Differentiable approximation by means of the Radon transformation and its applications to neural networks

AbstractWe treat the problem of simultaneously approximating a several-times differentiable function in several variables and its derivatives by a superposition of a function, say g, in one variable. In our theory, the domain of approximation can be either compact subsets or the whole Euclidean space Rd. We prove that if the domain is compact, the function g can be used without scaling, and that even in the case where the domain of approximation is the whole space Rd, g can be used without scaling if it satisfies a certain condition. Moreover, g can be chosen from a wide class of functions. The basic tool is the inverse Radon transform. As a neural network can output a superposition of g, our results extend well-known neural approximation theorems which are useful in neural computation theory

A Comprehensive Survey on Functional Approximation

The theory of functional approximation has numerous applications in sciences and industry. This thesis focuses on the possible approaches to approximate a continuous function on a compact subset of R2 using a variety of constructions. The results are presented from the following four general topics: polynomials, Fourier series, wavelets, and neural networks. Approximation with polynomials on subsets of R leads to the discussion of the Stone-Weierstrass theorem. Convergence of Fourier series is characterized on the unit circle. Wavelets are introduced following the Fourier transform, and their construction as well as ability to approximate functions in L2(R) is discussed. At the end, the universal approximation theorem for artificial neural networks is presented, and the function representation and approximation with single- and multilayer neural networks on R2 is constructed

Wavelet Signal Processing of Physiologic Waveforms

The prime objective of this piece of work is to devise novel techniques for computer based classification of Electrocardiogram (ECG) arrhythmias with a focus on less computational time and better accuracy. As an initial stride in this direction, ECG beat classification is achieved by using feature extracting techniques to make a neural network (NN) system more effective. The feature extraction technique used is Wavelet Signal Processing. Coefficients from the discrete wavelet transform were used to represent the ECG diagnostic information and features were extracted using the coefficients and were normalised. These feature sets were then used in the classifier i.e. a simple feed forward back propagation neural network (FFBNN). This paper presents a detail study of the classification accuracy of ECG signal by using these four structures for computationally efficient early diagnosis. Neural network used in this study is a well-known neural network architecture named as multi-Layered perceptron (MLP) with back propagation training algorithm. The ECG signals have been taken from MIT-BIH ECG database, and are used in training to classify 3 different Arrhythmias out of ten arrhythmias. These are normal sinus rhythm, paced beat, left bundle branch block. Before testing, the proposed structures are trained by back propagation algorithm. The results show that the wavelet decomposition method is very effective and efficient for fast computation of ECG signal analysis in conjunction with the classifier