A novel pooling layer based on gaussian function with wavelet transform

Abstract

<p>Convolution is represent the basic layer in the convolutional neural network, but it can results in very big size of the data at its output, so this data need to be reduced or down sampled to reduce the required operation in the network and increase its efficiency by choosing the most important features of the input signal. Different pooling methods was used to perform down sampling the size of these features. In this paper, we have proposed a novel pooling method by using Gaussian based Wavelet Transform and named as (GWT). Gaussian probability distribution function is used to determine the basic and most important statistics of the signal in each pooling size, and depending on this function, the basic statistics with the most priority is determined with their weight ,which are used as coefficients for wavelet filter to extract the pooling features . According to the procedure of extract the wavelet coefficients filter, Three method are proposed ,the first method (GWT1 ) is used the normalized values of basic statistics as weight to be multiplied by original signal, the second method (GWT2) used the determined statistics as features of the original signal and multiply it with constant weights based on half Gaussian ,while the third method (GWT3) is work in similar way to (GWT1) except that, it depend on entire signal instead of every pool size for calculation the basic statistics. Also the proposed methods are combined with other standard methods such as max and pooling. The experiments are performed on different types of dataset , two dimension (images) and one dimension (such as ECG signal), the results are compared with other methods and show that the proposed methods perform or outperform the other methods and can increase the performance of the (CNN).</p>