I am dealing with a large dataset. My aim is to identify those pair of data item who separate like the picture in below for two classes?
There are many two-class classification algorithms you can take a look at that'll help you do that sort of classifications. Some popular algorithms (though currently antiquated) are to use the Perceptron Algorithm, Neural Networks, or Logistic Regression.
However, arguably the most popular algorithm currently used in practice would be using Support Vector Machines. I'm not familiar with what kind of programming languages you know, but if you are using MATLAB, then the Artificial Intelligence Toolbox has SVMs builtin, and can support training and classification. There are many good docs and examples:
http://www.mathworks.com/help/stats/support-vector-machines-svm.html
However, if you're a purist and prefer non-interpreted programming languages, then I'd recommend you look at LIBSVM. It's an awesome package for doing SVMs, and has a variety of different programming languages that it supports.
http://www.csie.ntu.edu.tw/~cjlin/libsvm/
Good luck.
- Ray.
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