Efficient Classification for Metric Data

Recent advances in large-margin classification of data residing in general metric spaces (rather than Hilbert spaces) enable classification under various natural metrics, such as string edit and earthmover distance. A general framework developed for this purpose by von Luxburg and Bousquet [JMLR, 2004] left open the questions of computational efficiency and of providing direct bounds on generalization error. We design a new algorithm for classification in general metric spaces, whose runtime and accuracy depend on the doubling dimension of the data points, and can thus achieve superior classification performance in many common scenarios. The algorithmic core of our approach is an approximate (rather than exact) solution to the classical problems of Lipschitz extension and of Nearest Neighbor Search. The algorithm's generalization performance is guaranteed via the fat-shattering dimension of Lipschitz classifiers, and we present experimental evidence of its superiority to some common kernel methods. As a by-product, we offer a new perspective on the nearest neighbor classifier, which yields significantly sharper risk asymptotics than the classic analysis of Cover and Hart [IEEE Trans. Info. Theory, 1967].Comment: This is the full version of an extended abstract that appeared in Proceedings of the 23rd COLT, 201

Face Identification by a Cascade of Rejection Classifiers

Nearest neighbor search is commonly employed in face recognition but it does not scale well to large dataset sizes. A strategy to combine rejection classifiers into a cascade for face identification is proposed in this paper. A rejection classifier for a pair of classes is defined to reject at least one of the classes with high confidence. These rejection classifiers are able to share discriminants in feature space and at the same time have high confidence in the rejection decision. In the face identification problem, it is possible that a pair of known individual faces are very dissimilar. It is very unlikely that both of them are close to an unknown face in the feature space. Hence, only one of them needs to be considered. Using a cascade structure of rejection classifiers, the scope of nearest neighbor search can be reduced significantly. Experiments on Face Recognition Grand Challenge (FRGC) version 1 data demonstrate that the proposed method achieves significant speed up and an accuracy comparable with the brute force Nearest Neighbor method. In addition, a graph cut based clustering technique is employed to demonstrate that the pairwise separability of these rejection classifiers is capable of semantic grouping.National Science Foundation (EIA-0202067, IIS-0329009); Office of Naval Research (N00014-03-1-0108

Study and Observation of the Variation of Accuracies of KNN, SVM, LMNN, ENN Algorithms on Eleven Different Datasets from UCI Machine Learning Repository

Machine learning qualifies computers to assimilate with data, without being solely programmed [1, 2]. Machine learning can be classified as supervised and unsupervised learning. In supervised learning, computers learn an objective that portrays an input to an output hinged on training input-output pairs [3]. Most efficient and widely used supervised learning algorithms are K-Nearest Neighbors (KNN), Support Vector Machine (SVM), Large Margin Nearest Neighbor (LMNN), and Extended Nearest Neighbor (ENN). The main contribution of this paper is to implement these elegant learning algorithms on eleven different datasets from the UCI machine learning repository to observe the variation of accuracies for each of the algorithms on all datasets. Analyzing the accuracy of the algorithms will give us a brief idea about the relationship of the machine learning algorithms and the data dimensionality. All the algorithms are developed in Matlab. Upon such accuracy observation, the comparison can be built among KNN, SVM, LMNN, and ENN regarding their performances on each dataset.Comment: To be published in the 4th IEEE International Conference on Electrical Engineering and Information & Communication Technology (iCEEiCT 2018

Comparison of Feature Selection and Classification for MALDI-MS Data

Introduction: In the classification of Mass Spectrometry (MS) proteomics data, peak detection, feature selection, and learning classifiers are critical to classification accuracy. To better understand which methods are more accurate when classifying data, some publicly available peak detection algorithms for Matrix assisted Laser Desorption Ionization Mass Spectrometry (MALDI-MS) data were recently compared; however, the issue of different feature selection methods and different classification models as they relate to classification performance has not been addressed. With the application of intelligent computing, much progress has been made in the development of feature selection methods and learning classifiers for the analysis of high-throughput biological data. The main objective of this paper is to compare the methods of feature selection and different learning classifiers when applied to MALDI-MS data and to provide a subsequent reference for the analysis of MS proteomics data. Results: We compared a well-known method of feature selection, Support Vector Machine Recursive Feature Elimination (SVMRFE), and a recently developed method, Gradient based Leave-one-out Gene Selection (GLGS) that effectively performs microarray data analysis. We also compared several learning classifiers including K-Nearest Neighbor Classifier (KNNC), Naïve Bayes Classifier (NBC), Nearest Mean Scaled Classifier (NMSC), uncorrelated normal based quadratic Bayes Classifier recorded as UDC, Support Vector Machines, and a distance metric learning for Large Margin Nearest Neighbor classifier (LMNN) based on Mahanalobis distance. To compare, we conducted a comprehensive experimental study using three types of MALDI-MS data. Conclusion: Regarding feature selection, SVMRFE outperformed GLGS in classification. As for the learning classifiers, when classification models derived from the best training were compared, SVMs performed the best with respect to the expected testing accuracy. However, the distance metric learning LMNN outperformed SVMs and other classifiers on evaluating the best testing. In such cases, the optimum classification model based on LMNN is worth investigating for future study

Classification with the nearest neighbor rule in general finite dimensional spaces: necessary and sufficient conditions

