arXiv subjects

Mieczysław A. Kłopotek

Publications and source records attributed to Mieczysław A. Kłopotek.

41 records · Page 3Linked to original sources

arXiv2017

Basic Formal Properties of A Relational Model of The Mathematical Theory of Evidence

The paper presents a novel view of the Dempster-Shafer belief function as a measure of diversity in relational data bases. It is demonstrated that under the interpretation The Dempster rule of evidence combination corresponds to the join operator of the relational database theory. This rough-set based interpretation is qualitative in nature and can represent a number of belief function operators. The interpretation has the property that Given a definition of the belief measure of objects in the interpretation domain we can perform operations in this domain and the measure of the resulting object is derivable from measures of component objects via belief operator. We demonstrated this property for Dempster rule of combination, marginalization, Shafer's conditioning, independent variables, Shenoy's notion of conditional independence of variables. The interpretation is based on rough sets (in connection with decision tables), but differs from previous interpretations of this type in that it counts the diversity rather than frequencies in a decision table.

cs.AI↗

arXiv2017

On the Consistency of $k$-means++ algorithm

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).

cs.LG↗

arXiv2017

Traditional PageRank versus Network Capacity Bound

In a former paper we simplified the proof of a theorem on personalized random walk that is fundamental to graph nodes clustering and generalized it to bipartite graphs for a specific case where the proobability of random jump was proprtional to the number of links of "personally prefereed" nodes. In this paper we turn to the more complex issue of graphs in which the random jump follows uniform distribution.

cs.SI↗

arXiv2017

Semantic classifier approach to document classification

In this paper we propose a new document classification method, bridging discrepancies (so-called semantic gap) between the training set and the application sets of textual data. We demonstrate its superiority over classical text classification approaches, including traditional classifier ensembles. The method consists in combining a document categorization technique with a single classifier or a classifier ensemble (SEMCOM algorithm - Committee with Semantic Categorizer).

cs.IR↗

arXiv2016

Grammatical Case Based IS-A Relation Extraction with Boosting for Polish

Pattern-based methods of IS-A relation extraction rely heavily on so called Hearst patterns. These are ways of expressing instance enumerations of a class in natural language. While these lexico-syntactic patterns prove quite useful, they may not capture all taxonomical relations expressed in text. Therefore in this paper we describe a novel method of IS-A relation extraction from patterns, which uses morpho-syntactical annotations along with grammatical case of noun phrases that constitute entities participating in IS-A relation. We also describe a method for increasing the number of extracted relations that we call pseudo-subclass boosting which has potential application in any pattern-based relation extraction method. Experiments were conducted on a corpus of about 0.5 billion web documents in Polish language.

cs.CL↗