Low dimension hierarchical subspace modelling of high dimensional data

Doctoral thesis English OPEN
Samko, Oksana
  • Subject: QA75

Building models of high-dimensional data in a low dimensional space has become extremely popular in recent years. Motion tracking, facial animation, stock market tracking, digital libraries and many other different models have been built and tuned to specific application domains. However, when the underlying structure of the original data is unknown, the modelling of such data is still an open question. The problem is of interest as capturing and storing large amounts of high dimensional data has become trivial, yet the capability to process, interpret, and use this data is limited. In this thesis, we introduce novel algorithms for modelling high dimensional data with an unknown structure, which allows us to represent the data with good accuracy and in a compact manner. This work presents a novel fully automated dynamic hierarchical algorithm, together with a novel automatic data partitioning method to work alongside existing specific models (talking head, human motion). Our algorithm is applicable to hierarchical data visualisation and classification, meaningful pattern extraction and recognition, and new data sequence generation. Also during our work we investigated problems related to low dimensional data representation: automatic optimal input parameter estimation, and robustness against noise and outliers. We show the potential of our modelling with many data domains: talking head, motion, audio, etc. and we believe that it has good potential in adapting to other domains.
  • References (125)
    125 references, page 1 of 13

    2 L iterature R ev iew 9 2.1 Reducing Dimensionality of theD ata Space ............................................. 9 2.1.1 Review of Dimensionality R eduction T e c h n iq u e s........................ 9 2.1.2 A pplications of Nonlinear Dim ensionality Reduction Techniques 13 2.1.3 Isomap Algorithm Problem s and Existing S o lu tio n s .................. 14 2.1.4 Partial D ata Representation: N M F ................................................ 16 2.2 D ata Intrinsic D im e n s io n a lity ....................................................................... 18 2.3 Subspace C lustering for High-DimensionalD a t a ...................................... 19 2.3.1 Flat Clustering A lg o rith m s................................................................. 20 2.3.2 Hierarchical Clustering A lg o r it h m s ................................................ 22 2.3.3 Clustering P r o b l e m s ........................................................................... 23 N o n l i n e a r D i m e n s i o n a l i t y R e d u c t i o n U s i n g I so m a p 3.1 I n t r o d u c t i o n ......................................................................................................

    3.2 Iso m a p A l g o r i t h m ............................................................................................

    3.3 K ernel Trick: New D a ta S a m p lin g in to Iso m a p S p a c e .............................

    3.4 Iso m a p Inverse P r o j e c t i o n ............................................................................

    3.5 O p tim a l N e ig h b o u rh o o d P a r a m e te r V alue for th e Isom ap A lg o rith m 3.6 E x p e rim e n ta l R e s u l t s ...................................................................................... 3.6.1 S c u lp tu r e Face D a ta S e t .................................................................... 3.6.2 S w i s s r o l l .................................................................................................. 3.6.3 S - C u r v e .................................................................................................. 3.6.4 E a r D a t a b a s e ........................................................................................ 3.6.5 C lassificatio n E x p e rim e n ts : O liv e tti FaceD a t a b a s e .................. 3.6.6 C lassificatio n E x p e rim e n ts : H a n d w r itte n D ig its, M N IS T D a ta 3.7 S u m m a r y ...........................................................................................................

    H ie r a r c h ic a l M o d e l l i n g o f H ig h D i m e n s i o n a l D a t a 4.1 I n t r o d u c t i o n ........................................................................................................

    4.2 H ierarchical C lu ste rin g A lg o rith m O v e r v i e w ...........................................

    4.3 Selecting a n A p p ro p ria te N u m b e r of C l u s t e r s ...........................................

    4.4 D a t a M odelling as a G a u ssia n M ix tu re M o d e l .........................................

    4.5 H ie ra rch ica l A gglom erative C lu s te rin g ..................................................

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