There is a increasing interest in analysis of large-scale multiway data. The concept of multiway data refers to arrays of data with more than two dimensions, that is, taking the form of tensors. To analyze such data, decomposition techniques are widely used. The two most common decompositions for tensors are the Tucker model and the more restricted PARAFAC model. Both models can be viewed as generalizations of the regular factor analysis to data of more than two modalities. Nonnegative matrix factorization (NMF), in conjunction with sparse coding, has recently been given much attention due to its part-based and easy interpretable representation. While NMF has been extended to the PARAFAC model, no such attempt has been done to extend NMF to the Tucker model. However, if the tensor data analyzed are nonnegative, it may well be relevant to consider purely additive (i.e., nonnegative) Tucker decompositions). To reduce ambiguities of this type of decomposition, we develop updates that can impose sparseness in any combination of modalities, hence, proposed algorithms for sparse nonnegative Tucker decompositions (SN-TUCKER). We demonstrate how the proposed algorithms are superior to existing algorithms for Tucker decompositions when the data and interactions can be considered nonnegative. We further illustrate how sparse coding can help identify what model (PARAFAC or Tucker) is more appropriate for the data as well as to select the number of components by turning off excess components. The algorithms for SN-TUCKER can be downloaded from Mørup (2007).

In the International Statistical Classification of Diseases, Tenth Revision(ICD-10) and Diagnostic and Statistical Manual of Mental Disorder, Third and Fourth Edition(DSM-III-IV), the presence of one of Schneider "first-rank symptoms" (FRS) is symptomatically sufficient for the schizophrenia diagnosis. Yet, it has been claimed that FRS may also be found in the nonschizophrenic conditions, and therefore, they are not specific or diagnostic for schizophrenia. This review was made to clarify the issue of diagnostic specificity. (1) A critical review of FRS studies published in English between 1970 and 2005. (2) A highlight of the 5 most frequently cited studies identified in the Web of Science. (3) Theoretical implications of the epistemological issues of FRS. The reviewed studies do not allow for either a reconfirmation or a rejection of Schneider's claims about FRS. The sources of disagreement between the studies are (1) including or excluding acute patients with potential degradation of consciousness; (2) assessing or not the phenomenological context; (3) assessing patients in different stages of their illness evolution; and (4) differential emphasis on mood symptoms and history of psychiatric symptoms. Both DSM-IV and ICD-10 emphasize FRS to a degree that is not supported by the empirical evidence. Until the status of FRS is clarified in depth, we suggest that the FRS, as these are currently defined, should be de-emphasized in the next revisions of our diagnostic systems. Future studies aiming at validation of FRS as diagnostic features need to apply a phenomenological perspective and include a homogenous group of patients across a wide spectrum of diagnoses.