scholarly journals The Fisher-Rao Distance between Multivariate Normal Distributions: Special Cases, Boundsand Applications

Entropy ◽  
2020 ◽  
Vol 22 (4) ◽  
pp. 404 ◽  
Author(s):  
Julianna Pinele ◽  
João E. Strapasson ◽  
Sueli I. R. Costa
Keyword(s):  
Statistical Model ◽  
Clustering Algorithm ◽  
Probability Distributions ◽  
Regularity Conditions ◽  
Multivariate Normal ◽  
Radar Systems ◽  
Special Cases ◽  
Metric Invariant ◽  
Hierarchical Clustering Algorithm ◽  
Rao Distance

The Fisher–Rao distance is a measure of dissimilarity between probability distributions, which, under certain regularity conditions of the statistical model, is up to a scaling factor the unique Riemannian metric invariant under Markov morphisms. It is related to the Shannon entropy and has been used to enlarge the perspective of analysis in a wide variety of domains such as image processing, radar systems, and morphological classification. Here, we approach this metric considered in the statistical model of normal multivariate probability distributions, for which there is not an explicit expression in general, by gathering known results (closed forms for submanifolds and bounds) and derive expressions for the distance between distributions with the same covariance matrix and between distributions with mirrored covariance matrices. An application of the Fisher–Rao distance to the simplification of Gaussian mixtures using the hierarchical clustering algorithm is also presented.

scholarly journals Unifying rational models of categorization via the hierarchical Dirichlet process

2019 ◽  
Author(s):  
Tom Griffiths ◽  
Kevin Canini ◽  
Adam N Sanborn ◽  
Danielle Navarro
Keyword(s):  
Statistical Model ◽  
Dirichlet Process ◽  
Probability Distributions ◽  
Hierarchical Dirichlet Process ◽  
Rational Models ◽  
Special Cases

Models of categorization make different representational assumptions, with categories being represented by prototypes, sets of exemplars, and everything in between. Rational models of categorization justify these representational assumptions in terms of different schemes for estimating probability distributions. However, they do not answer the question of which scheme should be used in representing a given category. We show that existing rational models of categorization are special cases of a statistical model called the hierarchical Dirichlet process, which can be used to automatically infer a representation of the appropriate complexity for a given category.

Handling WSD using Hierarchical Clustering Algorithm with sentences

2018 ◽  
pp. 83-88
Author(s):  
Mohana Priya K ◽  
Pooja Ragavi S ◽  
Krishna Priya G
Keyword(s):  
Hierarchical Clustering ◽  
Similarity Measure ◽  
Clustering Algorithm ◽  
Clustering Algorithms ◽  
Cosine Similarity Measure ◽  
Hierarchical Clustering Algorithm ◽  
Multiple Levels ◽  
Pos Tagger ◽  
Sentence Clustering ◽  
The Right

Clustering is the process of grouping objects into subsets that have meaning in the context of a particular problem. It does not rely on predefined classes. It is referred to as an unsupervised learning method because no information is provided about the "right answer" for any of the objects. Many clustering algorithms have been proposed and are used based on different applications. Sentence clustering is one of best clustering technique. Hierarchical Clustering Algorithm is applied for multiple levels for accuracy. For tagging purpose POS tagger, porter stemmer is used. WordNet dictionary is utilized for determining the similarity by invoking the Jiang Conrath and Cosine similarity measure. Grouping is performed with respect to the highest similarity measure value with a mean threshold. This paper incorporates many parameters for finding similarity between words. In order to identify the disambiguated words, the sense identification is performed for the adjectives and comparison is performed. semcor and machine learning datasets are employed. On comparing with previous results for WSD, our work has improvised a lot which gives a percentage of 91.2%

scholarly journals Hesitant Fuzzy Linguistic Agglomerative Hierarchical Clustering Algorithm and Its Application in Judicial Practice

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 370
Author(s):  
Shuangsheng Wu ◽  
Jie Lin ◽  
Zhenyu Zhang ◽  
Yushu Yang
Keyword(s):  
Hierarchical Clustering ◽  
Clustering Algorithm ◽  
Clustering Algorithms ◽  
Agglomerative Hierarchical Clustering ◽  
Research Gaps ◽  
Judicial Practice ◽  
Linguistic Term ◽  
Clustering Effect ◽  
Hierarchical Clustering Algorithm ◽  
Fuzzy Linguistic

The fuzzy clustering algorithm has become a research hotspot in many fields because of its better clustering effect and data expression ability. However, little research focuses on the clustering of hesitant fuzzy linguistic term sets (HFLTSs). To fill in the research gaps, we extend the data type of clustering to hesitant fuzzy linguistic information. A kind of hesitant fuzzy linguistic agglomerative hierarchical clustering algorithm is proposed. Furthermore, we propose a hesitant fuzzy linguistic Boole matrix clustering algorithm and compare the two clustering algorithms. The proposed clustering algorithms are applied in the field of judicial execution, which provides decision support for the executive judge to determine the focus of the investigation and the control. A clustering example verifies the clustering algorithm’s effectiveness in the context of hesitant fuzzy linguistic decision information.

scholarly journals Transmission Path Tracking of Maritime COVID-19 Pandemic via Ship Sailing Pattern Mining

2021 ◽  
Vol 13 (3) ◽  
pp. 1089
Author(s):  
Hailin Zheng ◽  
Qinyou Hu ◽  
Chun Yang ◽  
Jinhai Chen ◽  
Qiang Mei
Keyword(s):  
Clustering Algorithm ◽  
Pattern Mining ◽  
Transportation Networks ◽  
Automatic Identification ◽  
Identification System ◽  
Classification Models ◽  
Transmission Path ◽  
The Hierarchical Structure ◽  
Hierarchical Clustering Algorithm ◽  
And Control

Since the spread of the coronavirus disease 2019 (COVID-19) pandemic, the transportation of cargo by ship has been seriously impacted. In order to prevent and control maritime COVID-19 transmission, it is of great significance to track and predict ship sailing behavior. As the nodes of cargo ship transportation networks, ports of call can reflect the sailing behavior of the cargo ship. Accurate hierarchical division of ports of call can help to clarify the navigation law of ships with different ship types and scales. For typical cargo ships, ships with deadweight over 10,000 tonnages account for 95.77% of total deadweight, and 592,244 berthing ships’ records were mined from automatic identification system (AIS) from January to October 2020. Considering ship type and ship scale, port hierarchy classification models are constructed to divide these ports into three kinds of specialized ports, including bulk, container, and tanker ports. For all types of specialized ports (considering ship scale), port call probability for corresponding ship type is higher than other ships, positively correlated with the ship deadweight if port scale is bigger than ship scale, and negatively correlated with the ship deadweight if port scale is smaller than ship scale. Moreover, port call probability for its corresponding ship type is positively correlated with ship deadweight, while port call probability for other ship types is negatively correlated with ship deadweight. Results indicate that a specialized port hierarchical clustering algorithm can divide the hierarchical structure of typical cargo ship calling ports, and is an effective method to track the maritime transmission path of the COVID-19 pandemic.

A bio-inspired hierarchical clustering algorithm with backtracking strategy

2014 ◽  
Vol 42 (2) ◽  
pp. 174-194 ◽  
Author(s):  
Akil Elkamel ◽  
Mariem Gzara ◽  
Hanêne Ben-Abdallah
Keyword(s):  
Hierarchical Clustering ◽  
Clustering Algorithm ◽  
Hierarchical Clustering Algorithm
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