Differentiable Kernels in Generalized Matrix Learning Vector Quantization

In the present paper we investigate the application of differentiable kernel for generalized matrix learning vector quantization as an alternative kernel-based classifier, which additionally provides classification dependent data visualization. We show that the concept of differentiable kernels allows a prototype description in the data space but equipped with the kernel metric. Moreover, using the visualization properties of the original matrix learning vector quantization we are able to optimize the class visualization by inherent visualization mapping learning also in this new kernel-metric data space

Robustness of Generalized Learning Vector Quantization Models against Adversarial Attacks

Adversarial attacks and the development of (deep) neural networks robust against them are currently two widely researched topics. The robustness of Learning Vector Quantization (LVQ) models against adversarial attacks has however not yet been studied to the same extent. We therefore present an extensive evaluation of three LVQ models: Generalized LVQ, Generalized Matrix LVQ and Generalized Tangent LVQ. The evaluation suggests that both Generalized LVQ and Generalized Tangent LVQ have a high base robustness, on par with the current state-of-the-art in robust neural network methods. In contrast to this, Generalized Matrix LVQ shows a high susceptibility to adversarial attacks, scoring consistently behind all other models. Additionally, our numerical evaluation indicates that increasing the number of prototypes per class improves the robustness of the models.Comment: to be published in 13th International Workshop on Self-Organizing Maps and Learning Vector Quantization, Clustering and Data Visualizatio

Integration of Auxiliary Data Knowledge in Prototype Based Vector Quantization and Classification Models

This thesis deals with the integration of auxiliary data knowledge into machine learning methods especially prototype based classification models. The problem of classification is diverse and evaluation of the result by using only the accuracy is not adequate in many applications. Therefore, the classification tasks are analyzed more deeply. Possibilities to extend prototype based methods to integrate extra knowledge about the data or the classification goal is presented to obtain problem adequate models. One of the proposed extensions is Generalized Learning Vector Quantization for direct optimization of statistical measurements besides the classification accuracy. But also modifying the metric adaptation of the Generalized Learning Vector Quantization for functional data, i. e. data with lateral dependencies in the features, is considered.:Symbols and Abbreviations 1 Introduction 1.1 Motivation and Problem Description . . . . . . . . . . . . . . . . . 1 1.2 Utilized Data Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 Prototype Based Methods 19 2.1 Unsupervised Vector Quantization . . . . . . . . . . . . . . . . . . 22 2.1.1 C-means . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.1.2 Self-Organizing Map . . . . . . . . . . . . . . . . . . . . . . 25 2.1.3 Neural Gas . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.1.4 Common Generalizations . . . . . . . . . . . . . . . . . . . 30 2.2 Supervised Vector Quantization . . . . . . . . . . . . . . . . . . . . 35 2.2.1 The Family of Learning Vector Quantizers - LVQ . . . . . . 36 2.2.2 Generalized Learning Vector Quantization . . . . . . . . . 38 2.3 Semi-Supervised Vector Quantization . . . . . . . . . . . . . . . . 42 2.3.1 Learning Associations by Self-Organization . . . . . . . . . 42 2.3.2 Fuzzy Labeled Self-Organizing Map . . . . . . . . . . . . . 43 2.3.3 Fuzzy Labeled Neural Gas . . . . . . . . . . . . . . . . . . 45 2.4 Dissimilarity Measures . . . . . . . . . . . . . . . . . . . . . . . . . 47 2.4.1 Differentiable Kernels in Generalized LVQ . . . . . . . . . 52 2.4.2 Dissimilarity Adaptation for Performance Improvement . 56 3 Deeper Insights into Classification Problems - From the Perspective of Generalized LVQ- 81 3.1 Classification Models . . . . . . . . . . . . . . . . . . . . . . . . . . 81 3.2 The Classification Task . . . . . . . . . . . . . . . . . . . . . . . . . 84 3.3 Evaluation of Classification Results . . . . . . . . . . . . . . . . . . 88 3.4 The Classification Task as an Ill-Posed Problem . . . . . . . . . . . 92 4 Auxiliary Structure Information and Appropriate Dissimilarity Adaptation in Prototype Based Methods 93 4.1 Supervised Vector Quantization for Functional Data . . . . . . . . 93 4.1.1 Functional Relevance/Matrix LVQ . . . . . . . . . . . . . . 95 4.1.2 Enhancement Generalized Relevance/Matrix LVQ . . . . 109 4.2 Fuzzy Information About the Labels . . . . . . . . . . . . . . . . . 121 4.2.1 Fuzzy Semi-Supervised Self-Organizing Maps . . . . . . . 122 4.2.2 Fuzzy Semi-Supervised Neural Gas . . . . . . . . . . . . . 123 5 Variants of Classification Costs and Class Sensitive Learning 137 5.1 Border Sensitive Learning in Generalized LVQ . . . . . . . . . . . 137 5.1.1 Border Sensitivity by Additive Penalty Function . . . . . . 138 5.1.2 Border Sensitivity by Parameterized Transfer Function . . 139 5.2 Optimizing Different Validation Measures by the Generalized LVQ 147 5.2.1 Attention Based Learning Strategy . . . . . . . . . . . . . . 148 5.2.2 Optimizing Statistical Validation Measurements for Binary Class Problems in the GLVQ . . . . . . . . . . . . . 155 5.3 Integration of Structural Knowledge about the Labeling in Fuzzy Supervised Neural Gas . . . . . . . . . . . . . . . . . . . . . . . . . 160 6 Conclusion and Future Work 165 My Publications 168 A Appendix 173 A.1 Stochastic Gradient Descent (SGD) . . . . . . . . . . . . . . . . . . 173 A.2 Support Vector Machine . . . . . . . . . . . . . . . . . . . . . . . . 175 A.3 Fuzzy Supervised Neural Gas Algorithm Solved by SGD . . . . . 179 Bibliography 182 Acknowledgements 20

VQQL. Applying vector quantization to reinforcement learning

Proceeding of: RoboCup-99: Robot Soccer World Cup III, July 27 to August 6, 1999, Stockholm, SwedenReinforcement learning has proven to be a set of successful techniques for finding optimal policies on uncertain and/or dynamic domains, such as the RoboCup. One of the problems on using such techniques appears with large state and action spaces, as it is the case of input information coming from the Robosoccer simulator. In this paper, we describe a new mechanism for solving the states generalization problem in reinforcement learning algorithms. This clustering mechanism is based on the vector quantization technique for signal analog-to-digital conversion and compression, and on the Generalized Lloyd Algorithm for the design of vector quantizers. Furthermore, we present the VQQL model, that integrates Q-Learning as reinforcement learning technique and vector quantization as state generalization technique. We show some results on applying this model to learning the interception task skill for Robosoccer agents.Publicad