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Deep Learning ã®æ¬¡ã¯ã€TDA ã€Œãƒˆãƒãƒã‚¸ã‚«ãƒ«ãƒ»ãƒ‡ãƒ¼ã‚¿ãƒ»ã‚¢ãƒŠãƒªã‚·ã‚¹ã€ (Topological data analysis) ãŒæ¥ã‚‹ ? ï½ž ãã®æ¦‚è¦ã¨ã€Rè¨€èªž / Pythonè¨€èªž å®Ÿè£…ãƒ©ã‚¤ãƒ–ãƒ©ãƒª ã‚’ã¡ã‚‰ã£ã¨èª¿ã¹ã¦ã¿ãŸ - Qiita
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Welcome to the Python Mapper documentation! â€” Python Mapper documentation
teddy-g 2015/11/05
Mapperã®OSSç‰ˆã£ã¦ã“ã¨ã‚‰ã—ã„ã‚“ã ãŒã“ã‚Œã‚ã£ãŸã‚‰Ayasdi Coreã„ã‚‰ãªã„ã£ã¦ã“ã¨ï¼Ÿã£ã¦æ—©é€Ÿã‚¤ãƒ³ã‚¹ãƒˆãƒ¼ãƒ«ã—ã‚ˆã†ã¨æ€ã£ãŸã‘ã©ä½•ã‹ã†ã¾ãã„ã‹ã‚“ã€‚ã¤ã‹ãƒ‰ã‚ãƒ¥ãƒ¡ãƒ³ãƒˆé€”ä¸ã§åˆ‡ã‚Œã¦ã‚“ã ã‘ã©ã€‚

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Persistent Homology in R | phom
The pipeline for computing the persistent homology consists of two stages: the construction of a filtered simplicial complex, and the computation of the homology of the filtered complex. This package has two methods for creating filtered simplicial complexes from geometric data: Vietoris-Rips mode: This uses the Vietoris-Rips construction to build a sequence of simplicial complexes on the underlyi
teddy-g 2015/06/16
Rã§Package pHomã‚’ä½¿ã†ä¾‹ã€‚PersistenceDiagramï¼ˆç”Ÿå˜çŽ‡ã®åˆ†å¸ƒå›³ï¼‰ã§ã‚¢ã‚¦ãƒˆãƒ—ãƒƒãƒˆã™ã‚‹ã€‚

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Topological Data Analysis with R
Revolutions Milestones in AI, Machine Learning, Data Science, and visualization with R and Python since 2008 by Joseph Rickert When I was in graduate school in the mid '70s Mathematics departments were still under the spell of abstraction for its own sake. At that time, Algebraic Topology which uses concepts from Abstract Algebra to study topological spaces was a major gateway to the realm of abst
teddy-g 2015/06/16
Rã®Persistent Homologyãƒ‘ãƒƒã‚±ãƒ¼ã‚¸ã®pHomã‚’ä½¿ã†æ–¹æ³•ã€‚Barcodeã‚’ã‚¢ã‚¦ãƒˆãƒ—ãƒƒãƒˆã«ã™ã‚‹æ–¹æ³•ã€‚

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Using Topological Data Analysis on your BigData
teddy-g 2015/03/05
Ayasdiã®TDAï¼Persistent Homologyã®èª¬æ˜Žã¨åˆ†æžå†…å®¹ã®èª¬æ˜Žã€‚Persistent Homologyã®é©ç”¨æ³•ã€åˆ†æžã®åˆ‡ã‚Šå£ãŒã‚ˆãã‚ã‹ã‚‹ã€‚

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Vietorisâ€“Rips complex - Wikipedia
teddy-g 2015/02/08
VRè¤‡ä½“ã®èª¬æ˜Žã€‚è‹±èªžç‰ˆWikipediaã¯çµæ§‹åˆ†ã‹ã‚Šã‚„ã™ã„ã€‚

