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
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.
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…
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…
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…
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 …
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…
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…
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…
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…
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）
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 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 …
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 …
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…
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…
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…
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 …
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…
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…
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…
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…
For many text classification tasks, there is a major problem posed by the lack of labeled data in a target domain. Although classifiers for a target domain can be trained on labeled text data from a related source domain, the accuracy of such classifiers is usually lower in the cross-domain setting. Recently, string kernels have obtained state-of-the-art results in various text classification tasks such as native language identification or automatic essay scoring. Moreover, classifiers based on string kernels have been found to be robust to the distribution gap between different domains. In th…
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…
A Bayes point machine is a single classifier that approximates the majority decision of an ensemble of classifiers. This paper observes that kernel interpolation is a Bayes point machine for Gaussian process classification. This observation facilitates the transfer of results from both ensemble theory as well as an area of convex geometry known as Brunn-Minkowski theory to derive PAC-Bayes risk bounds for kernel interpolation. Since large margin, infinite width neural networks are kernel interpolators, the paper's findings may help to explain generalisation in neural networks more broadly. Sup…
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…
We investigate quantum algorithms for classification, a fundamental problem in machine learning, with provable guarantees. Given $n$ $d$-dimensional data points, the state-of-the-art (and optimal) classical algorithm for training classifiers with constant margin runs in $\tilde{O}(n+d)$ time. We design sublinear quantum algorithms for the same task running in $\tilde{O}(\sqrt{n} +\sqrt{d})$ time, a quadratic improvement in both $n$ and $d$. Moreover, our algorithms use the standard quantization of the classical input and generate the same classical output, suggesting minimal overheads when use…
We revisit the additive model learning literature and adapt a penalized spline formulation due to Eilers and Marx, to train additive classifiers efficiently. We also propose two new embeddings based two classes of orthogonal basis with orthogonal derivatives, which can also be used to efficiently learn additive classifiers. This paper follows the popular theme in the current literature where kernel SVMs are learned much more efficiently using a approximate embedding and linear machine. In this paper we show that spline basis are especially well suited for learning additive models because of th…
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…
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…
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…
Southeast University（东南大学）；Université de Rennes 1（雷涅第一大学）
In order to classify the nonlinear feature with linear classifier and improve the classification accuracy, a deep learning network named kernel principal component analysis network (KPCANet) is proposed. First, mapping the data into higher space with kernel principal component analysis to make the data linearly separable. Then building a two-layer KPCANet to obtain the principal components of image. Finally, classifying the principal components with linearly classifier. Experimental results show that the proposed KPCANet is effective in face recognition, object recognition and hand-writing dig…
The least-squares support vector machine is a frequently used kernel method for non-linear regression and classification tasks. Here we discuss several approximation algorithms for the least-squares support vector machine classifier. The proposed methods are based on randomized block kernel matrices, and we show that they provide good accuracy and reliable scaling for multi-class classification problems with relatively large data sets. Also, we present several numerical experiments that illustrate the practical applicability of the proposed methods.
The area under the ROC curve (AUC) is a measure of interest in various machine learning and data mining applications. It has been widely used to evaluate classification performance on heavily imbalanced data. The kernelized AUC maximization machines have established a superior generalization ability compared to linear AUC machines because of their capability in modeling the complex nonlinear structure underlying most real-world data. However, the high training complexity renders the kernelized AUC machines infeasible for large-scale data. In this paper, we present two nonlinear AUC maximizatio…
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…
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）
AKBR: Learning Adaptive Kernel-based Representations for Graph Classification
School of Artificial Intelligence, Beijing Normal University（北京师范大学人工智能学院）；School of Information, Central University of Finance and Economics（中央财经大学信息学院）；Zhejiang Normal University（浙江师范大学）；School of Computer and Information Technology, Shanxi University（山西大学计算机与信息技术学院）；University of Illinois at Chicago（伊利诺伊大学芝加哥分校）；University of York（约克大学）
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…
Indian Institute of Technology Indore（印度理工学院印多尔分校）
Multi-kernel learning has been well explored in the recent past and has exhibited promising outcomes for multi-class classification and regression tasks. In this paper, we present a multiple kernel learning approach for the One-class Classification (OCC) task and employ it for anomaly detection. Recently, the basic multi-kernel approach has been proposed to solve the OCC problem, which is simply a convex combination of different kernels with equal weights. This paper proposes a Localized Multiple Kernel learning approach for Anomaly Detection (LMKAD) using OCC, where the weight for each kernel…
