Theoretical Interpretations and Applications of Radial Basis Function Networks

Medical applications usually used Radial Basis Function Networks just as Artificial Neural Networks. However, RBFNs are Knowledge-Based Networks that can be interpreted in several way: Artificial Neural Networks, Regularization Networks, Support Vector Machines, Wavelet Networks, Fuzzy Controllers, Kernel Estimators, Instanced-Based Learners. A survey of their interpretations and of their corresponding learning algorithms is provided as well as a brief survey on dynamic learning algorithms. RBFNs' interpretations can suggest applications that are particularly interesting in medical domains

The Equi-Correlation Network: a New Kernelized-LARS with Automatic Kernel Parameters Tuning

Machine learning heavily relies on the ability to learn/approximate real functions. State variables, the perceptions, internal states, etc, of an agent are often represented as real numbers; grounded on them, the agent has to predict something, or act in some way. In this view, this outcome is a nonlinear function of the inputs. It is thus a very common task to fit a nonlinear function to observations, namely solving a regression problem. Among other approaches, the LARS is very appealing, for its nice theoretical properties, and actual efficiency to compute the whole $l_1$ regularization path of a supervised learning problem, along with the sparsity. In this paper, we consider the kernelized version of the LARS. In this setting, kernel functions generally have some parameters that have to be tuned. In this paper, we propose a new algorithm, the Equi-Correlation Network (ECON), which originality is that while computing the regularization path, ECON automatically tunes kernel hyper-parameters; thus, this opens the way to working with infinitely many kernel functions, from which, the most interesting are selected. Interestingly, our algorithm is still computationaly efficient, and provide state-of-the-art results on standard benchmarks, while lessening the hand-tuning burden

Evolutionary Optimization Of Support Vector Machines

Support vector machines are a relatively new approach for creating classifiers that have become increasingly popular in the machine learning community. They present several advantages over other methods like neural networks in areas like training speed, convergence, complexity control of the classifier, as well as a stronger mathematical background based on optimization and statistical learning theory. This thesis deals with the problem of model selection with support vector machines, that is, the problem of finding the optimal parameters that will improve the performance of the algorithm. It is shown that genetic algorithms provide an effective way to find the optimal parameters for support vector machines. The proposed algorithm is compared with a backpropagation Neural Network in a dataset that represents individual models for electronic commerce

Scalable and Compact 3D Action Recognition with Approximated RBF Kernel Machines

Despite the recent deep learning (DL) revolution, kernel machines still remain powerful methods for action recognition. DL has brought the use of large datasets and this is typically a problem for kernel approaches, which are not scaling up eciently due to kernel Gram matrices. Nevertheless, kernel methods are still attractive and more generally applicable since they can equally manage dierent sizes of the datasets, also in cases where DL techniques show some limitations. This work investigates these issues by proposing an explicit ap- proximated representation that, together with a linear model, is an equivalent, yet scalable, implementation of a kernel machine. Our approximation is directly inspired by the exact feature map that is induced by an RBF Gaussian kernel but, unlike the latter, it is nite dimensional and very compact. We justify the soundness of our idea with a theoretical analysis which proves the unbiasedness of the approximation, and provides a vanishing bound for its variance, which is shown to decrease much rapidly than in alternative methods in the literature. In a broad experimental validation, we assess the superiority of our approximation in terms of 1) ease and speed of training, 2) compactness of the model, and 3) improvements with respect to the state-of-the-art performance