A spectrum decomposition to the feature spaces and the application to big data analytics

In this paper, we investigate how to efficiently extract informative features of high-dimensional data through noisy channels. Specifically, we decompose the feature space of the data into a sequence of score functions with decreasing information volumes, such that different scores are uncorrelated. From this decomposition, the features of the data become a sequence of score functions such that the most informative lowdimensional feature can be selected as the first few scores. This greatly simplifies the feature selection problem. In addition, we apply this spectrum decomposition to data with high-dimensional structures, i.e., the hidden Markov model (HMM). We show that in HMM, it is desirable to consider a particular class of score functions called as the node scores, which allows us to efficiently extract informative features of the hidden variables by applying the spectrum decomposition approach. Finally, we develop efficient algorithms to extract such features from node scores, and present an example to illustrate the performance of the node scores.