Radial basis function kernel optimization for Support Vector Machine classifiers
University of Málaga（马拉加大学）；Biomedic Research Institute of Málaga (IBIMA)（马拉加生物医学研究所 (IBIMA)）；University of Michigan（密歇根大学）
Karl Thurnhofer-Hemsi, Ezequiel López-Rubio, Miguel A. Molina-Cabello, Kayvan Najarian
备注：
9 pages, 5 figures, 1 table (main paper), 8 pages, 6 figures, 2 tables (supplementary material). To be submitted to IEEE Transactions on Neural Networks and Learning Systems
Support Vector Machines (SVMs) are still one of the most popular and precise classifiers. The Radial Basis Function (RBF) kernel has been used in SVMs to separate among classes with considerable success. However, there is an intrinsic dependence on the initial value of the kernel hyperparameter. In this work, we propose OKSVM, an algorithm that automatically learns the RBF kernel hyperparameter and adjusts the SVM weights simultaneously. The proposed optimization technique is based on a gradient descent method. We analyze the performance of our approach with respect to the classical SVM for classification on synthetic and real data. Experimental results show that OKSVM performs better irrespective of the initial values of the RBF hyperparameter.
We propose a novel combination of optimization tools with learning theory bounds in order to analyze the sample complexity of optimal kernel sum classifiers. This contrasts the typical learning theoretic results which hold for all (potentially suboptimal) classifiers. Our work also justifies assumptions made in prior work on multiple kernel learning. As a byproduct of our analysis, we also provide a new form of Rademacher complexity for hypothesis classes containing only optimal classifiers.
Snap Research（Snap 研究院）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Microsoft Research（微软研究院）；National University of Singapore（新加坡国立大学）；Beckman Institute, University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校贝克曼研究所）
Similarity-based clustering and semi-supervised learning methods separate the data into clusters or classes according to the pairwise similarity between the data, and the pairwise similarity is crucial for their performance. In this paper, we propose a novel discriminative similarity learning framework which learns discriminative similarity for either data clustering or semi-supervised learning. The proposed framework learns classifier from each hypothetical labeling, and searches for the optimal labeling by minimizing the generalization error of the learned classifiers associated with the hyp…
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…
University of Science and Technology Beijing（北京科技大学）；Chinese Academy of Sciences（中国科学院）
Classifier ensemble generally should combine diverse component classifiers. However, it is difficult to give a definitive connection between diversity measure and ensemble accuracy. Given a list of available component classifiers, how to adaptively and diversely ensemble classifiers becomes a big challenge in the literature. In this paper, we argue that diversity, not direct diversity on samples but adaptive diversity with data, is highly correlated to ensemble accuracy, and we propose a novel technology for classifier ensemble, learning to diversify, which learns to adaptively combine classif…
Positive definite kernels and their associated Reproducing Kernel Hilbert Spaces provide a mathematically compelling and practically competitive framework for learning from data. In this paper we take the approximation theory point of view to explore various aspects of smooth kernels related to their inferential properties. We analyze eigenvalue decay of kernels operators and matrices, properties of eigenfunctions/eigenvectors and "Fourier" coefficients of functions in the kernel space restricted to a discrete set of data points. We also investigate the fitting capacity of kernels, giving expl…
Michigan State University（密歇根州立大学）；GE Global Research（通用电气全球研究中心）
In this paper, we study the problem of sparse multiple kernel learning (MKL), where the goal is to efficiently learn a combination of a fixed small number of kernels from a large pool that could lead to a kernel classifier with a small prediction error. We develop an efficient algorithm based on the greedy coordinate descent algorithm, that is able to achieve a geometric convergence rate under appropriate conditions. The convergence rate is achieved by measuring the size of functional gradients by an empirical $\ell_2$ norm that depends on the empirical data distribution. This is in contrast t…
People typically learn through exposure to visual concepts associated with linguistic descriptions. For instance, teaching visual object categories to children is often accompanied by descriptions in text or speech. In a machine learning context, these observations motivates us to ask whether this learning process could be computationally modeled to learn visual classifiers. More specifically, the main question of this work is how to utilize purely textual description of visual classes with no training images, to learn explicit visual classifiers for them. We propose and investigate two baseli…
