"cyan")), lwd=2) lines3d(w[2]*c(min(x),max(x))*d$vectors[1,2], w[2]*c(min(y),max(y))*d$vectors[2,2], c(0,0), col=ifelse(is.complex(d$value[2]), "brown", ifelse(d$value[2]>0, "blue", "cyan")), lwd=2) } x <- seq(-1 [...] byrow=TRUE, nrow=2, ncol=2) # convex, axis-aligned M[[2]] <- matrix(c(10,0,0,5), byrow=TRUE, nrow=2, ncol=2) # convex, axis-aligned M[[3]] <- matrix(c(10,0,0,1), byrow=TRUE, nrow=2, ncol=2) # convex, axis-aligned [...] byrow=TRUE, nrow=2, ncol=2) # convex, not aligned to axes M[[5]] <- matrix(c(-10,0,0,-5), byrow=TRUE, nrow=2, ncol=2) # concave M[[6]] <- matrix(c(10,0,0,-10), byrow=TRUE, nrow=2, ncol=2) # neither convex …

2.31 24 2.15 442 35 2.39 30 2.31 35 2.38 441 16 1.83 37 2.44 47 2.50 441 27 2.24 44 2.49 28 2.28 441 26 2.20 42 2.47 32 2.33 442 32 2.37 37 2.43 30 2.27 442 23 2.13 40 2.46 37 2.40 442 Thüringen 64 2.72 [...] Bremen 48 2.46 38 2.39 14 1.68 432 37 2.37 36 2.35 27 2.20 431 37 2.38 37 2.39 26 2.16 428 47 2.46 37 2.38 15 1.70 431 34 2.33 41 2.43 25 2.14 430 23 2.06 45 2.45 32 2.32 429 29 2.25 34 2.32 37 2.39 429 25 [...] 2.22 19 1.87 450 36 2.31 31 2.19 33 2.27 450 22 1.99 34 2.26 45 2.38 450 32 2.25 42 2.36 26 2.10 449 25 2.10 43 2.37 32 2.23 449 40 2.34 36 2.30 25 2.07 450 29 2.20 38 2.33 33 2.24 449 Thüringen 64 2.62 …

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2.0 2.8 0.33 63 1.0 2.1 0.57 17 2.0 2.3 0.60 47 1.0 1.5 0.30 21 2.0 2.1 0.24 85 1.0 2.3 0.82 27 1.0 1.8 0.22 47 2.0 5.1 2.01 22 1.0 2.0 0.27 53 2.0 2.1 0.56 9 2.0 2.0 0.22 53 2.0 2.0 0.14 140 1.0 2.7 0 [...] 04 2,859 4.2 0.04 2,862 3.4* 0.04 2,858 3.4* 0.04 2,862 2.5 0.04 2,844 3.4* 0.04 2,861 2.8* 0.04 2,848 3.4 0.04 2,856 3.7* 0.04 2,860 3.1 0.04 2,844 2.3* 0.05 2,819 2.5* 0.05 1,888 Deutschland 3.1 0.03 6 [...] 20,289 2,158 10.6 2,611 12.9 2,320 11.4 2,273 11.2 2,568 12.7 2,461 12.1 2,502 12.3 2,078 10.2 1,198 5.9 120 0.6 Thüringen 15,415 1,142 7.4 2,060 13.4 2,290 14.9 1,548 10.0 1,057 6.9 1,502 9.7 2,216 14 …

Beispiel: d = 2, ~xi , ~xj ∈ R2. K2(~xi , ~xj ) = 〈 ~xi , ~xj 〉2 = (xi1xj1 + xi2xj2 )2 = x2 i1x 2 j1 + 2xi1xj1xi2xj2 + x2 i2x 2 j2 = 〈 (x2 i1 , √ 2xi1xi2 , x 2 i2 ) , (x2 j1 , √ 2xj1xj2 , x 2 j2 ) 〉 =: 〈 Φ(~xi [...] Ableiten des dualen Problems nach α2 ergibt das Optimum für αnew 2 αnew 2 = αold 2 + y2((f (~x1)−y1)−(f (~x2)−y2)) η = αold 2 + y2(E1−E2) η η = k(x1, x1) + k(x2, x2)− 2k(x1, x2) Allerdings gibt es aufgrund der [...] Bereich. 37 von 1 Optimales α2 Somit wählen wir zum Update: α̂2 =  H wenn αnew 2 ≥ H αnew 2 wenn L < αnew 2 < H L wenn αnew 2 ≤ L Optimales α̂1 = α1 + y1y2 (α2 − α̂2) Prinzip des Optimierens: Nullsetzen …

