Tensor representation and tensor decompositions are natural approaches to deal with large amounts of data with multiple aspects and high dimensionality in modern applications, such as environmental analysis, chemometrices, pharmaceutical analysis, spectral analysis, neuroscience. The two most popular decomposition/factorization models for N-th order tensors are the Tucker model and the more restricted PARAFAC model. The Tucker decomposition allows for the extraction of different numbers of factors in each of the modes, and permits interactions within each modality while PARAFAC does not. This advantage, however, is also one of the weakness of this decomposition. The difficult problem is to identify the dominant relationships between components, and to establish unique representation. In this paper, we will introduce a new measure index which is called the Joint Rate (JR) index, in order to evaluate interactions among various components in the general Tucker decomposition. The Hinton diagram is also extended to 3-D visualization. The use of the JR index will be illustrated with the analysis of EEG data for classification and BCI applications.
|Number of pages||5|
|Publication status||Published - 2009|
|Event||Asia-Pacific Signal and Information Processing Association 2009 Annual Summit and Conference, APSIPA ASC 2009 - Sapporo, Japan|
Duration: 4 Oct 2009 → 7 Oct 2009
|Conference||Asia-Pacific Signal and Information Processing Association 2009 Annual Summit and Conference, APSIPA ASC 2009|
|Period||4/10/09 → 7/10/09|