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We consider correspondence analysis (CA) and taxicab correspondence analysis (TCA) of relational datasets that can mathematically be described as weighted loopless graphs. Such data appear in particular in network analysis. We present CA and TCA as relaxation methods for the graph partitioning problem. Examples of real datasets are provided. [ABSTRACT FROM AUTHOR]

We present an analysis of a health survey data by multiple cor- respondence analysis (MCA) and multiple taxicab correspondence analysis (MTCA), MTCA being a robust L1 variant of MCA. The survey has one passive item, gender, and 22 active substantive items representing health services offered by municipal authorities; each active item has four answer categories: this service is used, never tried, tried with no access, non re- sponse. We show that the first principal MTCA factor is perfectly charac- terized by the sum score of the category this service is used over all service items. Further, we prove that such a sum score characterization always exists for any survey data. [ABSTRACT FROM AUTHOR]

The aim of this paper is the introduction of a new method for the numerical computation of the rank of a three-way array X ∈ RI×J×K over R. We show that the rank of a three-way array over R is intimately related to the real solution set of a system of polynomial equations. Using this, we present some numerical results based on the computation of Gr¨obner bases. Also, we show that for I = (K − 1)(J − 1) + 1 and 2 ≤ K ≤ J ≤ I, the rank for generic data has more than one rank value, and the minimum attained value is I. [ABSTRACT FROM AUTHOR]

The article investigates vocalization differences among three herds of harp seals using discriminant analysis. Based on the interpretation of the disco values of the variables and the apparent rates of classification of the three herds, it was revealed that the first factor of the multiple correspondence analysis discriminates best for multiple-element calls. This suggests that the Jan Mayen herd does not communicate with the other two herds although the latter two herds communicate with each other.

Three-way arrays (or tensors) can be regarded as extensions of the traditional two-way data matrices that have a third dimension. Studying algebraic properties of arrays is relevant, for example, for the Tucker three-way PCA method, which generalizes principal component analysis to three-way data. One important algebraic property of arrays is concerned with the possibility of transformations to simplicity. An array is said to be transformed to a simple form when it can be manipulated by a sequence of invertible operations such that a vast majority of its entries become zero. This paper shows how 3×3×3 arrays, whether symmetric or nonsymmetric, can be transformed to a simple form with 18 out of its 27 entries equal to zero. We call this simple form the “knight's move pattern” due to a loose resemblance to the moves of a knight in a game of chess. The pattern was examined by Kiers, Ten Berge, and Rocci. It will be shown how the knight's move pattern can be found by means of a numeric–algebraic procedure based on the Gröbner basis. This approach seems to work almost surely for randomly generated arrays, whether symmetric or nonsymmetric. [ABSTRACT FROM AUTHOR]