Two Criteria for Model Selection in Multiclass Support Vector Machines

Practical applications call for efficient model selection criteria for multiclass support vector machine (SVM) classification. To solve this problem, this paper develops two model selection criteria by combining or redefining the radius–margin bound used in binary SVMs. The combination is justified by linking the test error rate of a multiclass SVM with that of a set of binary SVMs. The redefinition, which is relatively heuristic, is inspired by the conceptual relationship between the radius–margin bound and the class separability measure. Hence, the two criteria are developed from the perspective of model selection rather than a generalization of the radius–margin bound for multiclass SVMs. As demonstrated by extensive experimental study, the minimization of these two criteria achieves good model selection on most data sets. Compared with the k-fold cross validation which is often regarded as a benchmark, these two criteria give rise to comparable performance with much less computational overhead, particularly when a large number of model parameters are to be optimized

Support Vector Machine Implementations for Classification & Clustering

BACKGROUND: We describe Support Vector Machine (SVM) applications to classification and clustering of channel current data. SVMs are variational-calculus based methods that are constrained to have structural risk minimization (SRM), i.e., they provide noise tolerant solutions for pattern recognition. The SVM approach encapsulates a significant amount of model-fitting information in the choice of its kernel. In work thus far, novel, information-theoretic, kernels have been successfully employed for notably better performance over standard kernels. Currently there are two approaches for implementing multiclass SVMs. One is called external multi-class that arranges several binary classifiers as a decision tree such that they perform a single-class decision making function, with each leaf corresponding to a unique class. The second approach, namely internal-multiclass, involves solving a single optimization problem corresponding to the entire data set (with multiple hyperplanes). RESULTS: Each SVM approach encapsulates a significant amount of model-fitting information in its choice of kernel. In work thus far, novel, information-theoretic, kernels were successfully employed for notably better performance over standard kernels. Two SVM approaches to multiclass discrimination are described: (1) internal multiclass (with a single optimization), and (2) external multiclass (using an optimized decision tree). We describe benefits of the internal-SVM approach, along with further refinements to the internal-multiclass SVM algorithms that offer significant improvement in training time without sacrificing accuracy. In situations where the data isn't clearly separable, making for poor discrimination, signal clustering is used to provide robust and useful information – to this end, novel, SVM-based clustering methods are also described. As with the classification, there are Internal and External SVM Clustering algorithms, both of which are briefly described

Geometric Approach to Support Vector Machines Learning for Large Datasets

The dissertation introduces Sphere Support Vector Machines (SphereSVM) and Minimal Norm Support Vector Machines (MNSVM) as the new fast classification algorithms that use geometrical properties of the underlying classification problems to efficiently obtain models describing training data. SphereSVM is based on combining minimal enclosing ball approach, state of the art nearest point problem solvers and probabilistic techniques. The blending of the three speeds up the training phase of SVMs significantly and reaches similar (i.e., practically the same) accuracy as the other classification models over several big and large real data sets within the strict validation frame of a double (nested) cross-validation (CV). MNSVM is further simplification of SphereSVM algorithm. Here, relatively complex classification task was converted into one of the simplest geometrical problems -- minimal norm problem. This resulted in additional speedup compared to SphereSVM. The results shown are promoting both SphereSVM and MNSVM as outstanding alternatives for handling large and ultra-large datasets in a reasonable time without switching to various parallelization schemes for SVMs algorithms proposed recently. The variants of both algorithms, which work without explicit bias term, are also presented. In addition, other techniques aiming to improve the time efficiency are discussed (such as over-relaxation and improved support vector selection scheme). Finally, the accuracy and performance of all these modifications are carefully analyzed and results based on nested cross-validation procedure are shown

Clustering Via Supervised Support Vector Machines

An SVM-based clustering algorithm is introduced that clusters data with no a priori knowledge of input classes. The algorithm initializes by first running a binary SVM classifier against a data set with each vector in the set randomly labeled. Once this initialization step is complete, the SVM confidence parameters for classification on each of the training instances can be accessed. The lowest confidence data (e.g., the worst of the mislabeled data) then has its labels switched to the other class label. The SVM is then re-run on the data set (with partly re-labeled data). The repetition of the above process improves the separability until there is no misclassification. Variations on this type of clustering approach are shown

