We propose a new algorithm for recommender systems with numeric ratings which is based on Pattern Structures (RAPS). As the input the algorithm takes rating matrix, e.g., such that it contains movies rated by users. For a target user, the algorithm returns a rated list of items (movies) based on its previous ratings and ratings of other users. We compare the results of the proposed algorithm in terms of precision and recall measures with Slope One, one of the state-of-the-art item-based algorithms, on Movie Lens dataset and RAPS demonstrates the best or comparable quality.
Formal Concept Analysis (FCA) @cite_1 is a powerful algebraic framework for knowledge representation and processing @cite_8 @cite_5 . However, in its original formulation it deals with mainly Boolean data. Even though original numeric data can be represented by so called multi-valued context, it requires concept scaling to be transformed to a plain context (i.e. a binary object-attribute table). There are several extensions of FCA to numeric setting like Fuzzy Formal Concept Analysis @cite_10 @cite_12 . In this paper, to recommend particular user items of interest we use Pattern Structures, an extension of FCA to deal with data that have ordered descriptions. In fact, we use interval pattern structures that were proposed in @cite_13 and successfully applied, e.g., in gene expression data analysis @cite_6 .
@cite_13 @cite_8 @cite_1 @cite_6 @cite_5 @cite_10 @cite_12
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Pattern structures consist of objects with descriptions (called patterns) that allow a semilattice operation on them. Pattern structures arise naturally from ordered data, e.g., from labeled graphs ordered by graph morphisms. It is shown that pattern structures can be reduced to formal contexts, however sometimes processing the former is often more efficient and obvious than processing the latter. Concepts, implications, plausible hypotheses, and classifications are defined for data given by pattern structures. Since computation in pattern structures may be intractable, approximations of patterns by means of projections are introduced. It is shown how concepts, implications, hypotheses, and classifications in projected pattern structures are related to those in original ones. From the Publisher: This is the first textbook on formal concept analysis. It gives a systematic presentation of the mathematical foundations and their relation to applications in computer science, especially in data analysis and knowledge processing. Above all, it presents graphical methods for representing conceptual systems that have proved themselves in communicating knowledge. Theory and graphical representation are thus closely coupled together. The mathematical foundations are treated thoroughly and illuminated by means of numerous examples. This paper addresses the important problem of efficiently mining numerical data with formal concept analysis (FCA). Classically, the only way to apply FCA is to binarize the data, thanks to a so-called scaling procedure. This may either involve loss of information, or produce large and dense binary data known as hard to process. In the context of gene expression data analysis, we propose and compare two FCA-based methods for mining numerical data and we show that they are equivalent. The first one relies on a particular scaling, encoding all possible intervals of attribute values, and uses standard FCA techniques. The second one relies on pattern structures without a priori transformation, and is shown to be more computationally efficient and to provide more readable results. Experiments with real-world gene expression data are discussed and give a practical basis for the comparison and evaluation of the methods. This is the first part of a large survey paper in which we analyze recent literature on Formal Concept Analysis (FCA) and some closely related disciplines using FCA. We collected 1072 papers published between 2003 and 2011 mentioning terms related to Formal Concept Analysis in the title, abstract and keywords. We developed a knowledge browsing environment to support our literature analysis process. We use the visualization capabilities of FCA to explore the literature, to discover and conceptually represent the main research topics in the FCA community. In this first part, we zoom in on and give an extensive overview of the papers published between 2003 and 2011 on developing FCA-based methods for knowledge processing. We also give an overview of the literature on FCA extensions such as pattern structures, logical concept analysis, relational concept analysis, power context families, fuzzy FCA, rough FCA, temporal and triadic concept analysis and discuss scalability issues. This paper is a follow up to "Belohlavek, Vychodil: What is a fuzzy concept lattice?, Proc. CLA 2005, 34-45", in which we provided a then up-to-date overview of various approaches to fuzzy concept lattices and relationships among them. The main goal of the present paper is different, namely to provide an overview of conceptual issues in fuzzy concept lattices. Emphasized are the issues in which fuzzy concept lattices differ from ordinary concept lattices. In a sense, this paper is written for people familiar with ordinary concept lattices who would like to learn about fuzzy concept lattices. Due to the page limit, the pape. Formal Concept Analysis (FCA) is a mathematical technique that has been extensively applied to Boolean data in knowledge discovery, information retrieval, web mining, etc. applications. During the past years, the research on extending FCA theory to cope with imprecise and incomplete information made significant progress. In this paper, we give a systematic overview of the more than 120 papers published between 2003 and 2011 on FCA with fuzzy attributes and rough FCA. We applied traditional FCA as a text-mining instrument to 1072 papers mentioning FCA in the abstract. These papers were formatted in pdf files and using a thesaurus with terms referring to research topics, we transformed them into concept lattices. These lattices were used to analyze and explore the most prominent research topics within the FCA with fuzzy attributes and rough FCA research communities. FCA turned out to be an ideal metatechnique for representing large volumes of unstructured texts.