Why cannot we use neural networks for unsupervised learning problem. I do know that it can be used using the Kohenon’s Self Organizing Map (KSOM) but is this the only method that we can use or are there any other.
Yes, there are others. The most important dimensionality reduction technique in Deep Learning is Autoencoders. They are neural networks with a "funnel" structure, that shrinks the size of the signal, forcing the Network to learn how to represent the same information with less nodes.
Autoencoders are much more common than SOMs in practical DL. While SOMs are used mostly for data visualization (usually they reduce a dataset in a 2D representation), Autoencoders give you absolute freedom in the number of factors that you can extract. This makes them more useful for any research or production purpose.
A good theoretical introduction can be found here.
Please also take a look at this practical implementation in TensorFlow 2.0.