Statistical mechanics of linear and non-linear matrix factorization and a theoretical analysis of auto encoder

2015 Fiscal Year Final Research Report

• Project/Area Number: 26880028
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Single-year Grants
• Research Field: Soft computing
• Research Institution: The Institute of Statistical Mathematics
• Principal Investigator: Sakata Ayaka 統計数理研究所, 大学共同利用機関等の部局等, 助教 (80733071)
• Project Period (FY): 2014-08-29 – 2016-03-31
• Keywords: スパース性 / 行列分解 / レプリカ法

Outline of Final Research Achievements

We developed a matrix factorization algorithm that is applicable to the matrix factorization associated with kernel method. This algorithm can cover broad range of the matrix factorization problems. Our algorithm performs well in some problems compared with existing algorithms.
We developed a method for evaluating restricted isometry constant (RIC) that is a key constant for the identification of the reconstruction condition of L0 and L1 method in compressed sensing. Under the replica symmetric assumption, we derived a tighter bound of RIC than previous results. Furthermore, we found that the consideration of the replica symmetry breaking improves the estimation of the bound.

Free Research Field

情報科学、統計力学