Class information for:
Level 1: PERSISTENT HOMOLOGY//DISCRETE MORSE THEORY//COMPUTATIONAL TOPOLOGY

Basic class information
Class id #P Avg. number of
references		 Database coverage
of references
13008 866 24.6 44%


Bar chart of Publication_year

Last years might be incomplete

Hierarchy of classes
The table includes all classes above and classes immediately below the current class.


Cluster id Level Cluster label #P
9 4 COMPUTER SCIENCE, THEORY & METHODS//COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE//COMPUTER SCIENCE, INFORMATION SYSTEMS 1247339
26 3       COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE//PATTERN RECOGNITION//COMPUTER SCIENCE, SOFTWARE ENGINEERING 111824
589 2             COMPUTER GRAPHICS FORUM//ACM TRANSACTIONS ON GRAPHICS//COMPUTER SCIENCE, SOFTWARE ENGINEERING 14179
13008 1                   PERSISTENT HOMOLOGY//DISCRETE MORSE THEORY//COMPUTATIONAL TOPOLOGY 866

Terms with highest relevance score


rank Term termType Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 PERSISTENT HOMOLOGY authKW 2394719 9% 83% 82
2 DISCRETE MORSE THEORY authKW 1207461 6% 68% 50
3 COMPUTATIONAL TOPOLOGY authKW 838131 6% 49% 49
4 TOPOLOGICAL DATA ANALYSIS authKW 737956 3% 70% 30
5 REEB GRAPH authKW 408061 3% 46% 25
6 PERSISTENCE DIAGRAM authKW 362658 1% 86% 12
7 MORSE SMALE COMPLEX authKW 351358 2% 59% 17
8 HOM COMPLEX authKW 328174 1% 85% 11
9 TOPOLOGICAL PERSISTENCE authKW 293820 1% 83% 10
10 NATURAL PSEUDO DISTANCE authKW 282070 1% 100% 8

Web of Science journal categories


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 Mathematics 13998 55% 0% 474
2 Mathematics, Applied 5020 31% 0% 266
3 Computer Science, Software Engineering 4513 17% 0% 147
4 Computer Science, Theory & Methods 2826 16% 0% 140
5 Computer Science, Artificial Intelligence 344 6% 0% 50
6 Physics, Mathematical 116 4% 0% 34
7 Statistics & Probability 58 3% 0% 22
8 Robotics 25 1% 0% 5
9 Computer Science, Interdisciplinary Applications 10 2% 0% 14
10 Mathematics, Interdisciplinary Applications 10 1% 0% 11

Address terms


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 ADV ELECT SYST ERCOLE DE CASTRO 141035 0% 100% 4
2 ARCES 77032 3% 10% 23
3 MATMIDIA 45329 0% 43% 3
4 COMP SCI BIOENGN ROBOT SYST ENGN 37603 0% 27% 4
5 DPTO GEOMETRIA TOPOL 37323 1% 18% 6
6 CASC LLNL CS 35259 0% 100% 1
7 CNRSUMR 7324 35259 0% 100% 1
8 COMPUTAT CRD 35259 0% 100% 1
9 COMPUTAT SCI ENGN MED 35259 0% 100% 1
10 DEVIS CHILD ADOLESCENT PSYCHIAT 35259 0% 100% 1

Journals


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 DISCRETE & COMPUTATIONAL GEOMETRY 61561 7% 3% 60
2 FOUNDATIONS OF COMPUTATIONAL MATHEMATICS 60600 3% 7% 26
3 IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS 32323 6% 2% 48
4 HOMOLOGY HOMOTOPY AND APPLICATIONS 24365 2% 4% 16
5 COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS 18793 3% 2% 24
6 COMPUTER GRAPHICS FORUM 9137 3% 1% 28
7 JOURNAL OF COMBINATORIAL THEORY SERIES A 8390 3% 1% 28
8 ELECTRONIC JOURNAL OF COMBINATORICS 4065 2% 1% 17
9 COMBINATORICA 3760 1% 1% 12
10 APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING 3702 1% 1% 8

Author Key Words


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class		 LCSH search Wikipedia search
1 PERSISTENT HOMOLOGY 2394719 9% 83% 82 Search PERSISTENT+HOMOLOGY Search PERSISTENT+HOMOLOGY
2 DISCRETE MORSE THEORY 1207461 6% 68% 50 Search DISCRETE+MORSE+THEORY Search DISCRETE+MORSE+THEORY
3 COMPUTATIONAL TOPOLOGY 838131 6% 49% 49 Search COMPUTATIONAL+TOPOLOGY Search COMPUTATIONAL+TOPOLOGY
4 TOPOLOGICAL DATA ANALYSIS 737956 3% 70% 30 Search TOPOLOGICAL+DATA+ANALYSIS Search TOPOLOGICAL+DATA+ANALYSIS
5 REEB GRAPH 408061 3% 46% 25 Search REEB+GRAPH Search REEB+GRAPH
6 PERSISTENCE DIAGRAM 362658 1% 86% 12 Search PERSISTENCE+DIAGRAM Search PERSISTENCE+DIAGRAM
7 MORSE SMALE COMPLEX 351358 2% 59% 17 Search MORSE+SMALE+COMPLEX Search MORSE+SMALE+COMPLEX
8 HOM COMPLEX 328174 1% 85% 11 Search HOM+COMPLEX Search HOM+COMPLEX
9 TOPOLOGICAL PERSISTENCE 293820 1% 83% 10 Search TOPOLOGICAL+PERSISTENCE Search TOPOLOGICAL+PERSISTENCE
10 NATURAL PSEUDO DISTANCE 282070 1% 100% 8 Search NATURAL+PSEUDO+DISTANCE Search NATURAL+PSEUDO+DISTANCE

Core articles
The table includes core articles in the class. The following variables is taken into account for the relevance score of an article in a cluster c:
(1) Number of references referring to publications in the class.
(2) Share of total number of active references referring to publications in the class.
(3) Age of the article. New articles get higher score than old articles.
(4) Citation rate, normalized to year.