Generalization performance of classifiers in deep learning has recently become a subject of intense study. Deep models, typically over-parametrized, tend to fit the training data exactly. Despite this "overfitting", they perform well on test data, a phenomenon not yet fully understood. The first point of our paper is that strong performance of overfitted classifiers is not a unique feature of deep learning. Using six real-world and two synthetic datasets, we establish experimentally that kernel machines trained to have zero classification or near zero regression error perform very well on test…
School of Information Systems（信息系统学院）；Singapore Management University（新加坡管理大学）；Institute for Infocomm Research (I2R)（资讯通信研究院（I2R））；A*STAR（新加坡科技研究局）
Online learning with multiple kernels has gained increasing interests in recent years and found many applications. For classification tasks, Online Multiple Kernel Classification (OMKC), which learns a kernel based classifier by seeking the optimal linear combination of a pool of single kernel classifiers in an online fashion, achieves superior accuracy and enjoys great flexibility compared with traditional single-kernel classifiers. Despite being studied extensively, existing OMKC algorithms suffer from high computational cost due to their unbounded numbers of support vectors. To overcome thi…
The University of Western Australia（西澳大利亚大学）；Karachi Institute of Economics and Technology（卡拉奇经济与技术学院）；Korea Advanced Institute of Science and Technology (KAIST)（韩国科学技术院）
A simple yet effective architectural design of radial basis function neural networks (RBFNN) makes them amongst the most popular conventional neural networks. The current generation of radial basis function neural network is equipped with multiple kernels which provide significant performance benefits compared to the previous generation using only a single kernel. In existing multi-kernel RBF algorithms, multi-kernel is formed by the convex combination of the base/primary kernels. In this paper, we propose a novel multi-kernel RBFNN in which every base kernel has its own (local) weight. This n…
POCKET: Pruning Random Convolution Kernels for Time Series Classification from a Feature Selection Perspective
State Key Laboratory of Radio Frequency Heterogeneous Integration (Shenzhen University)（射频异质集成国家重点实验室（深圳大学））；School of Electrical and Electronic Engineering, University College Dublin（都柏林大学学院电气与电子工程学院）
School of Computing and Augmented Intelligence（计算与增强智能学院）；Arizona State University（亚利桑那州立大学）；Baidu Research（百度研究院）
Similarity-based clustering methods separate data into clusters according to the pairwise similarity between the data, and the pairwise similarity is crucial for their performance. In this paper, we propose {\em Clustering by Discriminative Similarity (CDS)}, a novel method which learns discriminative similarity for data clustering. CDS learns an unsupervised similarity-based classifier from each data partition, and searches for the optimal partition of the data by minimizing the generalization error of the learnt classifiers associated with the data partitions. By generalization analysis via …
This paper presents a novel kernel-based generative classifier which is defined in a distortion subspace using polynomial series expansion, named Kernel-Distortion (KD) classifier. An iterative kernel selection algorithm is developed to steadily improve classification performance by repeatedly removing and adding kernels. The experimental results on character recognition application not only show that the proposed generative classifier performs better than many existing classifiers, but also illustrate that it has different recognition capability compared to the state-of-the-art discriminative…
Kernel methods have had great success in Statistics and Machine Learning. Despite their growing popularity, however, less effort has been drawn towards developing kernel based classification methods on Riemannian manifolds due to difficulty in dealing with non-Euclidean geometry. In this paper, motivated by the extrinsic framework of manifold-valued data analysis, we propose a new positive definite kernel on planar Kendall shape space $Σ_2^k$, called extrinsic Veronese Whitney Gaussian kernel. We show that our approach can be extended to develop Gaussian kernels on any embedded manifold. Furth…
Kernel based methods have shown effective performance in many remote sensing classification tasks. However their performance significantly depend on its hyper-parameters. The conventional technique to estimate the parameter comes with high computational complexity. Thus, the objective of this letter is to propose an fast and efficient method to select the bandwidth parameter of the Gaussian kernel in the kernel based classification methods. The proposed method is developed based on the operators in the reproducing kernel Hilbert space and it is evaluated on Support vector machines and PerTurbo…
Czech Technical University in Prague（布拉格捷克理工大学）；Czech Academy of Sciences（捷克科学院）
Many classification problems focus on maximizing the performance only on the samples with the highest relevance instead of all samples. As an example, we can mention ranking problems, accuracy at the top or search engines where only the top few queries matter. In our previous work, we derived a general framework including several classes of these linear classification problems. In this paper, we extend the framework to nonlinear classifiers. Utilizing a similarity to SVM, we dualize the problems, add kernels and propose a componentwise dual ascent method.