Clustering Via Supervised Support Vector Machines

An SVM-based clustering algorithm is introduced that clusters data with no a priori knowledge of input classes. The algorithm initializes by first running a binary SVM classifier against a data set with each vector in the set randomly labeled. Once this initialization step is complete, the SVM confidence parameters for classification on each of the training instances can be accessed. The lowest confidence data (e.g., the worst of the mislabeled data) then has its labels switched to the other class label. The SVM is then re-run on the data set (with partly re-labeled data). The repetition of the above process improves the separability until there is no misclassification. Variations on this type of clustering approach are shown

Support Vector Methods for Higher-Level Event Extraction in Point Data

Phenomena occur both in space and time. Correspondingly, ability to model spatiotemporal behavior translates into ability to model phenomena as they occur in reality. Given the complexity inherent when integrating spatial and temporal dimensions, however, the establishment of computational methods for spatiotemporal analysis has proven relatively elusive. Nonetheless, one method, the spatiotemporal helix, has emerged from the field of video processing. Designed to efficiently summarize and query the deformation and movement of spatiotemporal events, the spatiotemporal helix has been demonstrated as capable of describing and differentiating the evolution of hurricanes from sequences of images. Being derived from image data, the representations of events for which the spatiotemporal helix was originally created appear in areal form (e.g., a hurricane covering several square miles is represented by groups of pixels). ii Many sources of spatiotemporal data, however, are not in areal form and instead appear as points. Examples of spatiotemporal point data include those from an epidemiologist recording the time and location of cases of disease and environmental observations collected by a geosensor at the point of its location. As points, these data cannot be directly incorporated into the spatiotemporal helix for analysis. However, with the analytic potential for clouds of point data limited, phenomena represented by point data are often described in terms of events. Defined as change units localized in space and time, the concept of events allows for analysis at multiple levels. For instance lower-level events refer to occurrences of interest described by single data streams at point locations (e.g., an individual case of a certain disease or a significant change in chemical concentration in the environment) while higher-level events describe occurrences of interest derived from aggregations of lower-level events and are frequently described in areal form (e.g., a disease cluster or a pollution cloud). Considering that these higher-level events appear in areal form, they could potentially be incorporated into the spatiotemporal helix. With deformation being an important element of spatiotemporal analysis, however, at the crux of a process for spatiotemporal analysis based on point data would be accurate translation of lower-level event points into representations of higher-level areal events. A limitation of current techniques for the derivation of higher-level events is that they imply bias a priori regarding the shape of higher-level events (e.g., elliptical, convex, linear) which could limit the description of the deformation of higher-level events over time. The objective of this research is to propose two newly developed kernel methods, support vector clustering (SVC) and support vector machines (SVMs), as means for iii translating lower-level event points into higher-level event areas that follow the distribution of lower-level points. SVC is suggested for the derivation of higher-level events arising in point process data while SVMs are explored for their potential with scalar field data (i.e., spatially continuous real-valued data). Developed in the field of machine learning to solve complex non-linear problems, both of these methods are capable of producing highly non-linear representations of higher-level events that may be more suitable than existing methods for spatiotemporal analysis of deformation. To introduce these methods, this thesis is organized so that a context for these methods is first established through a description of existing techniques. This discussion leads to a technical explanation of the mechanics of SVC and SVMs and to the implementation of each of the kernel methods on simulated datasets. Results from these simulations inform discussion regarding the application potential of SVC and SVMs

A Quadratic Loss Multi-Class SVM for which a Radius-Margin Bound Applies

International audienceTo set the values of the hyperparameters of a support vector machine (SVM), the method of choice is cross-validation. Several upper bounds on the leave-one-out error of the pattern recognition SVM have been derived. One of the most popular is the radius-margin bound. It applies to the hard margin machine, and, by extension, to the 2-norm SVM. In this article, we introduce the first quadratic loss multi-class SVM: the M-SVM^2. It can be seen as a direct extension of the 2-norm SVM to the multi-class case, which we establish by deriving the corresponding generalized radius-margin bound