Subspace Analysis for Visual Attention Detection (1): Estimate the Number of Subspace
By mapping the image feature into new pixel space where homogeneious regions correspond to subspaces (what is the dimension of these subspaces???) and the contrast between different regions related with projection error of its corresponding subspaces. The Visual Attention Detection is transformed to find the subspace with largest error when all data projected onto it.
Now the first issue is the estimation of subspace number. It is not a trival task since the real image data are always noisy. GPCA [1] currently use the rank of veronese map matrix of data to estimate the number of subspace. Due to the rank of a noisy matrix is always full rank, so the author applied simple SVD thresholding method to decide the rank of this matrix. This method (1) only considers the angle/energy of subspace distribution but not clustering level of data; (2) the threshold value for singular value ratio is different among images thus can't be decided generally. Defect (1) can be illustrated in one simple case. Given a data distribution with one main cluster in a subspace and several noise in the perpendicular direction of this subspace. If these noises have largest distances to the subspace, SVD rank estimation will return a rank > 1. It is wrong because there isn't a cluster for noisy data.
Thinking:
(1). How to integrate subspace constraint and cluster constraint?
(2). Is there an possible solution using LSE (Least Square Error)?
Now the first issue is the estimation of subspace number. It is not a trival task since the real image data are always noisy. GPCA [1] currently use the rank of veronese map matrix of data to estimate the number of subspace. Due to the rank of a noisy matrix is always full rank, so the author applied simple SVD thresholding method to decide the rank of this matrix. This method (1) only considers the angle/energy of subspace distribution but not clustering level of data; (2) the threshold value for singular value ratio is different among images thus can't be decided generally. Defect (1) can be illustrated in one simple case. Given a data distribution with one main cluster in a subspace and several noise in the perpendicular direction of this subspace. If these noises have largest distances to the subspace, SVD rank estimation will return a rank > 1. It is wrong because there isn't a cluster for noisy data.
Thinking:
(1). How to integrate subspace constraint and cluster constraint?
(2). Is there an possible solution using LSE (Least Square Error)?
