Dimensionality Reduction Method

Dimensionality Reduction Method

    Dimensionality reduction method can be diveded into two kinds:linear dimensionality reduction and nonlinear dimensionality reduction(NDR) methods. Linear dimensionality reduction methods include :PCA(principal component analysis), ICA(independent component analysis ) ,LDA( linear discriminate analysis) ,LFA(local feature analysis) and so on.

    Nonlinear dimensionality reduction methods also can be categorized into two kinds: kernel-based methods and eigenvalue-based methods. Kernel-based methods include : KPCA(kernel principal componet analysis) ,KICA(kernel independent component analysis), KDA(kernel discriminate analysis),and so on. Eigenvalue-based methods include : Isomap( Isometric Feature Mapping) [1], LLE(locally linear embedding) [2] ,Laplacian Eigenmaps[3] ,and so on.

    Isomap is an excellent NDR method. Isomap uses approximate geodesic distance instead of Euclidean distance ,and represents a set of images as a set of points in a low-dimensional space which is corresponding to natural parameterizations of the image set. Because there are similarityes within adjacent frames of sequence ,Isomap is very suitabel to analyze moving pictures and videos.

    Reference

   [1] J.B.Tenebaum, A global geometric framework for nonlinear dimensionality reduction .

   [2] Sma T. Roweis, Nonlinear dimensionality reduction by locally linear embedding .

   [3] M.Belkin and P.Niyogi  Laplacian eigenmaps and spectral techniques for embedding and clustering.