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# Anisotropic Diffusion Expert

New Delhi, India

## Sumeet A

Bachelor of Science, Physics Quantum Coding, Osmania University

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I am a certified academic assistant who is currently working with Matlab Assignment Experts to provide educational support to college and university students. My primary area of specialization is a computer vision and so far I have delivered numerous projects from different topics such as projective geometry, graph cut estimation, level set method, motion field, and vector, medial axis, particle filtering, gesture recognition, Markov random fields, optical flow and more. We should definitely collaborate if you are looking for top quality solutions, to meet your deadlines, and to better your understanding of computer vision.

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## Neural Network Implemented in Matlab

demo.m is the main file that computer and execute calculations via functions (another m. files) app_newton – own version of the algorithm in Matlab using the approximate Hessian matrix with second-order network derivatives backdrop-function that calculates derivatives (jacobian) and Hessian matrix exact_newton - Netwon’s algorithm using the exact Hessians computed with the R-propagation algorithm gradient_descent– classical backpropagation algorithm model_network – model description from the figure in neural networks coursework2.pdf weight_initilaization – function for random weight matrix initialization In order to build and compare the efficiency of 3 learning algorithms, I performed multiple steps: 1) model description and generate input data (X, Y) for training algorithms. 2) multilayer perceptron weight and parameter initialization 3) simulation parameter choosing (num_epoch, learning rate) 4) main cycle over epoch with 3 algorithms training on the same input data: a) the classical backpropagation algorithm (studied during the lectures); and b) the Netwon’s algorithm using the exact Hessian computed with the R-propagation algorithm (given in the books below). c) Newton algorithm approximate Hessian matrix with second-order network derivatives 5) plot loss function over iterations to find difference convergence speed for 3 chosen algorithms Figure 1. Convergence plot for 3 learning algorithms with simulation dataset  In the first step, I generate data with the following simple neural network. The function model_network performed this step with an output of 10000 samples (x-y).  Then I initialize a neural network with 5 hidden units suitable for training.  For weight initialization, I created function weight_initilaization() that performs a random generator for hidden and output weight matrices. Firstly, I implemented my own version of the gradient descent (GD) algorithm in Matlab using the calculation of first derivatives with respect to the weights with backpropagation.  In this function gradient_descent() I also calculated the Hessian matrix with the R-backpropagation algorithm from Nabney, I. (2002). Netlab: Algorithms for Pattern Recognition, Springer series Advances in Pattern Recognition. pp.160-163 Fast Multiplication by the Hessian (R-propagation algorithm). The output of this function is used for Newton's second-order optimizer. And for comparison, I also implemented the approximate Hessian matrix second-order algorithm in app_newton() function. To sum up, I implemented 3 optimizer algorithms: 1) the classical backpropagation algorithm 2) the Netwon’s algorithm using the exact Hessian computed with the R-propagation algorithm 3) the Netwon’s algorithm using the approximate Hessian computed with the Levenberg-Marquardt optimization algorithm Figure 2. Convergence plot for 3 learning algorithms with sunspot dataset Monte-Carlo simulation was run with 500 epoch, the learning rate was 0.001. Figure 1 shows that Netwon’s algorithm using the approximate Hessian computed with the Levenberg-Marquardt optimization algorithm (red curve) has the best performance in comparison with the classical backpropagation algorithm (blue curve) and Netwon’s algorithm using the exact Hessian computed with the R-propagation algorithm (green curve). I also performed some tests for 3 learning algorithms for the sunspot dataset (sunspot.dat). Figure 2 shows that newton's algorithm using the exact Hessian computed with the R-propagation algorithm (green curve) has the best performance. Before model building, I have feature normalization. From the above results, we can conclude that MLP is not the best and highest performance neural network architecture for time series prediction