Further studies of extreme learning machine and compressed signal detection

Abstract

In this thesis, we present further studies of extreme learning machine and signal detection in compressed sensing. In Chapter 1, we give literature reviews of extreme learning machine (ELM) and compressed sensing (CS). In part I of the thesis (Chapters 2, 3, and 4), we consider the recent ELM for training neural networks and present several improved algorithms. We first propose a composite function wavelet neural network (WNN) learning with the recent ELM algorithm in Chapter 2. The main contributions of the proposed WNN comparing with traditional ones are using composite functions at the hidden nodes and applying ELM algorithm to WNN as a learning algorithm. To reduce the network size and optimize the hidden node parameters, we then introduce an improvement method for training the proposed WNN by incorporating the global optimization algorithm Differential Evolution into searching for the optimal network input weights and the dilation and translation values in Chapter 3. To further enhance the classification rate of the ELM, we propose an improved algorithm named voting based ELM (V-ELM) for signal classification in Chapter 4. In V-ELM, the voting method is incorporated into the ELM in classification applications. Several individual ELMs with the same network structure are trained with the same dataset and the final class label of a test sample is determined by majority voting method on all the results obtained by these independent ELMs. Numerical simulations are provided to illustrate the efficiency of our proposed methods. In part II of the thesis (Chapters 5 and 6), we study the signal detection in CS. We first consider the theoretical bound of the probability of error by detecting the signal reconstructed in CS with the Bayesian approach in Chapter 5. Utilizing the oracle estimator in CS, we provide a theoretical bound of the probability of error when the noise in CS is white Gaussian noise. We then consider the Bayesian approach to signal detection in CS using compressed measurements directly in Chapter 6. We start by revisiting the classical signal detection problem and show that with an additive Gaussian noise, the probability of error for unequal prior probabilities of the hypotheses is always smaller than the one with equal prior probability. We then consider signal detection with compressed measurements directly, assuming that the additive noise is Gaussian but with unequal variances. A general expression is obtained for the probability of error where the prior probabilities could be equal or unequal. We have also derived performance bounds for the probability of error using the restricted isometry property constant and then the computationally more feasible mutual coherence of a given sampling matrix in CS. An approximate but simpler expression of the probability of error and its approximate upper bound are also obtained. % the measurement domain which is easier to calculate than computing the Numerical simulations are given to verify the new theoretical results. In Chapter 7, conclusions and future work are provided.