Support vector machines (SVM) and other kernel techniques represent a family of powerful statistical classification methods with high accuracy and broad applicability. Because they use all or a significant portion of the training data, however, they can be slow, especially for large problems. Piecewise linear classifiers are similarly versatile, yet have the additional advantages of simplicity, ease of interpretation and, if the number of component linear classifiers is not too large, speed. Here we show how a simple, piecewise linear classifier can be trained from a kernel-based classifier in…
Kernel method-based one-class classifier is mainly used for outlier or novelty detection. In this letter, kernel ridge regression (KRR) based one-class classifier (KOC) has been extended for learning using privileged information (LUPI). LUPI-based KOC method is referred to as KOC+. This privileged information is available as a feature with the dataset but only for training (not for testing). KOC+ utilizes the privileged information differently compared to normal feature information by using a so-called correction function. Privileged information helps KOC+ in achieving better generalization pe…
In this paper, we study the spectrum and the eigenvectors of radial kernels for mixtures of distributions in $\mathbb{R}^n$. Our approach focuses on high dimensions and relies solely on the concentration properties of the components in the mixture. We give several results describing of the structure of kernel matrices for a sample drawn from such a mixture. Based on these results, we analyze the ability of kernel PCA to cluster high dimensional mixtures. In particular, we exhibit a specific kernel leading to a simple spectral algorithm for clustering mixtures with possibly common means but dif…
Indian Institute of Technology Indore（印度理工学院印多尔分校）
A brain can detect outlier just by using only normal samples. Similarly, one-class classification (OCC) also uses only normal samples to train the model and trained model can be used for outlier detection. In this paper, a multi-layer architecture for OCC is proposed by stacking various Graph-Embedded Kernel Ridge Regression (KRR) based Auto-Encoders in a hierarchical fashion. These Auto-Encoders are formulated under two types of Graph-Embedding, namely, local and global variance-based embedding. This Graph-Embedding explores the relationship between samples and multi-layers of Auto-Encoder pr…
Kernel extreme learning machine (KELM) is a novel feedforward neural network, which is widely used in classification problems. To some extent, it solves the existing problems of the invalid nodes and the large computational complexity in ELM. However, the traditional KELM classifier usually has a low test accuracy when it faces multiclass classification problems. In order to solve the above problem, a new classifier, Mexican Hat wavelet KELM classifier, is proposed in this paper. The proposed classifier successfully improves the training accuracy and reduces the training time in the multiclass…
Abstract We present PAC-Bayesian bounds for the generalisation error of the K-nearest-neighbour classifier (K-NN). This is achieved by casting the K-NN classifier into a kernel space framework in the limit of vanishing kernel bandwidth. We establish a relation between prior measures over the coefficients in the kernel expansion and the induced measure on the weight vectors in kernel space. Defining a sparse prior over the coefficients allows the application of a PAC-Bayesian folk theorem that leads to a generalisation bound that is a function of the number of redundant training examples: those…
We prove that a particular deep network architecture is more efficient at approximating radially symmetric functions than the best known 2 or 3 layer networks. We use this architecture to approximate Gaussian kernel SVMs, and subsequently improve upon them with further training. The architecture and initial weights of the Deep Radial Kernel Network are completely specified by the SVM and therefore sidesteps the problem of empirically choosing an appropriate deep network architecture.
