Online Kernel matrix factorization
Andrés Esteban Páez Torres
MindLab
Universidad Nacional de Colombia
Motivation
- In the last years the growth of information production has rendered impossible its processing and analysis.
- 300 video hours uploaded to Youtube per minute.
- 350,000 tweets per minute published in Twitter.
Motivation
- There are many well studied and tested matrix factorization methods.
- These MF methods are specially apt for dimensionality reduction, manifold learning, dictionary learning and clustering tasks.
Motivation
- Matrix factorization kernel methods are very useful in data analysis and machine learning tasks.
- However, KMF have high computational cost.
Problem
The challenge is to devise effective and efficient mechanisms to perform matrix factorization in high dimensional feature spaces implicitly defined by kernels.
Method
Let's consider the following factorization
And its reconstruction error
Method
Which we can express as
Using the kernel function
Method
But the terms have a dimension
which leads to the impossibility to apply the factorization to a large number of samples
Method
To solve that problem let's consider the following factorization
Method
With the factorization stated we pose this optimization problem using stochastic gradient descent
Method
In order to use SGD we must calculate the gradient
Method
With the gradients we get the update rules
Online Kernel Matrix Factorization
By Andres Esteban Paez Torres
Online Kernel Matrix Factorization
My thesis presentation
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