Some scientists (like my advisor) suppose that SVM is part of neural network theory. But I think it's differnr algorythm for classification. They both part of machine learning. And now neural leraning stay aprt to other classification algoryth. This is 2 differnt way to solve a problem:

1. Extract feature vector (like a HOG for computer vision)

2. Learn classifier

1. Train a good neural network on pure data. (some times with statiscal cleaning)

But there is a small disclaimer when we use NN good practice to use pretraning:

unsupervized learning (like simple kmeans) or use RBM to create autoassotion model (decoder-encoder) to build better model.

Сonclusion: SVM and NN is different in practice

In Phillip De Wilde's book 'Neural Network Models', he gives the following characteristics for the neural networks:

* Do parallel processing

*Are fail soft devices(degrades gracefully)

*Are distributed systems

While some changes can be done to SVMs to satisfy the above three properties(such as Balanced Kernel Perceptron and parallel implementations), it is not inherent of the SVM. In addition the initial goal of NNs was to simulate biological networks which SVMs were not inspired on biology but in statistical learning theory.

In my biased perception I would not consider them a neural network.

ANN and SVM are two popular way for supervised machine learning and classification. It's not often clear which method is better for a particular project. Of course, SVM is a kind of neural network

The paper "Connections between Support Vector Machines, Wasserstein distance and gradient-penalty GANs" argues that a link between SVMs and Generative Adversarial Networks (GANs) exists. You can find it here: Preprint Connections between Support Vector Machines, Wasserstein dis...

The basics about NN can bring some insights about if SVM can be considered "part" of a NN. The first hidden layer builds hyperplanes. So, if having one neuron a hyperplane is created. The above is the same thing as SVM. Obviously, support vectors are not part of a NN. Things are darker when increasing number of neurons, number of classes, etc.