Local Canonical Correlation Analysis for Nonlinear Common Variables Discovery

HE need to study and analyze complex systems arises in many fields. Nowadays, in more and more applications and devices, many sensors are used to collect and to record multiple channels of data, a fact that increases the amount of information available to analyze the state of the system of interest. In such cases, it is typically insufficient to study each channel separately. Yet, the ability to gain a deep understanding of the true state of the system from the overwhelming amount of collected data from multiple (usually different) sources of information is challenging; it calls for the development of new technologies and novel ways to observe the system of interest and to fuse the available information [1]. For example, the study of human physiology in many fields of medicine is performed by simultaneously monitoring various medical features through electroencephalography (EEG) signals, electrocardiography (ECG) signals, respiratory signals, etc. Each type of measurement carries different and specific information, while our purpose is to systematically discover an accurate description of the state of the patient/person. A commonly-used method that has the ability to reveal correlations between multiple different sets, which often furthers our understanding of the system, is the Canonical Correlation Analysis (CCA) [2]-[4]. CCA is a well known and studied algorithm, where linear projections maximizing the correlation between the two data sets are constructed.