A Novel Kernel for RBF Based Neural Networks

Abstract

Radial basis function (RBF) is well known to provide excellent performance in function approximation and pattern classification. The conventional RBF uses basis functions which rely on distance measures such as Gaussian kernel of Euclidean distance (ED) between feature vector and neuron’s center, and so forth. In this work, we introduce a novel RBF artificial neural network (ANN) where the basis function utilizes a linear combination of ED based Gaussian kernel and a cosine kernel where the cosine kernel computes the angle between feature and center vectors. Novelty of the proposed work relies on the fact that we have shown that there may be scenarios where the two feature vectors (FV) are more prominently distinguishable via the proposed cosine measure as compared to the conventional ED measure. We discuss adaptive symbol detection for multiple phase shift keying (MPSK) signals as a practical example to show where the angle information can be pivotal which in turn justifies our proposed RBF kernel. To corroborate our theoretical developments, we investigate the performance of the proposed RBF for the problems pertaining to three different domains. Our results show that the proposed RBF outperforms the conventional RBF by a remarkable margin.

On Modelling and Comparative Study of LMS and RLS Algorithms for Synthesis of MSA

“…Normalized spread used for LMS algorithm is 0.151. The number of epochs used in training is 100, and subtractive clustering approach is utilized as in the previous work of [13]. Training results for LMS is shown in Figure 4.…”

“…There exist numerous models in literature that account for the determination of dimension of patch based on artificial neural networks (ANN) for modelling purposes [9,10] but an algorithmic comparison of such models is unavailable. Nevertheless, ANN in general and radial basis function (RBF) in particular have been extensively used with excellent results in modelling and simulation techniques for other nonlinear mechanical systems [11,12] and signal processing routines [13] and in the design aspects of MSA [14][15][16][17]. The design of MSA using ANN is subdivided into forward modelling and backward modelling.…”

Colocación con funciones de base radial para la solución de modelos matemáticos en fenoménos de transporte

“…Una función de base radial (Radial basis function RBF), es una función real cuyo valor depende de la distancia entre dos puntos o nodos, un nodo fuente que actúa como centro y un nodo de campo o punto donde se evalúa la función. La norma usada para la distancia es frecuentemente la norma euclidiana aunque otras pueden ser admisibles en aplicaciones especificas (Aftab, Moinuddin, y Shaikh, 2014) o en problemas sobre manifolds (Hubbert, L.Gia, y Morton, 2015;Levesley y Ragozin, 2007).…”

Chaotic Time Series Prediction using Spatio-Temporal RBF Neural Networks

“…In [19], an adaptive learning method is proposed for system identification task. In [20], a novel fusion of multiple kernel is proposed. In [21], kernel optimization method is proposed using Nelder Mead Simplex algorithm.…”