Support vector data description (SVDD) is a popular technique for detecting anomalies. The SVDD classifier partitions the whole space into an inlier region, which consists of the region near the training data, and an outlier region, which consists of points away from the training data. The computation of the SVDD classifier requires a kernel function, and the Gaussian kernel is a common choice for the kernel function. The Gaussian kernel has a bandwidth parameter, whose value is important for good results. A small bandwidth leads to overfitting, and the resulting SVDD classifier overestimates …
We combine K-means clustering with the least-squares kernel classification method. K-means clustering is used to extract a set of representative vectors for each class. The least-squares kernel method uses these representative vectors as a training set for the classification task. We show that this combination of unsupervised and supervised learning algorithms performs very well, and we illustrate this approach using the MNIST dataset
Frankfurt University of Applied Sciences（法兰克福应用科学大学）
The parameters of support vector machines (SVMs) such as the penalty parameter and the kernel parameters have a great impact on the classification accuracy and the complexity of the SVM model. Therefore, the model selection in SVM involves the tuning of these parameters. However, these parameters are usually tuned and used as a black box, without understanding the mathematical background or internal details. In this paper, the behavior of the SVM classification model is analyzed when these parameters take different values with balanced and imbalanced data. This analysis including visualization…
Indian Institute of Technology Indore（印度理工学院印多尔分校）；Nanyang Technological University（南洋理工大学）；Aarhus University（奥胡斯大学）
In this paper, a multi-layer architecture (in a hierarchical fashion) by stacking various Kernel Ridge Regression (KRR) based Auto-Encoder for one-class classification is proposed and is referred as MKOC. MKOC has many layers of Auto-Encoders to project the input features into new feature space and the last layer was regression based one class classifier. The Auto-Encoders use an unsupervised approach of learning and the final layer uses semi-supervised (trained by only positive samples) approach of learning. The proposed MKOC is experimentally evaluated on 15 publicly available benchmark data…
A Kernel Fisher Discriminant Analysis-Based Tree Ensemble Classifier: KFDA Forest
School of Industrial Management Engineering, Korea University（韩国大学工业管理工程学院）；School of Mechanical Engineering, Chungnam National University（Chungnam国立大学机械工程学院）
Indian Institute of Technology Indore（印度理工学院印多尔分校）
One-class classification (OCC) needs samples from only a single class to train the classifier. Recently, an auto-associative kernel extreme learning machine was developed for the OCC task. This paper introduces a novel extension of this classifier by embedding minimum variance information within its architecture and is referred to as VAAKELM. The minimum variance embedding forces the network output weights to focus in regions of low variance and reduces the intra-class variance. This leads to a better separation of target samples and outliers, resulting in an improvement in the generalization …
In this paper, we propose a special fusion method for combining ensembles of base classifiers utilizing new neural networks in order to improve overall efficiency of classification. While ensembles are designed such that each classifier is trained independently while the decision fusion is performed as a final procedure, in this method, we would be interested in making the fusion process more adaptive and efficient. This new combiner, called Neural Network Kernel Least Mean Square1, attempts to fuse outputs of the ensembles of classifiers. The proposed Neural Network has some special propertie…
Indian Institute of Technology Indore（印度理工学院印多尔分校）；Nanyang Technological University（南洋理工大学）
This paper presents an online learning with regularized kernel based one-class extreme learning machine (ELM) classifier and is referred as online RK-OC-ELM. The baseline kernel hyperplane model considers whole data in a single chunk with regularized ELM approach for offline learning in case of one-class classification (OCC). Further, the basic hyper plane model is adapted in an online fashion from stream of training samples in this paper. Two frameworks viz., boundary and reconstruction are presented to detect the target class in online RKOC-ELM. Boundary framework based one-class classifier …
As recent literature has demonstrated how classifiers often carry unintended biases toward some subgroups, deploying machine learned models to users demands careful consideration of the social consequences. How should we address this problem in a real-world system? How should we balance core performance and fairness metrics? In this paper, we introduce a MinDiff framework for regularizing classifiers toward different fairness metrics and analyze a technique with kernel-based statistical dependency tests. We run a thorough study on an academic dataset to compare the Pareto frontier achieved by …
Seoul National University（首尔国立大学）；Korea University（高丽大学）
