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Matrix factorization has proven to be one of the most accurate recommendation approaches. However, it faces one major shortcoming: the latent features that result from the factorization are not directly interpretable. Providing interpretation for these features is important not only to help explain the recommendations presented to users, but also to understand the underlying relations between the users and the items. This paper consists of 2 contributions. First, we propose to automatically interpret features as users, referred to as representative users. This interpretation relies on the study of the matrices that result from the factorization and on their link with the original rating matrix. Such an interpretation is not only performed automatically, as it does not require any human expertise, but it also helps to explain the recommendations. The second proposition of this paper is to exploit this interpretation to alleviate the content-less new item cold-start problem. The experiments conducted on several benchmark datasets confirm that the features discovered by a NonNegative Matrix Factorization can be interpreted as users and that representative users are a reliable source of information that allows to accurately estimate ratings on new items. They are thus a promising way to solve the new item cold-start problem.

One of the difficult problems that arises during football competitions is match-fixing. In terms of negative effect, such shameful phenomena are commensurate with the problem of doping. This paper has analyzed known methods for the possible detection of match-fixing, including sociological analysis of participants in match-fixing, methods for predicting the outcome of the match, analysis of bets and performance of the player or team during the match. It is noted that the assessment of match-fixed results in the considered methods is carried out based on the analysis of a large amount of data. But such information is not always available. Given the insufficient formalization of the problem area, it is relevant to conduct research that does not require a large amount of non-publicly available data but, at the same time, makes it possible to effectively identify potentially suspicious matches regarding a fixed result. The description of the input data is formalized in the form of a data structure containing a chronological history of the results of football seasons, the ranking of teams and matches of the season depending on the overall result of the teams in the season. A method for detecting suspicious football matches with a fixed result has been built using conformal predictors and power martingales within which a new measure of non-conformity has been introduced to determine atypical football matches. To obtain a generalization of the statistics of atypical matches, a power submartingale was used. Evaluation of the effectiveness of the developed method for detecting suspicious football matches was carried out based on precision and recall of the classification metrics using data on the 2013–2014 season of the French II League. The quality of work of the developed method reaches 85 % in terms of precision metric, 96 % in terms of recall metric, and 0.853 in terms of metric F1.

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