Rank Reference # ref.
in cl.		 Shr. of ref. in
cl.		 Citations
1 HEINE, C , LEITTE, H , HLAWITSCHKA, M , IURICICH, F , DE FLORIANI, L , SCHEUERMANN, G , HAGEN, H , GARTH, C , (2016) A SURVEY OF TOPOLOGY-BASED METHODS IN VISUALIZATION.COMPUTER GRAPHICS FORUM. VOL. 35. ISSUE 3. P. 643 -667 63 51% 0
2 DE FLORIANI, L , FUGACCI, U , IURICICH, F , MAGILLO, P , (2015) MORSE COMPLEXES FOR SHAPE SEGMENTATION AND HOMOLOGICAL ANALYSIS: DISCRETE MODELS AND ALGORITHMS.COMPUTER GRAPHICS FORUM. VOL. 34. ISSUE 2. P. 761 -785 41 79% 1
3 BIASOTTI, S , DE FLORIANI, L , FALCIDIENO, B , FROSINI, P , GIORGI, D , LANDI, C , PAPALEO, L , SPAGNUOLO, M , (2008) DESCRIBING SHAPES BY GEOMETRICAL-TOPOLOGICAL PROPERTIES OF REAL FUNCTIONS.ACM COMPUTING SURVEYS. VOL. 40. ISSUE 4. P. - 48 47% 53
4 FROSINI, P , CERRI, A , (2015) NECESSARY CONDITIONS FOR DISCONTINUITIES OF MULTIDIMENSIONAL PERSISTENT BETTI NUMBERS.MATHEMATICAL METHODS IN THE APPLIED SCIENCES. VOL. 38. ISSUE 4. P. 617 -629 21 100% 1
5 BUBENIK, P , (2015) STATISTICAL TOPOLOGICAL DATA ANALYSIS USING PERSISTENCE LANDSCAPES.JOURNAL OF MACHINE LEARNING RESEARCH. VOL. 16. ISSUE . P. 77 -102 18 95% 12
6 LESNICK, M , (2015) THE THEORY OF THE INTERLEAVING DISTANCE ON MULTIDIMENSIONAL PERSISTENCE MODULES.FOUNDATIONS OF COMPUTATIONAL MATHEMATICS. VOL. 15. ISSUE 3. P. 613 -650 19 100% 4
7 DORAISWAMY, H , NATARAJAN, V , (2013) COMPUTING REEB GRAPHS AS A UNION OF CONTOUR TREES.IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS. VOL. 19. ISSUE 2. P. 249 -262 21 91% 6
8 ALLILI, M , KACZYNSKI, T , LANDI, C , (2017) REDUCING COMPLEXES IN MULTIDIMENSIONAL PERSISTENT HOMOLOGY THEORY.JOURNAL OF SYMBOLIC COMPUTATION. VOL. 78. ISSUE . P. 61 -75 17 100% 0
9 FROSINI, P , JABLONSKI, G , (2016) COMBINING PERSISTENT HOMOLOGY AND INVARIANCE GROUPS FOR SHAPE COMPARISON.DISCRETE & COMPUTATIONAL GEOMETRY. VOL. 55. ISSUE 2. P. 373 -409 17 94% 1
10 BUBENIK, P , DLOTKO, P , (2017) A PERSISTENCE LANDSCAPES TOOLBOX FOR TOPOLOGICAL STATISTICS.JOURNAL OF SYMBOLIC COMPUTATION. VOL. 78. ISSUE . P. 91 -114 20 80% 0

Classes with closest relation at Level 1


Rank Class id link
1 14133 CD INDEX//EULERIAN POSET//FLAG F VECTOR
2 17365 VECTOR FIELD VISUALIZATION//UNCERTAINTY VISUALIZATION//VECTOR FIELD TOPOLOGY
3 12356 MESH DENOISING//SURFACE RECONSTRUCTION//FEATURE PRESERVING
4 35346 C INFINITY TOPOLOGY//ORBIT PRESERVING DIFFEOMORPHISM//2 JET
5 7169 3D MODEL RETRIEVAL//PROCEDURAL MODELING//3D SHAPE RETRIEVAL
6 9189 MONOMIAL IDEALS//EDGE IDEAL//STANLEY DEPTH
7 19910 SMALL COVER//QUASITORIC MANIFOLD//ELLIPTIC GENERA
8 7220 VOLUME RENDERING//VOLUME VISUALIZATION//IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS
9 23167 EXCESS MASS//SIZER//LEVEL SET ESTIMATION
10 19064 CIRCULAR CHROMATIC NUMBER//CIRCULAR COLORING//PACKING CHROMATIC NUMBER

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