Fundamenta Informaticae - Volume 172, issue 4

Authors: Bera, Somnath | Mahalingam, Kalpana

Article Type: Research Article

Abstract: This paper investigates properties of words such that their Parikh q -matrices commute. For any two words u ,   v   ∈ ∑ k * , the concept of q -weak ratio property between u and v is introduced. Based on this property a necessary and sufficient condition for the Parikh q -matrices of any two words over binary alphabet to commute is given. This paper also provides a special class of words over an arbitrary alphabet ∑k such that their Parikh q -matrices commute.

Keywords: Parikh q-matrix mapping, commutativity, q-ambiguity, q-weak ratio property

DOI: 10.3233/FI-2020-1907

Citation: Fundamenta Informaticae, vol. 172, no. 4, pp. 327-341, 2020

Authors: Kheirfam, Behrouz

Article Type: Research Article

Abstract: In this article, we present a second-order corrector infeasible interior-point method based on one-norm large neighborhood for symmetric optimization. We consider the classical Newton direction as the sum of two other directions associated with the negative and positive parts of the right-hand side of the centrality equation. In addition to equipping them with different step lengths, we add a corrector step that is multiplied by the square of the step length in the expression of the new iterate. The convergence analysis of the algorithm is discussed and it is proved that the new algorithm has the same complexity as small …neighborhood infeasible interiorpoint algorithms for the Nesterov-Todd (NT) direction, and the xs and sx directions. Show more

Keywords: Symmetric optimization, infeasible interior-point methods, Euclidean Jordan algebra, polynomial complexity

DOI: 10.3233/FI-2020-1908

Citation: Fundamenta Informaticae, vol. 172, no. 4, pp. 343-359, 2020

Authors: Kłopotek, Mieczysław A.

Article Type: Research Article

Abstract: We prove in this paper that the expected value of the objective function of the k -means++ algorithm for samples converges to population expected value. As k -means++, for samples, provides with constant factor approximation for k -means objectives, such an approximation can be achieved for the population with increase of the sample size. This result is of potential practical relevance when one is considering using subsampling when clustering large data sets (large data bases).

Keywords: mathematical foundations, data mining, k-means++, consistency, expected value, constant factor approximation, k-means cost function

DOI: 10.3233/FI-2020-1909

Citation: Fundamenta Informaticae, vol. 172, no. 4, pp. 361-377, 2020

Authors: Koczkodaj, Waldemar W. | Smarzewski, Ryszard | Szybowski, Jacek

Article Type: Research Article

Abstract: In this study, the orthogonalization process for different inner products is applied to pairwise comparisons. Properties of consistent approximations of a given inconsistent pairwise comparisons matrix are examined. A method of a derivation of a priority vector induced by a pairwise comparison matrix for a given inner product has been introduced. The mathematical elegance of orthogonalization and its universal use in most applied sciences has been the motivating factor for this study. However, the finding of this study that approximations depend on the inner product assumed, is of considerable importance.

Keywords: pairwise comparisons, inconsistency, approximation, inner product, orthogonal basis

DOI: 10.3233/FI-2020-1910

Citation: Fundamenta Informaticae, vol. 172, no. 4, pp. 379-397, 2020

Authors: Tzacheva, Angelina A. | Shankar, Ramya A. | Ramachandran, Sridharan | Bagavathi, Arunkumar

Article Type: Research Article

Abstract: A knowledge discovery system is prone to yielding plenty of patterns, presented in the form of rules. Sifting through to identify useful and interesting patterns is a tedious and time consuming process. An important measure of interestingness is: whether or not the pattern can be used in the decision making process of a business to increase profit. Hence, actionable patterns, such as action rules, are desirable. Action rules may suggest actions to be taken based on the discovered knowledge. In this way contributing to business strategies and scientific research. The large amounts of knowledge in the form of …rules presents a challenge of identifying the essence, the most important part, of high usability. We focus on decreasing the space of action rules through generalization. In this work, we present a new method for computing the lowest cost of action rules and their generalizations. We discover action rules of lowest cost by taking into account the correlations between individual atomic action sets . Show more

Keywords: action rules, interestingness, actionable knowledge discovery, generalization, cost of action rules

DOI: 10.3233/FI-2020-1911

Citation: Fundamenta Informaticae, vol. 172, no. 4, pp. 399-412, 2020

Authors: Zheng, Tingting

Article Type: Research Article

Abstract: Some scholars have proposed homomorphisms between information systems based on consistent functions. However, the binary relations in the codomain induced by consistent functions thoroughly depend on the binary relations induced by the original domain systems. This paper introduces the concept of core knowledge to analyze the intrinsical topology structures of binary approximation spaces, binary knowledge bases and binary information systems. Because of the three different categories, we use the term “morphism” from category theory to depict the communication into the three categories. A morphism can be regarded as the composition of a natural projection induced by core knowledge and an …embedding, which are more general than homomorphisms. What’s more, this paper proposes the notion of isomorphism and shows that the two isomorphic categories can be seen as one category based on the topological invariance. Considering that the reduction of knowledge and attributes should be based on the premise of maintaining the structure of core knowledge, isomorphisms will provide the theoretical basis of the reduction. Show more

Keywords: Morphism, core knowledge, homomorphism, binary approximation space (BAS), binary knowledge base (BKB), binary information system (BIS), isomorphism

DOI: 10.3233/FI-2020-1912

Citation: Fundamenta Informaticae, vol. 172, no. 4, pp. 413-434, 2020