강연 / 세미나
MINDS-CM2LA Seminar on mathematical data science
분야Field | |||
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날짜Date | 2023-12-12 ~ 2023-12-12 | 시간Time | 17:00 ~ 18:00 |
장소Place | Math Bldg.404&Online streaming (Zoom) | 초청자Host | |
연사Speaker | Woo-Jin Kim | 소속Affiliation | KAIST |
TOPIC | MINDS-CM2LA Seminar on mathematical data science | ||
소개 및 안내사항Content | Title : Persistence Diagrams at the Crossroads of Algebra and Combinatorics Speaker : Woo-Jin Kim (KAIST) Abstract : Persistent Homology (PH) is a method used in Topological Data Analysis (TDA) to extract multiscale topological features from data. Via PH, the multiscale topological features of a given dataset are encoded into a persistence module (indexed by a totally ordered set) and in turn, summarized by a persistence diagram. In order to extend PH so as to be able to study wider types of data (e.g. time-varying point clouds), variations of the indexing set of persistence modules must inevitably occur, leading for example to multiparameter persistence modules, i.e. persistence modules indexed by the n-dimensional grid. It is however not always evident how to define a notion of persistence diagram for such variants. This talk will introduce a generalized notion of persistence diagram for such variants which arises through exploiting both the principle of inclusion and exclusion from combinatorics and the canonical map from the limit to the colimit of a diagram of vector spaces (these being notions from category theory). We also discuss (1) how the generalized persistence diagram subsumes some other well-known invariants of multiparameter persistence modules and (2) algorithmic considerations for computing the generalized persistence diagram. Link : https://us06web.zoom.us/j/6888961076?pwd=ejYxN05jNmhUa25PU2JzSUJvQ1haQT09 |
학회명Field | MINDS-CM2LA Seminar on mathematical data science | ||
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날짜Date | 2023-12-12 ~ 2023-12-12 | 시간Time | 17:00 ~ 18:00 |
장소Place | Math Bldg.404&Online streaming (Zoom) | 초청자Host | |
소개 및 안내사항Content | Title : Persistence Diagrams at the Crossroads of Algebra and Combinatorics Speaker : Woo-Jin Kim (KAIST) Abstract : Persistent Homology (PH) is a method used in Topological Data Analysis (TDA) to extract multiscale topological features from data. Via PH, the multiscale topological features of a given dataset are encoded into a persistence module (indexed by a totally ordered set) and in turn, summarized by a persistence diagram. In order to extend PH so as to be able to study wider types of data (e.g. time-varying point clouds), variations of the indexing set of persistence modules must inevitably occur, leading for example to multiparameter persistence modules, i.e. persistence modules indexed by the n-dimensional grid. It is however not always evident how to define a notion of persistence diagram for such variants. This talk will introduce a generalized notion of persistence diagram for such variants which arises through exploiting both the principle of inclusion and exclusion from combinatorics and the canonical map from the limit to the colimit of a diagram of vector spaces (these being notions from category theory). We also discuss (1) how the generalized persistence diagram subsumes some other well-known invariants of multiparameter persistence modules and (2) algorithmic considerations for computing the generalized persistence diagram. Link : https://us06web.zoom.us/j/6888961076?pwd=ejYxN05jNmhUa25PU2JzSUJvQ1haQT09 |
성명Field | MINDS-CM2LA Seminar on mathematical data science | ||
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날짜Date | 2023-12-12 ~ 2023-12-12 | 시간Time | 17:00 ~ 18:00 |
소속Affiliation | KAIST | 초청자Host | |
소개 및 안내사항Content | Title : Persistence Diagrams at the Crossroads of Algebra and Combinatorics Speaker : Woo-Jin Kim (KAIST) Abstract : Persistent Homology (PH) is a method used in Topological Data Analysis (TDA) to extract multiscale topological features from data. Via PH, the multiscale topological features of a given dataset are encoded into a persistence module (indexed by a totally ordered set) and in turn, summarized by a persistence diagram. In order to extend PH so as to be able to study wider types of data (e.g. time-varying point clouds), variations of the indexing set of persistence modules must inevitably occur, leading for example to multiparameter persistence modules, i.e. persistence modules indexed by the n-dimensional grid. It is however not always evident how to define a notion of persistence diagram for such variants. This talk will introduce a generalized notion of persistence diagram for such variants which arises through exploiting both the principle of inclusion and exclusion from combinatorics and the canonical map from the limit to the colimit of a diagram of vector spaces (these being notions from category theory). We also discuss (1) how the generalized persistence diagram subsumes some other well-known invariants of multiparameter persistence modules and (2) algorithmic considerations for computing the generalized persistence diagram. Link : https://us06web.zoom.us/j/6888961076?pwd=ejYxN05jNmhUa25PU2JzSUJvQ1haQT09 |
성명Field | MINDS-CM2LA Seminar on mathematical data science | ||
---|---|---|---|
날짜Date | 2023-12-12 ~ 2023-12-12 | 시간Time | 17:00 ~ 18:00 |
호실Host | 인원수Affiliation | Woo-Jin Kim | |
사용목적Affiliation | 신청방식Host | KAIST | |
소개 및 안내사항Content | Title : Persistence Diagrams at the Crossroads of Algebra and Combinatorics Speaker : Woo-Jin Kim (KAIST) Abstract : Persistent Homology (PH) is a method used in Topological Data Analysis (TDA) to extract multiscale topological features from data. Via PH, the multiscale topological features of a given dataset are encoded into a persistence module (indexed by a totally ordered set) and in turn, summarized by a persistence diagram. In order to extend PH so as to be able to study wider types of data (e.g. time-varying point clouds), variations of the indexing set of persistence modules must inevitably occur, leading for example to multiparameter persistence modules, i.e. persistence modules indexed by the n-dimensional grid. It is however not always evident how to define a notion of persistence diagram for such variants. This talk will introduce a generalized notion of persistence diagram for such variants which arises through exploiting both the principle of inclusion and exclusion from combinatorics and the canonical map from the limit to the colimit of a diagram of vector spaces (these being notions from category theory). We also discuss (1) how the generalized persistence diagram subsumes some other well-known invariants of multiparameter persistence modules and (2) algorithmic considerations for computing the generalized persistence diagram. Link : https://us06web.zoom.us/j/6888961076?pwd=ejYxN05jNmhUa25PU2JzSUJvQ1haQT09 |