Spectral Clustering – Lecture Notes

\(L_{\text{shi-malik}}\) \(=D^{-1}L=I-D^{-1}A\) [ ShMa00 ] ➜ random walk normalized: \(L_{\text{rw}}\) \(=D^{-1/2}LD^{-1/2} = I-D^{-1/2}A D^{-1/2}\) [ NgJoWe01 ] compute the \(k+1\) eigenvectors to the smallest [...] symmetric and positive semi-definite the smallest eigenvalue is always \(0\) (with eigenvector \((1,1,\ldots ,1)/\sqrt{n}\) if connected) if the graph has \(k\) components, there are \(k\) eigenvalues \(0\) [...] fast? Graph Laplacian Standard graph Laplacian matrix: \(L = D - A\) where \(D=\operatorname {diag}(d_1,\ldots ,d_n)\) is the degree matrix \(A\) is the adjacency matrix Some properties: \(L=M^TM\) where …

Frequent Pattern Growth – Lecture Notes

First scan: it. it. it. a 4 g 1 m 4 b 4 h 1 n 2 c 5 i 2 o 2 d 1 j 2 p 3 e 1 k 1 s 2 f 6 l 2 → minsupp=3: item f 6 c 5 a 4 b 4 m 4 p 3 → Reduced & reordered: tid frequent items 1 \(\{ f, c, a, m, p\}\) 2 \(\{ [...] D\} \times 1\) : The FP-tree is a compressed summary of the transaction database. Construction of an FP-tree The FP-tree is constructed in two phases: First database scan: determine frequent 1-itemsets (based [...] of the FP-growth algorithm . Proceedings of the 1st international workshop on open source data mining: Frequent pattern mining implementations (2005), 1–5. [HaPeYi00] Han, J., Pei, J. and Yin, Y. 2000 …

Bachelor_Nebenfach_Physik

Jährlich im WS Dauer 1 Semester Studiensemester 1 Credits 4 Zuordnung Curriculum B. Sc. Mathematik Modulstruktur Lf.Nr. Lehrveranstaltung Typ CP SWS Präsenz- zeit Eigen- studium 1 Physik A2 V 3 2 30 60 [...] Alternativ können 30 Leistungspunkte in folgenden zwei Modulen erworben werden: a. Physik 1 ( 15 Leistungspunkte, empfohlen im 1. Semester), b. Physik 2 ( 15 Leistungspunkte, empfohlen im 2. Semester). Hinweise: [...] 60 2 Übung zu Physik A2 Ü 1 1 15 15 Summen 4 3 45 75 Modulverantwortliche(r) Dekan der Fakultät Physik Dozent(in) Hochschullehrer der Fakultät Physik (Für das jeweilige Semester siehe Aushang.) Sprache …

Spectral Clustering – Lecture Notes

\(L_{\text{shi-malik}}\) \(=D^{-1}L=I-D^{-1}A\) [ ShMa00 ] ➜ random walk normalized: \(L_{\text{rw}}\) \(=D^{-1/2}LD^{-1/2} = I-D^{-1/2}A D^{-1/2}\) [ NgJoWe01 ] compute the \(k+1\) eigenvectors to the smallest [...] symmetric and positive semi-definite the smallest eigenvalue is always \(0\) (with eigenvector \((1,1,\ldots ,1)/\sqrt{n}\) if connected) if the graph has \(k\) components, there are \(k\) eigenvalues \(0\) [...] fast? Graph Laplacian Standard graph Laplacian matrix: \(L = D - A\) where \(D=\operatorname {diag}(d_1,\ldots ,d_n)\) is the degree matrix \(A\) is the adjacency matrix Some properties: \(L=M^TM\) where …

Frequent Pattern Growth – Lecture Notes

First scan: it. it. it. a 4 g 1 m 4 b 4 h 1 n 2 c 5 i 2 o 2 d 1 j 2 p 3 e 1 k 1 s 2 f 6 l 2 → minsupp=3: item f 6 c 5 a 4 b 4 m 4 p 3 → Reduced & reordered: tid frequent items 1 \(\{ f, c, a, m, p\}\) 2 \(\{ [...] D\} \times 1\) : The FP-tree is a compressed summary of the transaction database. Construction of an FP-tree The FP-tree is constructed in two phases: First database scan: determine frequent 1-itemsets (based [...] of the FP-growth algorithm . Proceedings of the 1st international workshop on open source data mining: Frequent pattern mining implementations (2005), 1–5. [HaPeYi00] Han, J., Pei, J. and Yin, Y. 2000 …

umgekehrt aber nicht. Def.: Eine Klausel C1 ist genereller als eine andere Klausel C2, gdw. gilt: C1 subsumiert C2 (C1 =θ C2). Def.: θ-Subsumtion: C1 =θ C2 gdw. C1θ ⊆ C2, θ ist eine geeignete Substitution [...] unter θ-Subsumtion: C1 =θ C2 gdw. C1 =θ C2 und C2 =θ C1. Boris Shulimovich 8/20 24.10.2001PG402 RDT/DB Logikorientiertes induktives Lernen (ILP) Crashkurs, Teil 4 Def.: Eine Klausel C1 ist echt genereller [...] reie Hornklausel bzgl. gegebenem Hintergrundwissen (Theorie) B: C1 =B C2 gdw. ∃σ, so dass C1Kopf σ = C2Kopf und B, ¬C2Körper θ ? ∃ (¬C1Körper σθ), θ eine Skolemsubstitution, σ eine (Term-)Substitution …