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What is the difference between SVM and Neural Network? Is it true that linear svm is the same NN, and for non-linear separable problems, NN uses adding hidden layers and SVM uses changing space dimensions?

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Support Vector Machine (SVM) works as a discriminative classifier, which uses the working of separating hyperplane. The data points given for training of SVM outputs an optimal hyperplane of three dimensions which separates new examples. In two dimensions, this hyperplane got converted to the separation line which divides the plane.

Support vector machines use kernels, which makes SVM really powerful for machine learning. 

You can use different kernels according to training data. Kernels are linear, RBF and polynomial kernel. 

Neural Networks: A neural network is a network or circuit of neurons, an artificial neural network is composed of artificial neurons or nodes inspired by biological neural networks. They are commonly used for solving artificial intelligence (AI) problems. 

A simple neural network works the same as the support vector machine. If you train a deep neural network, then it may perform way better than SVM for complex problems like speech processing, face recognition and many more.

Hope this answer helps.

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