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    Probabilistic Relational Connectivity Analysis of Bigram Models
    (Ieee, 2019) Alnahas, Dima; Alagoz, Bans Baykant
    This study demonstrates an application of probabilistic relational graph connectivity analysis in bigram models (2-gram) of texts. The probabilistic relation matrices are calculated by estimating bigram co-occurrence probabilities in word sequence of a given short text. Then, deeper probabilistic connectivity relations among word sequences can be considered by calculating powers of probabilistic relation matrix of bigram models. Cosine similarity measure is used to evaluate similarity of probabilistic connectivity patterns of lexemes in a given message. Illustrative analysis examples are presented to discuss results of sentence-wise and short text analyses.
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    Revisiting Probabilistic Relation Analysis: Using Probabilistic Relation Graphs for Relational Similarity Analysis of Words in Short Texts
    (2023) Alnahas, Dima; Ateş, Abdullah; Aydın, Ahmet Arif; Alagöz, Barış Baykant
    Relation graphs provide useful tools for structural and relational analyses of highly complex multi-component systems. Probabilistic relation graph models can represent relations between system components by their probabilistic links. These graph types have been widely used for the graphical representation of Markov models and bigram probabilities. This study presents an implication of relational similarities within probabilistic graph models of textual entries. The article discusses several utilization examples of two fundamental similarity measures in the probabilistic analysis of short texts. To this end, the construction of probabilistic graph models by using bigram probability matrices of textual entries is illustrated, and vector spaces of input word-vectors and output word-vectors are formed. In this vector space, the utilization of cosine similarity and mean squared error measures are demonstrated to evaluate the probabilistic relational similarity between lexeme pairs in short texts. By using probabilistic relation graphs of the short texts, relational interchangeability analyses of lexeme pairs are conducted, and confidence index parameters are defined to express the reliability of these analyses. Potential applications of these graphs in language processing and linguistics are discussed on the basis of the analysis results of example texts. The performance of the applied similarity measures is evaluated in comparison to the similarity index of the word2vec language model. Results of the comparative study in one of the illustrative examples reveal that synonyms with 0.18157 word2vec similarity value scored 1.0 cosine similarity value according to the proposed method.
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    A Theoretical Study on Event Spreading Prediction by Probabilistic Connectivity Analysis in Dispersive Networks
    (Ieee, 2019) Alnahas, Dima; Alagoz, Baris Baykant
    This study discusses a potential use of probabilistic connectivity analysis for prediction of future progresses of events in stochastic network models. Probabilistic relation graphs provide a useful mathematical tool for representation of stochastic network models such as Markov chain models and random transitive networks. These stochastic network models have been widely and effectively used for analysis purpose in a range of application areas (e.g. statistics, language processing, genetics...). In this fashion, the current study investigates applications of the graph connectivity analysis based on taking powers of probabilistic relation matrices. Such probabilistic connectivity analysis can provide knowledge for prediction of future progress of spreading stochastic events in dispersive networks. Some properties of a stochastic dispersive network can be explored by taking power of probabilistic relation matrix, which indeed yields a probabilistic projection for future progress of the network in probability domain. Paper aims to develop a basic understanding for applications of probabilistic connectivity analysis for dispersive networks. Accordingly, applications of this analysis are considered, and illustrative examples are presented for discussion.