Extracting Knowledge from the Geometric Shape of Social Network Data Using Topological Data Analysis

Topological data analysis is a noble approach to extract meaningful information from high-dimensional data and is robust to noise. It is based on topology, which aims to study the geometric shape of data. In order to apply topological data analysis, an algorithm called mapper is adopted. The output...

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Main Authors: Khaled Almgren, Minkyu Kim, Jeongkyu Lee
Format: Article
Language:English
Published: MDPI AG 2017-07-01
Series:Entropy
Subjects:
Online Access:https://www.mdpi.com/1099-4300/19/7/360
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author Khaled Almgren
Minkyu Kim
Jeongkyu Lee
author_facet Khaled Almgren
Minkyu Kim
Jeongkyu Lee
author_sort Khaled Almgren
collection DOAJ
description Topological data analysis is a noble approach to extract meaningful information from high-dimensional data and is robust to noise. It is based on topology, which aims to study the geometric shape of data. In order to apply topological data analysis, an algorithm called mapper is adopted. The output from mapper is a simplicial complex that represents a set of connected clusters of data points. In this paper, we explore the feasibility of topological data analysis for mining social network data by addressing the problem of image popularity. We randomly crawl images from Instagram and analyze the effects of social context and image content on an image’s popularity using mapper. Mapper clusters the images using each feature, and the ratio of popularity in each cluster is computed to determine the clusters with a high or low possibility of popularity. Then, the popularity of images are predicted to evaluate the accuracy of topological data analysis. This approach is further compared with traditional clustering algorithms, including k-means and hierarchical clustering, in terms of accuracy, and the results show that topological data analysis outperforms the others. Moreover, topological data analysis provides meaningful information based on the connectivity between the clusters.
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spelling doaj.art-6255fb3a022c40fa89ff2e568f97adbb2022-12-22T02:57:16ZengMDPI AGEntropy1099-43002017-07-0119736010.3390/e19070360e19070360Extracting Knowledge from the Geometric Shape of Social Network Data Using Topological Data AnalysisKhaled Almgren0Minkyu Kim1Jeongkyu Lee2Computer Science and Engineering Department, University of Bridgeport, Bridgeport, CT 06614, USAASML, 77 Danbury RD, Wilton, CT 06897, USAComputer Science and Engineering Department, University of Bridgeport, Bridgeport, CT 06614, USATopological data analysis is a noble approach to extract meaningful information from high-dimensional data and is robust to noise. It is based on topology, which aims to study the geometric shape of data. In order to apply topological data analysis, an algorithm called mapper is adopted. The output from mapper is a simplicial complex that represents a set of connected clusters of data points. In this paper, we explore the feasibility of topological data analysis for mining social network data by addressing the problem of image popularity. We randomly crawl images from Instagram and analyze the effects of social context and image content on an image’s popularity using mapper. Mapper clusters the images using each feature, and the ratio of popularity in each cluster is computed to determine the clusters with a high or low possibility of popularity. Then, the popularity of images are predicted to evaluate the accuracy of topological data analysis. This approach is further compared with traditional clustering algorithms, including k-means and hierarchical clustering, in terms of accuracy, and the results show that topological data analysis outperforms the others. Moreover, topological data analysis provides meaningful information based on the connectivity between the clusters.https://www.mdpi.com/1099-4300/19/7/360topologytopological data analysisgeometrysocial networks analysis and mininghigh-dimensional data analysis
spellingShingle Khaled Almgren
Minkyu Kim
Jeongkyu Lee
Extracting Knowledge from the Geometric Shape of Social Network Data Using Topological Data Analysis
Entropy
topology
topological data analysis
geometry
social networks analysis and mining
high-dimensional data analysis
title Extracting Knowledge from the Geometric Shape of Social Network Data Using Topological Data Analysis
title_full Extracting Knowledge from the Geometric Shape of Social Network Data Using Topological Data Analysis
title_fullStr Extracting Knowledge from the Geometric Shape of Social Network Data Using Topological Data Analysis
title_full_unstemmed Extracting Knowledge from the Geometric Shape of Social Network Data Using Topological Data Analysis
title_short Extracting Knowledge from the Geometric Shape of Social Network Data Using Topological Data Analysis
title_sort extracting knowledge from the geometric shape of social network data using topological data analysis
topic topology
topological data analysis
geometry
social networks analysis and mining
high-dimensional data analysis
url https://www.mdpi.com/1099-4300/19/7/360
work_keys_str_mv AT khaledalmgren extractingknowledgefromthegeometricshapeofsocialnetworkdatausingtopologicaldataanalysis
AT minkyukim extractingknowledgefromthegeometricshapeofsocialnetworkdatausingtopologicaldataanalysis
AT jeongkyulee extractingknowledgefromthegeometricshapeofsocialnetworkdatausingtopologicaldataanalysis