Variable selection is essential in high-dimensional data analysis. Although various variable selection methods have been developed, most rely on the linear model assumption. This article proposes a nonparametric variable selection method for the large-margin classifier defined by reproducing the kernel Hilbert space (RKHS). we propose a gradient-based representation of the large-margin classifier and then regularize the gradient functions by the group-lasso penalty to obtain sparse gradients that naturally lead to the variable selection. The groupwise-majorization-decent algorithm (GMD, Yang a…
University of Birmingham（伯明翰大学）；Helsinki Institute for Information Technology（赫尔辛基信息技术研究所）；Aalto University（阿尔托大学）
Indefinite similarity measures can be frequently found in bio-informatics by means of alignment scores, but are also common in other fields like shape measures in image retrieval. Lacking an underlying vector space, the data are given as pairwise similarities only. The few algorithms available for such data do not scale to larger datasets. Focusing on probabilistic batch classifiers, the Indefinite Kernel Fisher Discriminant (iKFD) and the Probabilistic Classification Vector Machine (PCVM) are both effective algorithms for this type of data but, with cubic complexity. Here we propose an extens…
University of British Columbia（不列颠哥伦比亚大学）；Technische Universität Darmstadt（达姆施塔特工业大学）；Stewart Blusson Quantum Matter Institute（斯图尔特·布吕松量子物质研究所）
Machine learning is considered to be one of the most promising applications of quantum computing. Therefore, the search for quantum advantage of the quantum analogues of machine learning models is a key research goal. Here, we show that variational quantum classifiers and support vector machines with quantum kernels can solve a classification problem based on the $k$-Forrelation problem, which is known to be PromiseBQP-complete. Because the PromiseBQP complexity class includes all Bounded-Error Quantum Polynomial-Time (BQP) decision problems, our results imply that there exists a feature map a…
University of Science and Technology of China（中国科学技术大学）
In this paper, we focus on subspace-based learning problems, where data elements are linear subspaces instead of vectors. To handle this kind of data, Grassmann kernels were proposed to measure the space structure and used with classifiers, e.g., Support Vector Machines (SVMs). However, the existing discriminative algorithms mostly ignore the instability of subspaces, which would cause the classifiers misled by disturbed instances. Thus we propose considering all potential disturbance of subspaces in learning processes to obtain more robust classifiers. Firstly, we derive the dual optimization…
University College London（伦敦大学学院）；Laval University（拉瓦尔大学）
In this paper, we correct an upper bound, presented in~\cite{hs-11}, on the generalisation error of classifiers learned through multiple kernel learning. The bound in~\cite{hs-11} uses Rademacher complexity and has an\emph{additive} dependence on the logarithm of the number of kernels and the margin achieved by the classifier. However, there are some errors in parts of the proof which are corrected in this paper. Unfortunately, the final result turns out to be a risk bound which has a \emph{multiplicative} dependence on the logarithm of the number of kernels and the margin achieved by the clas…
National Time Service Center, Chinese Academy of Sciences（中国科学院国家授时中心）；Graduate University of Chinese Academy of Sciences（中国科学院研究生院）；Cornell University（康奈尔大学）；Lehigh University（理海大学）；Tulane University（杜兰大学）
In this paper, we propose a multi-kernel classifier learning algorithm to optimize a given nonlinear and nonsmoonth multivariate classifier performance measure. Moreover, to solve the problem of kernel function selection and kernel parameter tuning, we proposed to construct an optimal kernel by weighted linear combination of some candidate kernels. The learning of the classifier parameter and the kernel weight are unified in a single objective function considering to minimize the upper boundary of the given multivariate performance measure. The objective function is optimized with regard to cl…
University of Toronto（多伦多大学）；Concordia University（康考迪亚大学）
Random convolution kernel transform (Rocket) is a fast, efficient, and novel approach for time series feature extraction using a large number of independent randomly initialized 1-D convolution kernels of different configurations. The output of the convolution operation on each time series is represented by a partial positive value (PPV). A concatenation of PPVs from all kernels is the input feature vector to a Ridge regression classifier. Unlike typical deep learning models, the kernels are not trained and there is no weighted/trainable connection between kernels or concatenated features and …
Multithreshold Entropy Linear Classifier (MELC) is a density based model which searches for a linear projection maximizing the Cauchy-Schwarz Divergence of dataset kernel density estimation. Despite its good empirical results, one of its drawbacks is the optimization speed. In this paper we analyze how one can speed it up through solving an approximate problem. We analyze two methods, both similar to the approximate solutions of the Kernel Density Estimation querying and provide adaptive schemes for selecting a crucial parameters based on user-specified acceptable error. Furthermore we show ho…
In this paper we propose a multi-task linear classifier learning problem called D-SVM (Dictionary SVM). D-SVM uses a dictionary of parameter covariance shared by all tasks to do multi-task knowledge transfer among different tasks. We formally define the learning problem of D-SVM and show two interpretations of this problem, from both the probabilistic and kernel perspectives. From the probabilistic perspective, we show that our learning formulation is actually a MAP estimation on all optimization variables. We also show its equivalence to a multiple kernel learning problem in which one is tryi…
