The Number of Topics Optimization: Clustering Approach Anastasiia Sen, Fedor Krasnov March 21, 2019 

Presentation outline • Introduction; • Methodology: o Topic model; o Metrics; o Scheme; • Experiments: o Experiment 1: scientific articles; o Experiment 2: patents; • Conclusion. 

Introduction Existing estimates: • Perplexity: for complete set of topics; • HDP : for the whole collection of documents; • Renyi and Tsallis entropies: for the big collection; • Matrix approach; • Partition coefficient, Dunn index, Davies Bouldin Index, silhouette coefficient: quality of clusters. Regularization dense representation cDBI 

Methodology. Topic model Distribution of topics: 1) uniform 2) sparse for main and dense for supporting 

Methodology. Metrics Internal metrics: • Core: = { ∈ ≥ ℎ • Size of core: | | • Purity: = ∈ (|) • Contrast: 1 || ∈ (|) • Coherence: ℎ = 2 (−1) =1 −1 =1 , , where , = log Algorithm for cDBI: ∶ = ((, , )) ∈ : ∶= ∈ () ∶= 1 dim ∈ ⋅ () | | ∶= 1 dim ∈ 

Methodology. Scheme Corpus preparation Change the order of documents Perplexity minimization ARTM learning Calculation of the metrics for different number of topics Writing result to the database Dictionary creation Search to optimal regularization parameters Transformation of sparse topics representation to dense representation 

First experiment Collection of 1695 scientific articles Dense presentation projection of the topics with preservation of distances. Dependencies of the main internal metrics of the quality on the number of topics 

First experiment Cluster Validation Metrics: 1) Silhouette Coefficient; 2) Calinski-Harabaz index 

First experiment Cosine Davies Bouldin index 

Second experiment Collection of 50 000 patents Average kernel size Dependencies of the main internal metrics of the quality on the number of topics 

Second experiment Cluster Validation Metrics: 1) Silhouette Coefficient; 2) Calinski-Harabaz index 

Second experiment Cosine Davies Bouldin index 

Conclusion • Method od determination the optimal number of topic; • Metric of approach optimization – cosine Davies Bouldin index; • Tests on two collections:  Small (science article);  Big (patents). • Using.