scholarly journals Topological Persistence in Geometry and Analysis

2020 ◽  
Author(s):  
Leonid Polterovich ◽  
Daniel Rosen ◽  
Karina Samvelyan ◽  
Jun Zhang
Keyword(s):  
Topological Persistence

scholarly journals Percolating length scales from topological persistence analysis of micro‐CTimages of porous materials

2016 ◽  
Vol 52 (1) ◽  
pp. 315-329 ◽  
Author(s):  
Vanessa Robins ◽  
Mohammad Saadatfar ◽  
Olaf Delgado‐Friedrichs ◽  
Adrian P. Sheppard
Keyword(s):  
Porous Materials ◽  
Length Scales ◽  
Topological Persistence

scholarly journals Topological Persistence of the Unit Eigenvectors of a Perturbed Fredholm Operator of Index Zero

2014 ◽  
Vol 33 (3) ◽  
pp. 347-367 ◽  
Author(s):  
Raffaele Chiappinelli ◽  
Massimo Furi ◽  
Maria Patrizia Pera
Keyword(s):  
Fredholm Operator ◽  
Index Zero ◽  
Topological Persistence

scholarly journals A Topological Method for Comparing Document Semantics

2020 ◽  
Author(s):  
Yuqi Kong ◽  
Fanchao Meng ◽  
Ben Carterette
Keyword(s):  
Information Retrieval ◽  
Natural Language Processing ◽  
Language Processing ◽  
State Of The Art ◽  
Vector Space Model ◽  
The Other ◽  
Space Model ◽  
Topological Persistence ◽  
Art Methods ◽  
Novel Algorithm

Comparing document semantics is one of the toughest tasks in both Natural Language Processing and Information Retrieval. To date, on one hand, the tools for this task are still rare. On the other hand, most relevant methods are devised from the statistic or the vector space model perspectives but nearly none from a topological perspective. In this paper, we hope to make a different sound. A novel algorithm based on topological persistence for comparing semantics similarity between two documents is proposed. Our experiments are conducted on a document dataset with human judges’ results. A collection of state-of-the-art methods are selected for comparison. The experimental results show that our algorithm can produce highly human-consistent results, and also beats most state-of-the-art methods though ties with NLTK.

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