This is an interesting question with lots of possible answers.

For a good overview of hyperspectral image classification, see

S. De Backer, Unsupervised Pattern Recognition, Ph.D. thesis, University of Antwerp, 2002:

http://webh01.ua.ac.be/visielab/theses/debacker/SteveThesis.pdf

Multispectral (hyperspectral) classification is covered, starting in Section 3.3, page 53. Supervised and unsupervised classification are introduced in Section 1.3, starting on page 8.

@Jame excellent! It seems you have cultivated interest in geoinforfamatics. No doubt, geoinformatics can do little without application of mathematics and applied computational mathematics and algorithms. Anyway, Great and Congratulations!

A hyper-spectral image contain hundreds of bands and normal display devices support only 3 dimensions for display of color images so dimentionality reduction needs to be applied to visualize a hyperspectral image. 

Generally speaking, unsupervised classification give you colored image where each color represent different class. You have to compare the image with ground truth after classification to see the accuracy of results.

In supervised classification, you have to select the region and mark it as a class. This procedure is done for every known class (e.g. roads, buildings, roofs, trees, grass etc) and then region growing is performed. Final result contain classes with colors but some region may be uncolored as they may not match any other class.  

Supervised Hyperspectral Image Classification Algorithms:

SAM

SVM

MLP

MLC

SAD

Unsupervised Hyperspectral Image Classification Algorithms:

IsoData

KMeans

Basically, you should decouple the supervised and unsupervised setting with the fact it is applied on hyperspectral imagery.

Do you have labels of classes over pixels of your hyperspectral image?

- Yes: this is a supervised setting: you can learn a model based on these labels and then classify the rest of your image

- No: this is an unsupervised setting: you want to group your image in different classes but have no example to learn a model

There is then semi-supervised learning which stands in the middle, where you have labels and also exploits the rest of your image. We have a paper around that that you can have a look at: Article Kernel Low-Rank and Sparse Graph for Unsupervised and Semi-S...

Best