Innovation Center (HTIC), Indian Institute of Technology (IIT-M)（印度理工学院马德拉斯分校医疗技术与创新中心）；Indian Institute of Technology, Madras (IITM)（印度理工学院马德拉斯分校）
Cardiac arrhythmia is a prevalent and significant cause of morbidity and mortality among cardiac ailments. Early diagnosis is crucial in providing intervention for patients suffering from cardiac arrhythmia. Traditionally, diagnosis is performed by examination of the Electrocardiogram (ECG) by a cardiologist. This method of diagnosis is hampered by the lack of accessibility to expert cardiologists. For quite some time, signal processing methods had been used to automate arrhythmia diagnosis. However, these traditional methods require expert knowledge and are unable to model a wide range of arr…
A fast Non-linear and non-iterative learning and classification algorithm is synthesized and validated. This algorithm named the "Reverse Ripple Effect(R.R.E)", achieves 100% learning accuracy but is computationally expensive upon classification. The R.R.E is a (deterministic) algorithm that super imposes Gaussian weighted functions on training points. In this work, the R.R.E algorithm is compared against known learning and classification techniques/algorithms such as: the Perceptron Criterion algorithm, Linear Support Vector machines, the Linear Fisher Discriminant and a simple Neural Network…
Interpretable AI for Time-Series: Multi-Model Heatmap Fusion with Global Attention and NLP-Generated Explanations
Department of Electrical and Computer Engineering, Iowa State University, Ames, 50011 IA USA（电气与计算机工程系，爱荷华州立大学）；Department of Agricultural Biosystem Engineering, Iowa State University, Ames,IA 50011 USA（农业生物系统工程系，爱荷华州立大学）
