Unsupervised machine learning approaches to the q-state Potts model
In this paper, we study phase transitions of the q -state Potts model through a number of unsupervised machine learning techniques, namely Principal Component Analysis (PCA), k -means clustering, Uniform Manifold Approximation and Projection (UMAP), and Topological Data Analysis (TDA). Even though i...
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| Veröffentlicht in: | The European physical journal. B, Condensed matter physics Condensed matter physics, 2022-11, Vol.95 (11), Article 189 |
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| container_title | The European physical journal. B, Condensed matter physics |
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| creator | Tirelli, Andrea Carvalho, Danyella O. Oliveira, Lucas A. de Lima, José P. Costa, Natanael C. dos Santos, Raimundo R. |
| description | In this paper, we study phase transitions of the
q
-state Potts model through a number of unsupervised machine learning techniques, namely Principal Component Analysis (PCA),
k
-means clustering, Uniform Manifold Approximation and Projection (UMAP), and Topological Data Analysis (TDA). Even though in all cases we are able to retrieve the correct critical temperatures
T
c
(
q
)
, for
q
=
3
,
4
and 5, results show that non-linear methods as UMAP and TDA are less dependent on finite-size effects. This study may be considered as a benchmark for the use of different unsupervised machine learning algorithms in the investigation of phase transitions.
Graphical abstract |
| doi_str_mv | 10.1140/epjb/s10051-022-00453-3 |
| format | Article |
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q
-state Potts model through a number of unsupervised machine learning techniques, namely Principal Component Analysis (PCA),
k
-means clustering, Uniform Manifold Approximation and Projection (UMAP), and Topological Data Analysis (TDA). Even though in all cases we are able to retrieve the correct critical temperatures
T
c
(
q
)
, for
q
=
3
,
4
and 5, results show that non-linear methods as UMAP and TDA are less dependent on finite-size effects. This study may be considered as a benchmark for the use of different unsupervised machine learning algorithms in the investigation of phase transitions.
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q
-state Potts model through a number of unsupervised machine learning techniques, namely Principal Component Analysis (PCA),
k
-means clustering, Uniform Manifold Approximation and Projection (UMAP), and Topological Data Analysis (TDA). Even though in all cases we are able to retrieve the correct critical temperatures
T
c
(
q
)
, for
q
=
3
,
4
and 5, results show that non-linear methods as UMAP and TDA are less dependent on finite-size effects. This study may be considered as a benchmark for the use of different unsupervised machine learning algorithms in the investigation of phase transitions.
Graphical abstract</description><subject>Algorithms</subject><subject>Cluster analysis</subject><subject>Clustering</subject><subject>Complex Systems</subject><subject>Condensed Matter Physics</subject><subject>Data analysis</subject><subject>Fluid- and Aerodynamics</subject><subject>Machine learning</subject><subject>Phase transitions</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Principal components analysis</subject><subject>Regular Article - Statistical and Nonlinear Physics</subject><subject>Size effects</subject><subject>Solid State Physics</subject><subject>Unsupervised learning</subject><subject>Vector quantization</subject><issn>1434-6028</issn><issn>1434-6036</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNqFkE9LAzEQxYMoWKufwYDn2GQnyWaPUvwHgh7sOaSbSbul3d0mqeC3d-uKHj3NMLz35vEj5FrwWyEkn2G_Wc6S4FwJxouCcS4VMDghEyFBMs1Bn_7uhTknFyltOOdCCzkh80WbDj3GjyahpztXr5sW6RZdbJt2RV3fx244YqK5o3mNdM9SdhnpW5dzorvO4_aSnAW3TXj1M6dk8XD_Pn9iL6-Pz_O7F1YDyMzQQ4nSGC1NKL1XzteGK6mXPuhqqO9UHVThlKmKJUgQCNoEjhxCBT5ICVNyM-YOnfYHTNluukNsh5e2KEFpKSooB1U5qurYpRQx2D42Oxc_reD2SMweidmRmB2I2W9iFganGZ1pcLQrjH_5_1m_ALSmccE</recordid><startdate>20221101</startdate><enddate>20221101</enddate><creator>Tirelli, Andrea</creator><creator>Carvalho, Danyella O.</creator><creator>Oliveira, Lucas A.</creator><creator>de Lima, José P.</creator><creator>Costa, Natanael C.</creator><creator>dos Santos, Raimundo R.</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-7411-4321</orcidid></search><sort><creationdate>20221101</creationdate><title>Unsupervised machine learning approaches to the q-state Potts model</title><author>Tirelli, Andrea ; Carvalho, Danyella O. ; Oliveira, Lucas A. ; de Lima, José P. ; Costa, Natanael C. ; dos Santos, Raimundo R.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c334t-ed37e488648f7dd5adc80546bdf69005a5cf52a5892b3431e368f0e03f93df443</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Algorithms</topic><topic>Cluster analysis</topic><topic>Clustering</topic><topic>Complex Systems</topic><topic>Condensed Matter Physics</topic><topic>Data analysis</topic><topic>Fluid- and Aerodynamics</topic><topic>Machine learning</topic><topic>Phase transitions</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Principal components analysis</topic><topic>Regular Article - Statistical and Nonlinear Physics</topic><topic>Size effects</topic><topic>Solid State Physics</topic><topic>Unsupervised learning</topic><topic>Vector quantization</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Tirelli, Andrea</creatorcontrib><creatorcontrib>Carvalho, Danyella O.</creatorcontrib><creatorcontrib>Oliveira, Lucas A.</creatorcontrib><creatorcontrib>de Lima, José P.</creatorcontrib><creatorcontrib>Costa, Natanael C.</creatorcontrib><creatorcontrib>dos Santos, Raimundo R.</creatorcontrib><collection>CrossRef</collection><jtitle>The European physical journal. B, Condensed matter physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Tirelli, Andrea</au><au>Carvalho, Danyella O.</au><au>Oliveira, Lucas A.</au><au>de Lima, José P.</au><au>Costa, Natanael C.</au><au>dos Santos, Raimundo R.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Unsupervised machine learning approaches to the q-state Potts model</atitle><jtitle>The European physical journal. B, Condensed matter physics</jtitle><stitle>Eur. Phys. J. B</stitle><date>2022-11-01</date><risdate>2022</risdate><volume>95</volume><issue>11</issue><artnum>189</artnum><issn>1434-6028</issn><eissn>1434-6036</eissn><abstract>In this paper, we study phase transitions of the
q
-state Potts model through a number of unsupervised machine learning techniques, namely Principal Component Analysis (PCA),
k
-means clustering, Uniform Manifold Approximation and Projection (UMAP), and Topological Data Analysis (TDA). Even though in all cases we are able to retrieve the correct critical temperatures
T
c
(
q
)
, for
q
=
3
,
4
and 5, results show that non-linear methods as UMAP and TDA are less dependent on finite-size effects. This study may be considered as a benchmark for the use of different unsupervised machine learning algorithms in the investigation of phase transitions.
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| language | eng |
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| subjects | Algorithms Cluster analysis Clustering Complex Systems Condensed Matter Physics Data analysis Fluid- and Aerodynamics Machine learning Phase transitions Physics Physics and Astronomy Principal components analysis Regular Article - Statistical and Nonlinear Physics Size effects Solid State Physics Unsupervised learning Vector quantization |
| title | Unsupervised machine learning approaches to the q-state Potts model |
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