Given an $n$-sample of random vectors $(X_i,Y_i)_{1 \leq i \leq n}$ whose joint law is unknown, the long-standing problem of supervised classification aims to \textit{optimally} predict the label $Y$ of a given a new observation $X$. In this context, the nearest neighbor rule is a popular flexible and intuitive method in non-parametric situations. Even if this algorithm is commonly used in the machine learning and statistics communities, less is known about its prediction ability in general finite dimensional spaces, especially when the support of the density of the observations is $\mathbb{R}^d$. This paper is devoted to the study of the statistical properties of the nearest neighbor rule in various situations. In particular, attention is paid to the marginal law of $X$, as well as the smoothness and margin properties of the \textit{regression function} $\eta(X) = \mathbb{E}[Y | X]$. We identify two necessary and sufficient conditions to obtain uniform consistency rates of classification and to derive sharp estimates in the case of the nearest neighbor rule. Some numerical experiments are proposed at the end of the paper to help illustrate the discussion.Comment: 53 Pages, 3 figure

Stabilized Nearest Neighbor Classifier and Its Statistical Properties

The stability of statistical analysis is an important indicator for reproducibility, which is one main principle of scientific method. It entails that similar statistical conclusions can be reached based on independent samples from the same underlying population. In this paper, we introduce a general measure of classification instability (CIS) to quantify the sampling variability of the prediction made by a classification method. Interestingly, the asymptotic CIS of any weighted nearest neighbor classifier turns out to be proportional to the Euclidean norm of its weight vector. Based on this concise form, we propose a stabilized nearest neighbor (SNN) classifier, which distinguishes itself from other nearest neighbor classifiers, by taking the stability into consideration. In theory, we prove that SNN attains the minimax optimal convergence rate in risk, and a sharp convergence rate in CIS. The latter rate result is established for general plug-in classifiers under a low-noise condition. Extensive simulated and real examples demonstrate that SNN achieves a considerable improvement in CIS over existing nearest neighbor classifiers, with comparable classification accuracy. We implement the algorithm in a publicly available R package snn.Comment: 48 Pages, 11 Figures. To Appear in JASA--T&

Comparison of feature selection and classification for MALDI-MS data

INTRODUCTION: In the classification of Mass Spectrometry (MS) proteomics data, peak detection, feature selection, and learning classifiers are critical to classification accuracy. To better understand which methods are more accurate when classifying data, some publicly available peak detection algorithms for Matrix assisted Laser Desorption Ionization Mass Spectrometry (MALDI-MS) data were recently compared; however, the issue of different feature selection methods and different classification models as they relate to classification performance has not been addressed. With the application of intelligent computing, much progress has been made in the development of feature selection methods and learning classifiers for the analysis of high-throughput biological data. The main objective of this paper is to compare the methods of feature selection and different learning classifiers when applied to MALDI-MS data and to provide a subsequent reference for the analysis of MS proteomics data. RESULTS: We compared a well-known method of feature selection, Support Vector Machine Recursive Feature Elimination (SVMRFE), and a recently developed method, Gradient based Leave-one-out Gene Selection (GLGS) that effectively performs microarray data analysis. We also compared several learning classifiers including K-Nearest Neighbor Classifier (KNNC), Naïve Bayes Classifier (NBC), Nearest Mean Scaled Classifier (NMSC), uncorrelated normal based quadratic Bayes Classifier recorded as UDC, Support Vector Machines, and a distance metric learning for Large Margin Nearest Neighbor classifier (LMNN) based on Mahanalobis distance. To compare, we conducted a comprehensive experimental study using three types of MALDI-MS data. CONCLUSION: Regarding feature selection, SVMRFE outperformed GLGS in classification. As for the learning classifiers, when classification models derived from the best training were compared, SVMs performed the best with respect to the expected testing accuracy. However, the distance metric learning LMNN outperformed SVMs and other classifiers on evaluating the best testing. In such cases, the optimum classification model based on LMNN is worth investigating for future study

Maximum Margin Multiclass Nearest Neighbors

We develop a general framework for margin-based multicategory classification in metric spaces. The basic work-horse is a margin-regularized version of the nearest-neighbor classifier. We prove generalization bounds that match the state of the art in sample size $n$ and significantly improve the dependence on the number of classes $k$. Our point of departure is a nearly Bayes-optimal finite-sample risk bound independent of $k$. Although $k$-free, this bound is unregularized and non-adaptive, which motivates our main result: Rademacher and scale-sensitive margin bounds with a logarithmic dependence on $k$. As the best previous risk estimates in this setting were of order $\sqrt k$, our bound is exponentially sharper. From the algorithmic standpoint, in doubling metric spaces our classifier may be trained on $n$ examples in $O(n^2\log n)$ time and evaluated on new points in $O(\log n)$ time

Efficient discriminative learning of parametric nearest neighbor classifiers

Linear SVMs are efficient in both training and testing, however the data in real applications is rarely linearly separable. Non-linear kernel SVMs are too computationally intensive for applications with large-scale data sets. Recently locally linear classifiers have gained popularity due to their efficiency whilst remaining competitive with kernel methods. The vanilla nearest neighbor algorithm is one of the simplest locally linear classifiers, but it lacks robustness due to the noise often present in real-world data. In this paper, we introduce a novel local classifier, Parametric Nearest Neighbor (P-NN) and its extension Ensemble of P-NN (EP-NN). We parameterize the nearest neighbor algorithm based on the minimum weighted squared Euclidean distances between the data points and the prototypes, where a prototype is represented by a locally linear combination of some data points. Meanwhile, our method attempts to jointly learn both the prototypes and the classifier parameters discriminatively via max-margin. This makes our classifiers suitable to approximate the classification decision boundaries locally based on nonlinear functions. During testing, the computational complexity of both classifiers is linear in the product of the dimension of data and the number of prototypes. Our classification results on MNIST, USPS, LETTER, and Chars 74K are comparable and in some cases are better than many other methods such as the state-of-the-art locally linear classifiers