Indian Institute of Technology Indore（印度理工学院印多尔分校）；Microsoft ATC（微软先进技术中心）
One-Class Classification (OCC) has been prime concern for researchers and effectively employed in various disciplines. But, traditional methods based one-class classifiers are very time consuming due to its iterative process and various parameters tuning. In this paper, we present six OCC methods based on extreme learning machine (ELM) and Online Sequential ELM (OSELM). Our proposed classifiers mainly lie in two categories: reconstruction based and boundary based, which supports both types of learning viz., online and offline learning. Out of various proposed methods, four are offline and rema…
The problem of development of the SVM classifier based on the modified particle swarm optimization has been considered. This algorithm carries out the simultaneous search of the kernel function type, values of the kernel function parameters and value of the regularization parameter for the SVM classifier. Such SVM classifier provides the high quality of data classification. The idea of particles' «regeneration» is put on the basis of the modified particle swarm optimization algorithm. At the realization of this idea, some particles change their kernel function type to the one which corresponds…
INFOTEC Centro de Investigación e Innovación en Tecnologías de la Información y Comunicación（INFOTEC信息与通信技术研究与创新中心）；Universidad Michoacana de San Nicolás de Hidalgo（米却肯州圣尼古拉斯·伊达尔戈大学）；CONACyT Consejo Nacional de Ciencia y Tecnología（国家科学技术委员会）
Improving the performance of classifiers is the realm of feature mapping, prototype selection, and kernel function transformations; these techniques aim for reducing the complexity, and also, improving the accuracy of models. In particular, our objective is to combine them to transform data's shape into another more convenient distribution; such that some simple algorithms, such as Naïve Bayes or k-Nearest Neighbors, can produce competitive classifiers. In this paper, we introduce a family of classifiers based on feature mapping and kernel functions, orchestrated by a model selection scheme th…
Based on the experimental results, all concepts drift types have their respective hyperparameter configurations. Simple and gradual concept drift have similar pattern which requires a smaller α value than recurring concept drift because, in this type of drift, a new concept appear continuously, so it needs a high-frequency model adaptation. However, in recurring concepts, the new concept may repeat in the future, so the lower frequency adaptation is better. Furthermore, high-frequency model adaptation could lead to an overfitting problem. Implementing CMGMM component pruning mechanism help to …
Neural Networks and Deep Learning lab.（神经网络与深度学习实验室）；Moscow Institute of Physics and Technology（莫斯科物理技术学院）
Recent research has been focused on two different approaches to studying neural networks training in the limit of infinite width (1) a mean-field (MF) and (2) a constant neural tangent kernel (NTK) approximations. These two approaches have different scaling of hyperparameters with the width of a network layer and as a result, different infinite-width limit models. We propose a general framework to study how the limit behavior of neural models depends on the scaling of hyperparameters with network width. Our framework allows us to derive scaling for existing MF and NTK limits, as well as an unc…
AUC (Area under the ROC curve) is an important performance measure for applications where the data is highly imbalanced. Learning to maximize AUC performance is thus an important research problem. Using a max-margin based surrogate loss function, AUC optimization problem can be approximated as a pairwise rankSVM learning problem. Batch learning methods for solving the kernelized version of this problem suffer from scalability and may not result in sparse classifiers. Recent years have witnessed an increased interest in the development of online or single-pass online learning algorithms that de…
Bilkent university（比尔肯特大学）；university of Surrey（萨里大学）
The paper introduces a new efficient nonlinear one-class classifier formulated as the Rayleigh quotient criterion optimisation. The method, operating in a reproducing kernel Hilbert space, minimises the scatter of target distribution along an optimal projection direction while at the same time keeping projections of positive observations distant from the mean of the negative class. We provide a graph embedding view of the problem which can then be solved efficiently using the spectral regression approach. In this sense, unlike previous similar methods which often require costly eigen-computati…
University of Texas Southwestern Medical Center（德克萨斯大学西南医学中心）
Most statistical classifiers are designed to find patterns in data where numbers fit into rows and columns, like in a spreadsheet, but many kinds of data do not conform to this structure. To uncover patterns in non-conforming data, we describe an approach for modifying established statistical classifiers to handle non-conforming data, which we call dynamic kernel matching (DKM). As examples of non-conforming data, we consider (i) a dataset of T-cell receptor (TCR) sequences labelled by disease antigen and (ii) a dataset of sequenced TCR repertoires labelled by patient cytomegalovirus (CMV) ser…
