A principal components analysis self-organizing map

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Intelligent Database Systems Lab 國國國國國國國國 National Yunlin University of Science and T echnology Advisor : Dr. Hsu Student : Sheng-Hsuan Wang Department of Information Management A principal components analysis self-organizing map Neural Network 17 (2004) 261-270 Ezequiel Lopez-Rubio, Jose Munoz-Perez, Jose Antonio Gomez-Ruiz
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A principal components analysis self-organizing map. Ezequiel Lopez-Rubio, Jose Munoz-Perez, Jose Antonio Gomez-Ruiz. Advisor : Dr. Hsu Student : Sheng-Hsuan Wang Department of Information Management. Neural Network 17 (2004) 261-270. Outline. Motivation Objective - PowerPoint PPT Presentation

Transcript of A principal components analysis self-organizing map

Research Progress ReportAdvisor : Dr. Hsu
Student : Sheng-Hsuan Wang
Ezequiel Lopez-Rubio, Jose Munoz-Perez, Jose Antonio Gomez-Ruiz
Intelligent Database Systems Lab
Motivation
The adaptive subspace self-organizing map (ASSOM) is an alternative to the standard principal component analysis (PCA) algorithm
Look for the most relevant features of the input data.
However, its training equations are complexes.
Separate ability in the classical PCA and ASSOM.
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Objective
This paper proposed a new self-organizing neural model that performs principal components analysis
Like the ASSOM, but has a broader capability to represent the input distribution.
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N.Y.U.S.T. I. M.
The ASSOM network
The ASSOM network uses subspaces in each node rather than just single weights.
The ASSOM network is based on training not just using single samples but sets of slightly translated, rotated and/or scaled signal or image samples, called episodes.
Each neuron of an ASSOM network represents a subset of the input data with a vector basis which is adapted so that the local geometry of the input data is build.
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orthogonal projection
A vector x on an orthonormal vector basis B={bh|h=1,…,K}
The vector x can be decomposed into two vectors
orthogonal projection and projection error.
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N.Y.U.S.T. I. M.
The ASSOM network
The input vectors are grouped into episodes in order to be presented to the network.
An episode S(t) has many time instants tp belongs to S(t), each with an input vector x(tp).
episodes: sets of slightly translated, rotated or scaled samples.
Intelligent Database Systems Lab
Intelligent Database Systems Lab
The objective function is the average expected spatially weighted normalized squared projection error over the episodes.
The Robbins-Monro stochastic approximation is used to minimize objective function, which leads to Basis vectors rotation.
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Use the covariance matrix to store the information.
The covariance matrix of an input vector x is defined as
M input samples
If we obtain N new input samples
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the new approximations.
N.Y.U.S.T. I. M.
The PCASOM network
Competition among neurons
The neuron c that has the minimum sum of projection errors is the winner:
Orth(x, B) is the orthogonal projection of vector x on basis B.
Intelligent Database Systems Lab
Intelligent Database Systems Lab
For every unit i, obtain the initial covariance matrix R(0).
For every unit i, build the vector ei(0) by using small random value.
At time instant t, select the input vectors x(t). Compute the winning neuron c.
For every unit i; update the vector ei and the matrix Ri
Convergence condition.
Matrix sums
It has a wider capability to represent the input distribution.
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Intelligent Database Systems Lab
projection error norm for BMU
the norm of the input vector
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Related to the ASSOM
Its training equations are much simpler
Its input representation capability is broader
Experiments show that the new model has better performance than the ASSOM network.
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