09 325 2.9 0.07 327 2.4* 0.07 326 2.5* 0.07 325 2.5* 0.07 327 2.1 0.06 327 Westdeutschland 2.9* 0.04 2,870 3.7* 0.03 2,872 4.7* 0.03 2,881 4.1* 0.04 2,877 2.8 0.03 2,877 2.2* 0.03 2,883 2.3* 0.03 2,878 2 [...] 3.7 0.05 2,156 4.5 0.04 2,148 3.3 0.05 2,129 3.7 0.05 2,150 2.7 0.05 2,138 2.3 0.04 2,101 4.4 0.05 2,158 3.8 0.05 2,158 3.9 0.05 2,131 4.0 0.04 2,151 2.9 0.04 2,152 3.2 0.05 2,151 3.7 0.06 2,161 3.8 0 [...] 05 2,146 2.8 0.04 2,149 2.1 0.03 2,149 2.3 0.03 2,147 2.3 0.04 2,146 2.0 0.03 2,141 Feste Gruppenstruktur 2.9 0.05 1,810 3.6 0.05 1,810 4.6 0.05 1,816 3.9 0.05 1,816 2.7 0.04 1,812 2.2 0.04 1,815 2.3 0 …

+0.1 Der Paritätische 8.0 8.2 8.6 8.5 8.6 8.9 8.9 9.0 9.0 9.0 +1.0 DRK 2.5 2.4 2.5 2.5 2.5 2.5 2.6 2.6 2.6 2.7 +0.2 Sonstige Träger 12.0 13.4 14.5 15.2 15.7 16.2 16.6 17.0 17.2 17.7 +5.7 Quelle: Statistisches [...] 9 6.2 8.7 +2.5 5.6 8.5 +2.9 4.8 6.9 +2.2 3.6 6.0 +2.4 7.0 8.4 +1.4 10.7 11.2 +0.4 5.9 8.5 +2.6 10.2 12.9 +2.6 10 oder 11 6.4 9.0 +2.6 5.9 7.8 +1.9 5.5 8.8 +3.3 4.0 6.7 +2.8 6.9 10.1 +3.2 7.3 9.4 +2.1 6 [...] 10.3 +2.8 3.2 4.7 +1.5 11.3 13.8 +2.5 2.2 2.6 +0.4 5.1 4.4 -0.7 2.3 2.3 +0.0 14 oder 15 10.0 10.7 +0.7 11.7 9.0 -2.7 15.6 13.4 -2.2 9.0 10.0 +1.0 0.0 0.0 +0.0 12.6 13.9 +1.4 7.3 9.4 +2.2 17.1 16.7 -0.4 5 …

Daten? 1. Φ1(x1, x2) = (x21, x2) 2. Φ2(x1, x2) = (x31 − 2x1, x2) 3. Φ3(x1, x2) = (x31, x2) x1 x2 y -1.5 -2.0 +1 -1.0 0.0 +1 -0.5 1.0 +1 0.0 2.0 +1 0.5 1.0 +1 1.0 2.0 +1 1.5 3.75 +1 -1.0 -2.0 -1 -0.5 -1.0 [...] uni-dortmund.de/LEHRE/VORLESUNGEN/KDD/SS13/DATA/svm-data.csv -5 -4 -3 -2 -1 0 1 2 3 4 5 -5 -4 -3 -2 -1 0 1 2 3 4 5 Abbildung 2: Datenpunkte im R2 1. Beschreiben Sie, wie Sie die gegebenen Daten trennen würden [...] kis, 1979, Akademie Vg. [UB-Dortmund: Signatur M20947] 0 1 2 3 4 5 6 7 8 9 10 11 12 13 0 1 2 3 4 5 6 7 8 9 10 Abbildung 1: Datenpunkte im R2 Aufgabe 6.1 (3 Punkte) In dieser Aufgabe sollen Sie den naiven …