Nonlinear Dimensionality Reduction Based On Dictionary Learning

Most classic dimensionality reduction(DR)algorithms(such as PCA and LDA)focus on finding a low-dimensional embedding of original data,which are often not reversible.It is still challenging to make DR processes reversible in many applications.Sparse representation(SR)has shown its strong power on signals reconstruction and de-noising.Combining sparse coding and dictionary learning theory with dimensionality reduction is the main purpose of this study.1)Make deep research on sparse coding and dictionary learning theory.Discover the relationships between dimensionality reduction and dictionary learning.2)Through theoretical analysis,we propose a dictionary learning method based on geometry,which called GCDL algorithm.It can hold internal geometry between data,which could recover the original data from the low-dimensional features.Experimental results show that GCDL can reconstruct the image at a lower dimensional space.In addition,for noise-corrupted images,GCDL can obtain better compression performance than JPEG2000.3)We also propose another dictionary learning method based on trace quotient,which improve performance on dimensionality reduction and data recovery.we named it TQCDL algorithm.TQCDL algorithm is extension of GCDL,and it uses a unified framework.The LDA and LPP algorithm are included in the model,which would be discussed in this paper.