Triadic Formal Concept Analysis and triclustering: searching for optimal patterns
This paper presents several definitions of “optimal patterns” in triadic data and results of experimental comparison of five triclustering algorithms on real-world and synthetic datasets. The evaluation is carried over such criteria as resource efficiency, noise tolerance and quality scores involving cardinality, density, coverage, and diversity of the patterns. An ideal triadic pattern is a totally dense maximal cuboid (formal triconcept). Relaxations of this notion under consideration are: OAC-triclusters; triclusters optimal with respect to the least-square criterion; and graph partitions obtained by using spectral clustering. We show that searching for an optimal tricluster cover is an NP-complete problem, whereas determining the number of such covers is #P-complete. Our extensive computational experiments lead us to a clear strategy for choosing a solution at a given dataset guided by the principle of Pareto-optimality according to the proposed criteria.
In this paper we propose two novel methods for analyzing data collected from online social networks. In particular we will do analyses on Vkontake data (Russian online social network). Using biclustering we extract groups of users with similar interests and find communities of users which belong to similar groups. With triclustering we reveal users’ interests as tags and use them to describe Vkontakte groups. After this social tagging process we can recommend to a particular user relevant groups to join or new friends from interesting groups which have a similar taste. We present some preliminary results and explain how we are going to apply these methods on massive data repositories.
The paper makes a brief introduction into multiple classifier systems and describes a particular algorithm which improves classification accuracy by making a recommendation of an algorithm to an object. This recommendation is done under a hypothesis that a classifier is likely to predict the label of the object correctly if it has correctly classified its neighbors. The process of assigning a classifier to each object involves here the apparatus of Formal Concept Analysis. We explain the principle of the algorithm on a toy example and describe experiments with real-world datasets.
This book constitutes the second part of the refereed proceedings of the 10th International Conference on Formal Concept Analysis, ICFCA 2012, held in Leuven, Belgium in May 2012. The topics covered in this volume range from recent advances in machine learning and data mining; mining terrorist networks and revealing criminals; concept-based process mining; to scalability issues in FCA and rough sets.
Concept discovery is a Knowledge Discovery in Databases (KDD) research field that uses human-centered techniques such as Formal Concept Analysis (FCA), Biclustering, Triclustering, Conceptual Graphs etc. for gaining insight into the underlying conceptual structure of the data. Traditional machine learning techniques are mainly focusing on structured data whereas most data available resides in unstructured, often textual, form. Compared to traditional data mining techniques, human-centered instruments actively engage the domain expert in the discovery process. This volume contains the contributions to CDUD 2011, the International Workshop on Concept Discovery in Unstructured Data (CDUD) held in Moscow. The main goal of this workshop was to provide a forum for researchers and developers of data mining instruments working on issues with analyzing unstructured data. We are proud that we could welcome 13 valuable contributions to this volume. The majority of the accepted papers described innovative research on data discovery in unstructured texts. Authors worked on issues such as transforming unstructured into structured information by amongst others extracting keywords and opinion words from texts with Natural Language Processing methods. Multiple authors who participated in the workshop used methods from the conceptual structures field including Formal Concept Analysis and Conceptual Graphs. Applications include but are not limited to text mining police reports, sociological definitions, movie reviews, etc.
We combine bi- and triclustering to analyse data collected from the Russian online social network Vkontakte. Using biclustering we extract groups of users with similar interests and find communities of users which belong to similar groups. With triclustering we reveal users' interests as tags and use them to describe Vkontakte groups. After this social tagging process we can recommend to a particular user relevant groups to join or new friends from interesting groups which have a similar taste. We present some preliminary results and explain how we are going to apply these methods on massive data repositories.
The problem of management of the nonlinear object which is exposed to impact of uncontrollable indignations, is considered in a key of differential game. Synthesis of optimum managements is made with application of transformation of the nonlinear equation of initial object in the differential equation with the parameters depending on a condition. The square-law functional of quality allows to formulate synthesis conditions in the form of need of search of solutions of the equation of Rikkati. The solution of the equation of Rikkati with the parameters depending on a condition, is in a symbolical view with application of algebraic methods that allows to generalize a number of earlier published theoretical results, to receive rather constructive decisions in a number of statements of problems of management.
The article is based upon the fact that the growing demand for master data management systems has not yet produced a commonly accepted metodology for their design and development/ The article offers two mathematical models? that allow a master data management systems designer a way to formally describe their system before development and verify the system quality by measurements? unique to master data management systems.