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Betti number - Wikipedia
In algebraic topology, the Betti numbers are used to distinguish topological spaces based on the connectivity of n-dimensional simplicial complexes. For the most reasonable finite-dimensional spaces (such as compact manifolds, finite simplicial complexes or CW complexes), the sequence of Betti numbers is 0 from some point onward (Betti numbers vanish above the dimension of a space), and they are a
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ãƒ™ãƒƒãƒæ•° - Wikipedia
åŽŸæ–‡ã¨æ¯”ã¹ãŸçµæžœã€ã“ã®è¨˜äº‹ã«ã¯å¤šæ•°ã®ï¼ˆã¾ãŸã¯å†…å®¹ã®å¤§éƒ¨åˆ†ã«å½±éŸ¿ã‚ã‚‹ï¼‰èª¤è¨³ãŒã‚ã‚‹ã“ã¨ãŒåˆ¤æ˜Žã—ã¦ã„ã¾ã™ã€‚æƒ…å ±ã®åˆ©ç”¨ã«ã¯æ³¨æ„ã—ã¦ãã ã•ã„ã€‚ æ£ç¢ºãªè¡¨ç¾ã«æ”¹è¨³ã§ãã‚‹æ–¹ã‚’æ±‚ã‚ã¦ã„ã¾ã™ã€‚ ä»£æ•°çš„ä½ç›¸å¹¾ä½•å¦ã«ãŠã„ã¦ã€ãƒ™ãƒƒãƒæ•° (ãƒ™ãƒƒãƒã™ã†ã€è‹±èªž: Betti numbers) ã¯ã€ä½ç›¸ç©ºé–“ã«å¯¾ã™ã‚‹ä¸å¤‰é‡ã§ã‚ã‚Šã€è‡ªç„¶æ•°ã«å€¤ã‚’ã‚‚ã¤ã€‚ ãƒˆãƒ¼ãƒ©ã‚¹ã¯ã²ã¨ã¤ã®é€£çµæˆåˆ†(b0)ã‚’æŒã£ã¦ã„ã¦ã€äºŒã¤ã®å††çŠ¶ã®ç©´(b1)ï¼ˆã²ã¨ã¤ã¯ä¸å¿ƒã‚’åŽŸç‚¹ã¨ã™ã‚‹å††ã§ã€ã‚‚ã†ã²ã¨ã¤ã¯ã€ç®¡çŠ¶ã«ãªã£ã¦ã„ã‚‹ä¸ã®å††çŠ¶ã®éƒ¨åˆ†ï¼‰ã§ã‚ã‚Šã€2-æ¬¡å…ƒã®ä¸èº«ã®ãªã„éƒ¨åˆ†ã‚’ä¸ã«æŒã¤ï¼ˆå†…éƒ¨ãŒç®¡çŠ¶ã¨ãªã£ã¦ã„ã‚‹ï¼‰ã‚‚ã®ãŒã²ã¨ã¤(b2)ã§ã‚ã‚‹ã®ã§ã€ãƒ™ãƒƒãƒæ•°ã¯ 1(b0), 2(b1), 1(b2) ã¨ãªã‚‹ï¼Ž å³ã®å›³ã®ã‚ˆã†ãªãƒˆãƒ¼ãƒ©ã‚¹ã‚’è€ƒãˆã‚‹ã€‚ã“ã®ãƒˆãƒ¼ãƒ©ã‚¹ã«åˆ‡ã‚Šå£ãŒå††å‘¨ã«ãªã‚‹ã‚ˆã†ã«åˆ‡ã‚Œè¾¼ã¿ã‚’ã„ã‚ŒãŸã¨ãã€ãã®çµæžœäºŒã¤ã®ãƒ”ãƒ¼ã‚¹ã«åˆ†ã‹ã‚Œãªã„åˆ‡ã‚Šæ–¹ãŒã€ç©´ã®ã¾ã‚ã‚Šã«ãã£ã¦ä¸€å‘¨ã™ã‚‹æ–¹æ³•ã¨ã€ç¸¦ã«
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Ayasdi Case Study
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Persistent Homology
ç”» åƒ èª è˜ ã‚’ è¨ˆ ç®— æ©Ÿ ã§ è¡Œ ãªã†ãŸã‚ã« Edelsbrunner ã¨ Letscher ã¨ Zomorodian [ ELZ02 ] ã«ã‚ˆã‚Š å®š ç¾© ã•ã‚ŒãŸã‚‚ã®ã§ persistent homology ã¨ å‘¼ ã°ã‚Œã‚‹ã‚‚ã®ãŒã‚ã‚‹ ã€‚ Gunnar Carlsson ã‚‚ã‹ã‹ã‚ ã£ ã¦ã„ã‚‹ [ ZC05 ] ã‚ˆã†ã§ã‚ã‚‹ ã€‚ ç¾åœ¨ ã§ã¯ å¿œ ç”¨ ãƒˆãƒãƒã‚¸ ãƒ¼ ã® ä¸» è¦ ãª é“ å…· ã® ä¸€ ã¤ã«ãª ã£ ã¦ã„ã‚‹ ã€‚ 2012 å¹´ ã® Edinburgh ã§ã® å¿œ ç”¨ ãŠã‚ˆã³ è¨ˆ ç®— ãƒˆãƒãƒã‚¸ ãƒ¼ ã® é›† ä¼š ã§ã¯ , 8 å‰² ãã‚‰ã„ã® è¬› æ¼” ã§ ä½¿ ã‚ã‚Œã¦ã„ ãŸã‚ˆã†ã« æ€ ã† ã€‚ ãã® å¾Œ å‚ åŠ ã—ãŸ å¿œ ç”¨ ãƒˆãƒãƒã‚¸ ãƒ¼ ã® é›† ä¼š ã§ã‚‚ , ã»ã¨ã‚“ã©ã® è¬› æ¼” ã¯ persistent homology ã« é–¢ ã™ã‚‹ã‚‚ã®ã ã£ ãŸ ã€‚ ãã® ç† ç”± ã® ä¸€ ã¤ã¯ , å®Ÿ éš› ã«
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Reeb graph - Wikipedia
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Contour Trees
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