PhD Thesis Semi-Supervised Ensemble Methods for Computer Vision

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18 Chapter 2. Preliminaries and Notations the n-th selector h sel n is updated and the importance λ n is passed to the next selector h sel n+1. Contrary to the off-line version, the on-line classifier is available at any time of the training process as a linear combination of the N selectors. While the method’s schematics are illustrated in Figure 2.1 the detailed steps are depicted in Algorithm 2.2.
2.4. On-line Boosting 19 Algorithm 2.2 On-line Boosting for feature selection Require: training (labeled or unlabeled) example 〈x, y〉, y ∈ {−1, +1, #} Require: strong classifier F (initialized randomly) Require: weights λ corr n,m, λ wrong n,m (initialized with 1) 1: // for all selectors h sel n 2: for n = 1, 2, . . . , N do 3: // update the selector h sel n 4: for m = 1, 2, . . . , M do 5: // update each weak classifier 6: f n,m = update(h n,m , 〈x, y〉, λ) 7: // estimate errors 8: if fn,m weak (x) = y then 9: λ corr n,m = λ corr n,m + λ n 10: else 11: λ wrong n,m 12: end if 13: e n,m = 14: end for λ correct n,m = λ wrong n,m λ wrong n,m +λ wrong n,m + λ n 15: // choose weak classifier with the lowest error 16: m + = arg min m (e n,m ), e n = e n,m +, fn sel = f n,m + 17: if e n = 0 or e n > 1 then 2 18: exit 19: end if 20: // calculate voting ( ) weight 21: α n = 1 · ln 1−e n 2 e n 22: // update importance weight 23: if fn sel (x) = y then 1 24: λ = λ · 2·(1−e n) 25: else 1 26: λ = λ · 2·e n 27: end if 28: // replace worst weak classifier with a new one 29: m − = arg max m (e n,m ) 30: λ corr n,m = 1; λ wrong − n,m = 1; − 31: get new f weak n,m − 32: end for
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Page 5: Statutory Declaration I declare tha
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Page 10 and 11: learning. Finally, we hypothesize t
Page 12 and 13: sten Teil dieser Arbeit schlagen wi
Page 14 and 15: ii CONTENTS 3.6 Graph-based Methods
Page 16 and 17: iv CONTENTS 10 Conclusion 137 10.1
Page 18 and 19: vi LIST OF FIGURES 4.8 Performance
Page 20 and 21: viii LIST OF FIGURES 9.7 Comparison
Page 22 and 23: x LIST OF FIGURES
Page 24 and 25: xii LIST OF TABLES 8.2 Results and
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142 Chapter 10. Conclusion
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144 Chapter A. Publications (8) Mar
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148 Chapter B. Acronyms SVM Support
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150 BIBLIOGRAPHY [Balcan et al., 20
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152 BIBLIOGRAPHY [Chapelle and Zien
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154 BIBLIOGRAPHY [Gall and Lempinsk
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156 BIBLIOGRAPHY [Leistner et al.,
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158 BIBLIOGRAPHY [Nigam et al., 200
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162 BIBLIOGRAPHY [Xu et al., 2009]
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PhD Thesis Semi-Supervised Ensemble Methods for Computer Vision

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