Nowadays, given the rapid progress in pattern recognition, new ideas such as theoretical mathematics can be exploited to improve the efficiency of these tasks. In this paper, the Discrete Wavelet Transform (DWT) is used as a mathematical framework to demonstrate handwritten digit recognition in spiking Neural Networks (SNNs). The motivation behind this method is that the Wavelet transform can divide the spike information and noise into separate frequency subbands and also store the time information. The simulation results show that DWT is an effective and worthy choice and brings the network to an efficiency comparable to previous Networks in the spiking field. Initially, DWT is applied to MNIST images in the network input. Subsequently, a type of time encoding called constant-current-Leaky Integrate and Fire (LIF) encoding is applied to the transformed data. Following this, the encoded images are input to the multilayer convolutional spiking network. In this architecture, various Wavelets have been investigated, and the highest classification accuracy of 99.25% is achieved.

Forecasting currency exchange rates is an important financial problem that has received a great deal of attention especially because of its intrinsic difficulty and practical applications. The methods used for time series analyses are conventionally based on the concepts of stationarity and linearity. However, for cases in which the system dynamics are highly nonlinear, the performance of traditional models is very poor. On the other hand, artificial Neural Networks and Wavelettransformation have demonstrated great potential for time series forecasting. Therefore in this thesis we propose a forecasting approach which combines the strengths of Neural Networks and Wavelet transformation. In this approach the original exchange rates to be forecasted is first decomposed into various scale components using Wavelet transformation. In the next step Neural network techniques is applied for modeling components of the decomposed series. The final forecast of the original series is obtained by combining the components series forecasts. This approach is used for forecasting one-and ten-step ahead forecasts of daily exchange rates and its performance is compared whit those of ARIMA and Neural network models. Results show that performance of the proposed method in two and five-step ahead forecasting is better as compared to those of other models.

This paper provides an automated system based on machine learning and computer vision to detect cellphone usage during driving. We used Wavelet Scattering Networks, which is a simple and efficient type of architecture. The pre[1]sented model is straightforward and compact and requires little hyper-parameter tuning. The speed of this model is similar to the Convolutional Neural Networks. We monitored the driver from two viewpoints: a frontal view of the driver’s face and a side view of the driver’s whole body. We created a new dataset for the first view[1]point, and used a publicly available dataset for the second viewpoint. Our model achieved the test accuracy of 91% for our new dataset and 99% for the publicly available one.

This paper presents a CAD system for detection and diagnosis of microcalcification clusters in mammograms. The proposed algorithm is composed of three main stages. In the first stage, the image pixels are examined for corresponding to individual microcalcification objects. For this purpose, the Wavelet transform of the image is computed. Then two Wavelet coefficients as well as two statistical features are used with a Neural network for a primary classification of the image pixels. In the second stage, some noisy pixels extracted by the first step are eliminated. Then 18 features defined for each microcalcification are used with a nonlinear classifier for accurate detection of microcalcifications. For training of this classifier we used 16 regions from a database containing 379 microcalcifications. Finally, in the third stage five features defined for each microcalcification cluster with a Neural network are used to recognize malignant microcalcification clusters. For training of this network, 22 clusters including 8 malignant and 14 benign cases were used. The performance of the algorithm was evaluated using a separate image set composed of 22 clusters including 10 malignant and 12 benign cases. Using these tests images and the threshold value of 0.45, the sensitivity of the algorithm was 100% and its specificity was 91.6%.

In this paper a very intelligent tool with low computational complexity is presented for Electroencephalogram (ECG) signal classification. The proposed classifier is based on Discrete Wavelet Transform (DWT) and Probabilistic Neural Network (PNN). The novelty of this approach is that signal statistics, morphological analysis and DWT of the histogram of signal (density estimation) altogether have been used to achieve a higher recognition rate. ECG signals and their density estimation are decomposed into sub-classes using DWT. A PNN is used to classify ECG signals using statistical discriminating features which are extracted from ECG and its sub-classes. Experimental results on five classes of ECG signals from MIT-BIH arrhythmia database show that the proposed method learns very fast, low computational complexity, and a very high performance compared to the previous methods.

In this paper، the Wavelet transform and Neural Networks are used to produce more reliable forecasts of crude oil prices. In this combined model, we use the Wavelet transform to minimize the noise present in the data and then apply artificial Neural Networks to the smoothed data to forecast oil prices. Comparing the RMSEs of alternative models with the combined model confirms that reducing the noise and smoothing the data produces more reliable predictions of crude oil prices.

In this study the Wavelet Neural network (WNN) and artificial Neural network (ANN) were used to simulate barley breakage percentage in combine harvester. The models have been trained using the same data conditions. Air temperature, thresher cylinder speed, distance between thresher cylinder and concave (back and forth) and the percentage of barely moisture were as the input variables. The results showed that the Wavelet network (WNN, RASP 1) with 90.2% correlation coefficient for barely breakage would be an appropriate substitute for artificial Neural network with 88% correlation coefficient. The result of sensitivity analysis showed that all input variables had a significant effect on barely breakage. Speed of thresher cylinder had the most effect and the degree of air temperature had the least effect on barely breakage.

In this paper, a new method of ionospheric tomography is developed and evaluated based on the Neural Networks (NN). This new method is named ITNN. In this method, Wavelet Neural network (WNN) with particle swarm optimization (PSO) training algorithm is used to solve some of the ionospheric tomography problems. The results of ITNN method are compared with the residual minimization training Neural network (RMTNN) and modified RMTNN (MRMTNN). In all three methods, empirical orthogonal functions (EOFs) are used as a vertical objective function. To apply the methods for constructing a 3D-image of the electron density, GPS measurements of the Iranian permanent GPS network (in three days in 2007) are used. Besides, two GPS stations from international GNSS service (IGS) are used as test stations. The ionosonde data in Tehran (φ =35. 73820, λ =51. 38510) has been used for validating the reliability of the proposed methods. The minimum RMSE for RMTNN, MRMTNN, ITNN are 0. 5312, 0. 4743, 0. 3465 (1011ele. /m3) and the minimum bias are 0. 4682, 0. 3890, and 0. 3368 (1011ele. /m3) respectively. The results indicate the superiority of ITNN method over the other two methods.

Aware from electricity consumption in each period is necessary to Wright planning for main policy making. Therefore its demand forecasting is important between economic various sections. in this paper, was surveyed the comparative study of nonlinear manners of Artificial Neural Network and Wavelet Transform and liner process of ARMA in forecasting the electricity daily demand in time distance since one step to ten step ahead. The results presented the artificial Neural network and Wavelet transform on base of RMSE and MAPE indicators have high accuracy than ARMA in forecasting the electricity daily demand.