On the Scope of the Universal-Algebraic Approach to Constraint Satisfaction

The universal-algebraic approach has proved a powerful tool in the study of the complexity of CSPs. This approach has previously been applied to the study of CSPs with finite or (infinite) omega-categorical templates, and relies on two facts. The first is that in finite or omega-categorical structures A, a relation is primitive positive definable if and only if it is preserved by the polymorphisms of A. The second is that every finite or omega-categorical structure is homomorphically equivalent to a core structure. In this paper, we present generalizations of these facts to infinite structures that are not necessarily omega-categorical. (This abstract has been severely curtailed by the space constraints of arXiv -- please read the full abstract in the article.) Finally, we present applications of our general results to the description and analysis of the complexity of CSPs. In particular, we give general hardness criteria based on the absence of polymorphisms that depend on more than one argument, and we present a polymorphism-based description of those CSPs that are first-order definable (and therefore can be solved in polynomial time).Comment: Extended abstract appeared at 25th Symposium on Logic in Computer Science (LICS 2010). This version will appear in the LMCS special issue associated with LICS 201

Rotation in Multiple Correspondence Analysis: a planar rotation iterative procedure

Multiple Correspondence Analysis (MCA) is a well-known multivariate method for statistical description of categorical data (see for instance Greenacre and Blasius, 2006). Similarly to what is done in Principal Component Analysis (PCA) and Factor Analysis, the MCA solution can be rotated to increase the components simplicity. The idea behind a rotation is to find subsets of variables which coincide more clearly with the rotated components. This implies that maximizing components simplicity can help in factor interpretation and in variables clustering. In PCA, the probably most famous rotation criterion is the varimax one introduced by Kaiser (1958). Besides, Kiers (1991) proposed a rotation criterion in his method named PCAMIX developed for the analysis of both numerical and categorical data, and including PCA and MCA as special cases. In case of only categorical data, this criterion is a varimax-based one relying on the correlation ratio between the categorical variables and the MCA numerical components. The optimization of this criterion is then reached by the algorithm of De Leeuw and Pruzansky (1978). In this paper, we give the analytic expression of the optimal angle of planar rotation for this criterion. If more than two principal components are to be retained, similarly to what is done by Kaiser (1958) for PCA, this planar solution is computed in a practical algorithm applying successive pairwise planar rotations for optimizing the rotation criterion. A simulation study is used to illustrate the analytic expression of the angle for planar rotation. The proposed procedure is also applied on a real data set to show the possible benefits of using rotation in MCA.categorical data, multiple correspondence analysis, correlation ratio, rotation, varimax criterion

Clustering high dimensional categorical data via topographical features

Analysis of categorical data is a challenging task. In this paper, we propose to compute topographical features of high-dimensional categorical data. We propose an efficient algorithm to extract modes of the underlying distribution and their attractive basins. These topographical features provide a geometric view of the data and can be applied to visualization and clustering of real world challenging datasets. Experiments show that our principled method outperforms state-of-the-art clustering methods while also admits an embarrassingly parallel property

Частная собственность сквозь призму социологического институционализма

The author of this article makes an attempt to define the categorical matter of conceptual model of social institution. Thereto the institutional conceptualizations lately suggested by Ukrainian sociologists are used as initial patterns. The named categorical pattern will be applied in the future as a means to define theoretical and methodological basis for the analysis of integration/disintegration processes in the social structure of modern Ukrainian society that changed owing to the private property re-institutionalization in the course of privatization