Reduced hyperBF networks : practical optimization, regularization, and applications in bioinformatics.

A hyper basis function network (HyperBF) is a generalized radial basis function network (RBF) where the activation function is a radial function of a weighted distance. The local weighting of the distance accounts for the variation in local scaling and discriminative power along each feature. Such generalization makes HyperBF networks capable of interpolating decision functions with high accuracy. However, such complexity makes HyperBF networks susceptible to overfitting. Moreover, training a HyperBF network demands weights, centers and local scaling factors to be optimized simultaneously. In the case of a relatively large dataset with a large network structure, such optimization becomes computationally challenging. In this work, a new regularization method that performs soft local dimension reduction and weight decay is presented. The regularized HyperBF (Reduced HyperBF) network is shown to provide classification accuracy comparable to a Support Vector Machines (SVM) while requiring a significantly smaller network structure. Furthermore, the soft local dimension reduction is shown to be informative for ranking features based on their localized discriminative power. In addition, a practical training approach for constructing HyperBF networks is presented. This approach uses hierarchal clustering to initialize neurons followed by a gradient optimization using a scaled Rprop algorithm with a localized partial backtracking step (iSRprop). Experimental results on a number of datasets show a faster and smoother convergence than the regular Rprop algorithm. The proposed Reduced HyperBF network is applied to two problems in bioinformatics. The first is the detection of transcription start sites (TSS) in human DNA. A novel method for improving the accuracy of TSS recognition for recently published methods is proposed. This method incorporates a new metric feature based on oligonucleotide positional frequencies. The second application is the accurate classification of microarray samples. A new feature selection algorithm based on a Reduced HyperBF network is proposed. The method is applied to two microarray datasets and is shown to select a minimal subset of features with high discriminative information. The algorithm is compared to two widely used methods and is shown to provide competitive results. In both applications, the final Reduced HyperBF network is used for higher level analysis. Significant neurons can indicate subpopulations, while local active features provide insight into the characteristics of the subpopulation in specific and the whole class in general

Locally fitting hyperplanes to high-dimensional data

Problems such as data compression, pattern recognition and artificial intelligence often deal with a large data sample as observations of an unknown object. An effective method is proposed to fit hyperplanes to data points in each hypercubic subregion of the original data sample. Corresponding to a set of affine linear manifolds, the locally fitted hyperplanes optimally approximate the object in the sense of least squares of their perpendicular distances to the sample points. Its effectiveness and versatility are illustrated through approximation of nonlinear manifolds Möbius strip and Swiss roll, handwritten digit recognition, dimensionality reduction in a cosmological application, inter/extrapolation for a social and economic data set, and prediction of recidivism of criminal defendants. Based on two essential concepts of hyperplane fitting and spatial data segmentation, this general method for unsupervised learning is rigorously derived. The proposed method requires no assumptions on the underlying object and its data sample. Also, it has only two parameters, namely the size of segmenting hypercubes and the number of fitted hyperplanes for user to choose. These make the proposed method considerably accessible when applied to solving various problems in real applications

Development of an Algorithm for Multicriteria Optimization of Deep Learning Neural Networks

Nowadays, machine learning methods are actively used to process big data. A promising direction is neural networks, in which structure optimization occurs on the principles of self-configuration. Genetic algorithms are applied to solve this nontrivial problem. Most multicriteria evolutionary algorithms use a procedure known as non-dominant sorting to rank decisions. However, the efficiency of procedures for adding points and updating rank values in non-dominated sorting (incremental non-dominated sorting) remains low. In this regard, this research improves the performance of these algorithms, including the condition of an asynchronous calculation of the fitness of individuals. The relevance of the research is determined by the fact that although many scholars and specialists have studied the self-tuning of neural networks, they have not yet proposed a comprehensive solution to this problem. In particular, algorithms for efficient non-dominated sorting under conditions of incremental and asynchronous updates when using evolutionary methods of multicriteria optimization have not been fully developed to date. To achieve this goal, a hybrid co-evolutionary algorithm was developed that significantly outperforms all algorithms included in it, including error-back propagation and genetic algorithms that operate separately. The novelty of the obtained results lies in the fact that the developed algorithms have minimal asymptotic complexity. The practical value of the developed algorithms is associated with the fact that they make it possible to solve applied problems of increased complexity in a practically acceptable time. Doi: 10.28991/HIJ-2023-04-01-011 Full Text: PD