  This paper aims to develop new techniques to describe joint behavior of
stocks, beyond regression and correlation. For example, we want to identify the
clusters of the stocks that move together. Our work is based on applying Kernel
Principal Component Analysis(KPCA) and Functional Principal Component
Analysis(FPCA) to high frequency data from NSE. Since we dealt with high
frequency data with a tick size of 30 seconds, FPCA seems to be an ideal
choice. FPCA is a functional variant of PCA where each sample point is
considered to be a function in Hilbert space L^2. On the other hand, KPCA is an
extension of PCA using kernel methods. Results obtained from FPCA and Gaussian
Kernel PCA seems to be in synergy but with a lag. There were two prominent
clusters that showed up in our analysis, one corresponding to the banking
sector and another corresponding to the IT sector. The other smaller clusters
were seen from the automobile industry and the energy sector. IT sector was
seen interacting with these small clusters. The learning gained from these
interactions is substantial as one can use it significantly to develop trading
strategies for intraday traders.
