Combined Central and Subspace Clustering for Computer Vision Application
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Transcript of Combined Central and Subspace Clustering for Computer Vision Application
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Combined Central and Subspace Clustering for Computer Vision Application
Le Lu, Rene VidalJohn Hopkins University
( 担当:猪口 )
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Introduction
• Central Clustering– クラスタの中心の周辺にデータが分布– Application
• Image segmentation, – K-means , EM
• Subspace Clustering– 部分空間にデータが分布– Application
• Motion segmentation, face clustering with varying illumination, temporal video segmentation
– K-subspace, Generalized PCA
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GPCA→K-means
XY 平面に分布
YZ 平面に分布
GPCA は Y 軸上の点を,YZ 平面に,射影
K-means が B1 の点をA1 とラベル付け
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K-means
XY 平面に分布
YZ 平面に分布
K-means は異なる部分空間の近接なクラスタを分離できない
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問題定義• データ• 部分空間• クラスターの中心• 基準基底
• 問題
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• Central Clustering–
– K-means• クラスターの中心を決める• クラスターの中心からの距
離に応じて,各データを各クラスターに割り当てる.
• データからクラスタの中心を決める.
• Subspace Clustering– ,
– K-subspace• Subspace を決める• Subspace からの距離に応
じて,各データを各クラスタに割り当てる.
• データから Subspace を再計算.
Subspace を超平面と仮定
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データ xi は 1 つのクラスターに属する.
クラスター中心は平面上の点
ラグランジュの未定乗数法
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Algorithm
GPCA
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• Computing the membership
• Computing the cluster centers– を で偏微分して, を掛けると が使え
て
• Computing the normal vectors– 上と同様
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ノイズの超平面からの距離の分散 クラス分散
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Experiments (Simulated Data)
• 3 次元上のデータ, 600 点• Subspace は 2 つ,それぞれ 3 クラスター• 各クラスターは 100 点(正規分布, σμ=1.
5 )• Subspace は 20° ~ 90°• 各スペースの 3 つのクラスタの中心距離は
2.5σμ ~ 5σμ
• σb の Noise• 100 回,試行
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Experiments (Simulated Data)
• KM K-mean →6 つのクラスタを 2 つの平面に分ける• MP MPPC (Mixture of probabilistic PCA )→ 6 つのクラスタを 2 つの平面に分
ける• KK K-subspace→ それぞれの Subspace で K-means• GK GPCA→ それぞれの Subspace で K-means• JC 提案手法
KM
MPKK
GK
JC
KM
MP
KK
GK
JC
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Experiments (Illumination)
• 4 subjects (10 subject のうち )
• 4 poses ×64 illuminations
• 240 ×320 pixels
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• GPCA+K-means• Subject5 と Subject6 の交わりを Subject5 にクラスタリ
ング
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Experiments (Video)
• Video sequence → several video shots
• Each video contains 4 shots