Google Tech Talks
June 1, 2007
ABSTRACT
Big two dimensional data as photos or spreadsheets are very common in applications. Higher dimensional data as three dimensional picture, or picture with voices, or profile of a person from several angles lead to a higher dimensional data.
Usually this data has a lot of redundancy, has noise and may miss the information at all in certain percentage of data. In this talk I will discuss the following general problems:
* Reduction process which reduces the storage space of the data
* Denoising the data.
* Predicting the values of the missing data
For the two dimensional data the singular value decomposition (SVD) of an m x n matrix emerged as a very important tool in data analysis, data compression and data recovery in computer science, electrical engineering and biology. In this talk we will explain the significance of SVD and some recent applications to the following topics:
1. Fast low rank approximation of matrices using Monte-Carlo techniques.
2. A joint SVD decomposition of two or more matrices to compare several biological processes.
3. Estimation of missing values in given matrix data using the inverse eigenvalue problems techniques, and their applications to to DNA microarrays and image processing.
For higher dimensional data, i.e.{tensors}, SVD is not available. We will discuss briefly other approaches for tensors.
I will try to make the talk accessible to the general audience. Most of the results of this talk, as well as a previous version of the slides of the talk, are available at http://www.math.uic.edu/~friedlan/research.html
Speaker: Dr. Shmuel FriedlandGoogle Tech Talks
June 1, 2007
ABSTRACT
Big two dimensional data as photos or spreadsheets are very common in applications. Higher di...all »Google Tech Talks
June 1, 2007
ABSTRACT
Big two dimensional data as photos or spreadsheets are very common in applications. Higher dimensional data as three dimensional picture, or picture with voices, or profile of a person from several angles lead to a higher dimensional data.
Usually this data has a lot of redundancy, has noise and may miss the information at all in certain percentage of data. In this talk I will discuss the following general problems:
* Reduction process which reduces the storage space of the data
* Denoising the data.
* Predicting the values of the missing data
For the two dimensional data the singular value decomposition (SVD) of an m x n matrix emerged as a very important tool in data analysis, data compression and data recovery in computer science, electrical engineering and biology. In this talk we will explain the significance of SVD and some recent applications to the following topics:
1. Fast low rank approximation of matrices using Monte-Carlo techniques.
2. A joint SVD decomposition of two or more matrices to compare several biological processes.
3. Estimation of missing values in given matrix data using the inverse eigenvalue problems techniques, and their applications to to DNA microarrays and image processing.
For higher dimensional data, i.e.{tensors}, SVD is not available. We will discuss briefly other approaches for tensors.
I will try to make the talk accessible to the general audience. Most of the results of this talk, as well as a previous version of the slides of the talk, are available at http://www.math.uic.edu/~friedlan/research.html
Speaker: Dr. Shmuel Friedland«
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