A new method for automatic indexing and retrieval is described. The approach is to take advantage of implicit higher‐order structure in the association of terms with documents (“semantic structure”) in order to improve the detection of relevant documents on the basis of terms found in queries. The particular technique used is singular‐value decomposition, in which a large term by document matrix is decomposed into a set of ca. 100 orthogonal factors from which the original matrix can be approximated by linear combination. Documents are represented by ca. 100 item vectors of factor weights. Queries are represented as pseudo‐document vectors formed from weighted combinations of terms, and documents with supra‐threshold cosine values are returned. Initial tests find this completely automatic method for retrieval to be promising. © 1990 John Wiley & Sons, Inc.

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Several modifications have been proposed to speed up the alternating least squares (ALS) method of fitting the PARAFAC model. The most widely used is line search, which extrapolates from linear trends in the parameter changes over prior iterations to estimate the parameter values that would be obtained after many additional ALS iterations. We propose some extensions of this approach that incorporate a more sophisticated extrapolation, using information on nonlinear trends in the parameters and changing all the parameter sets simultaneously. The new method, called "enhanced line search (ELS)," can be implemented at different levels of complexity, depending on how many different extrapolation parameters (for different modes) are jointly optimized during each iteration. We report some tests of the simplest parameter version, using simulated data. The performance of this lowest-level of ELS depends on the nature of the convergence difficulty. It significantly outperforms standard LS when there is a "convergence bottleneck," a situation where some modes have almost collinear factors but others do not, but is somewhat less effective in classic "swamp" situations where factors are highly collinear in all modes. This is illustrated by examples. To demonstrate how ELS can be adapted to different N-way decompositions, we also apply it to a four-way array to perform a blind identification of an under-determined mixture (UDM). Since analysis of this dataset happens to involve a serious convergence "bottleneck" (collinear factors in two of the four modes), it provides another example of a situation in which ELS dramatically outperforms standard line search.