ASCLU Alternative Subspace Clustering Stephan Gnnemann Ines Frber - PowerPoint PPT Presentation

ASCLU – Alternative Subspace Clustering Stephan Günnemann Ines Färber Emmanuel Müller Thomas Seidl Data management and data exploration group RWTH Aachen University, Germany MultiClust at KDD 2010 July 25, 2010

Introduction Model Conclusion Why Subspace Clustering? data allows to be clustered through different perspectives each object in various groupings based on different attributes ⇒ multiple views due to locally relevant dimensions of clusters ⇒ subspace clustering ASCLU – Alternative Subspace Clustering 1 / 6

Introduction Model Conclusion Why Alternative Clustering? ����� ���� � � ������������������������� ���������������������� ������� ��������� �� � ������������������������� ���������������������������� ����� ���� often trivial groupings or already detected clusters given user not satisfied with previous results ⇒ aiming for alternative, yet comparable good groupings ⇒ avoid re-detection of already known clusters → combination of subspace clustering and alternative clustering ASCLU – Alternative Subspace Clustering 2 / 6

Introduction Model Conclusion What To Do? – The General Picture input: subspace clustering Known = { K 1 , . . . , K m } Cluster selection approach set of possible subspace clusters All → select optimal subset Res ⊆ All fulfilling specific properties dim 2 dim 4 avoid redundancy 1 → w.r.t. known clusters 3 → among novel clusters 1 select alternative clusters 2 dim 1 dim 3 3 2 4 ASCLU – Alternative Subspace Clustering 3 / 6

Introduction Model Conclusion Alternative Subspace Clustering Model – I Each cluster C ∈ Res ⊆ All should deviate from Known deviating w.r.t. subspaces 1 known clusters in alternative subspaces are already different enough InAlterSubspace ( Known , C ) = { ( O i , S i ) ∈ Known | | S ∩ S i | < β · | S |} deviating w.r.t. objects 2 known clusters in similar subspaces should cover different objects | O \ CoveredInSimilar ( Known , C ) | ≥ α | O | dim 2 dim 4 1 Is C 1 an 3 alternative to Known ? 1 2 dim 1 dim 3 3 2 4 ASCLU – Alternative Subspace Clustering 4 / 6

Introduction Model Conclusion Alternative Subspace Clustering Model – I Each cluster C ∈ Res ⊆ All should deviate from Known deviating w.r.t. subspaces 1 known clusters in alternative subspaces are already different enough InAlterSubspace ( Known , C ) = { ( O i , S i ) ∈ Known | | S ∩ S i | < β · | S |} deviating w.r.t. objects 2 known clusters in similar subspaces should cover different objects | O \ CoveredInSimilar ( Known , C ) | ≥ α | O | dim 2 dim 4 1 C 1 is a 3 valid alternative to Known ! 1 2 dim 1 dim 3 3 2 4 ASCLU – Alternative Subspace Clustering 4 / 6

Introduction Model Conclusion Alternative Subspace Clustering Model – II Avoiding redundancy so far: C ∈ Res different to given clusters ⇒ non-redundant w.r.t. Known redundancy between X , Y ∈ Res still possible solution: C ∈ Res valid alternative to remaining novel clusters Res \{ C } alternative e v i t a n r e t l a ASCLU – Alternative Subspace Clustering 5 / 6

Introduction Model Conclusion Alternative Subspace Clustering Model – II Avoiding redundancy so far: C ∈ Res different to given clusters ⇒ non-redundant w.r.t. Known redundancy between X , Y ∈ Res still possible solution: C ∈ Res valid alternative to remaining novel clusters Res \{ C } Optimal alternative subspace clustering Given previous clustering Known and set of possible subspace clusters All , choose Res ⊆ All such that ∀ C ∈ Res : C is a valid alternative to Known 1 ∀ C ∈ Res : C is a valid alternative to Res \{ C } 2 Res is the most interesting clustering fulfilling 1 & 2 3 ASCLU – Alternative Subspace Clustering 5 / 6

Introduction Model Conclusion Conclusion ASCLU – Alternative Subspace Clustering ASCLU detects alternatives based on → deviating subspaces → deviating object sets ASCLU avoids redundant clusters ASCLU – Alternative Subspace Clustering 6 / 6

Introduction Model Conclusion Conclusion ASCLU – Alternative Subspace Clustering ASCLU detects alternatives based on → deviating subspaces → deviating object sets ASCLU avoids redundant clusters Thank you for your attention. Questions? ASCLU – Alternative Subspace Clustering 6 / 6