  Physiological signals are often organized in the form of multiple dimensions
(e.g., channel, time, task, and 3D voxel), so it is better to preserve original
organization structure when processing. Unlike vector-based methods that
destroy data structure, Canonical Polyadic Decomposition (CPD) aims to process
physiological signals in the form of multi-way array, which considers
relationships between dimensions and preserves structure information contained
by the physiological signal. Nowadays, CPD is utilized as an unsupervised
method for feature extraction in a classification problem. After that, a
classifier, such as support vector machine, is required to classify those
features. In this manner, classification task is achieved in two isolated
steps. We proposed supervised Canonical Polyadic Decomposition by directly
incorporating auxiliary label information during decomposition, by which a
classification task can be achieved without an extra step of classifier
training. The proposed method merges the decomposition and classifier learning
together, so it reduces procedure of classification task compared with that of
respective decomposition and classification. In order to evaluate the
performance of the proposed method, three different kinds of signals, synthetic
signal, EEG signal, and MEG signal, were used. The results based on evaluations
of synthetic and real signals demonstrated that the proposed method is
effective and efficient.
