  We propose improved methods to identify stock groups using the correlation
matrix of stock price changes. By filtering out the marketwide effect and the
random noise, we construct the correlation matrix of stock groups in which
nontrivial high correlations between stocks are found. Using the filtered
correlation matrix, we successfully identify the multiple stock groups without
any extra knowledge of the stocks by the optimization of the matrix
representation and the percolation approach to the correlation-based network of
stocks. These methods drastically reduce the ambiguities while finding stock
groups using the eigenvectors of the correlation matrix.
