טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentGolts Alona
SubjectLinearized Kernel Dictionary Learning
DepartmentDepartment of Electrical Engineering
Supervisor Professor Michael Elad
Full Thesis textFull thesis text - English Version


Abstract

In this work we present a new approach of incorporating kernels into dictionary learning. The kernel K-SVD algorithm (KKSVD), which has been introduced recently, shows an improvement in classification performance, with relation to its linear counterpart K-SVD. However, this algorithm requires the storage and handling of a very large kernel matrix, which leads to high computational cost, while also limiting its use to setups with small number of training examples. We address these problems by combining two ideas: first we approximate the kernel matrix using a cleverly sampled subset of its columns using the Nystrom method; secondly, as we wish to avoid using this matrix altogether, we decompose it by SVD to form new "virtual samples", on which any linear dictionary learning can be employed. Our method, termed "Linearized Kernel Dictionary Learning" (LKDL), can be seamlessly applied as a pre-processing stage on top of any efficient off-the-shelf dictionary learning scheme, effectively "kernelizing" it. We demonstrate the effectiveness of our method on several tasks of both supervised and unsupervised classification and show the efficiency of the proposed scheme, its easy integration and performance boosting properties. We also suggest a mini-batch version of our algorithm, which deals with larger scale datasets and compare the performance of our method to randomized feature extraction approaches.