Visualisation

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Transcript Visualisation

GRB Classification using Self
Organizing Map (SOM)
Praveen Boinee
Ph.D student
Udine university
Presentation outline
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GRB classification
Neural networks
Self organizing Map
 Operations
 How it is used in the classification
Visualization Techniques with SOM
Experimenting with data
Research Plan
References
GRB Data Analysis
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Importance of analysis
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But …
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can be useful in understanding the physics of the gamma
ray sources
can be helpful in finding the GRB sources
GRB data is one of the complex astronomical data sets
High dimensionality
Analysis Techniques
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Statistical
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Artificial Neural Networks can be efficiently used in
data classification
GRB Classes
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Two GRB classes are known to exist
Burst class properties are indistinct
Difficult to assign individual GRB’s to a class
because of attribute overlap
More complexity has been added by
instrumental bias in the data
GRB classification process
Data
Base
PreProcessed
GRB Data
Data
Preparation
Classified
data
Data Mining
GRB
subclasses
Scientific
and
Logical
Assessment
Visualization
Neural Networks
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Set of interconnected neurons / information
processing units
A program designed to model how the brain
performs a particular task
Used to extract the pattern of information from
data sets where numbers are vast and has hidden
relations
Ability to handle noisy data
Neural Network Learning
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Learning = Training = knowing information
This information is stored on the links between the
neurons
Neural Network
Also called weights
Two types of learning Input
Weights
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Supervised
unsupervised
After Training Neural Network is ready to
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Classify the data
Find hidden patterns / relations
Output
Supervised vs. Unsupervised
Learning
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Imagine an organism or machine which experiences
a series of sensory inputs:x1, x2, x3, x4, . . .
Supervised learning: The machine is also given
desired outputs y1, y2, . . ., and its goal is to learn to
produce the correct output given a new input.
Unsupervised learning: The goal of the machine is to
build representations of x that can be used for
reasoning, decision making, predicting things,
communicating etc.
Goals of Unsupervised Learning
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To find useful representations of the data, for example:
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finding clusters
dimensionality reduction
finding the hidden causes or sources of the data
modelling the data density
Uses of Unsupervised Learning
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data compression
outlier detection
classification
make other learning tasks easier
a theory of human learning and perception
Self-Organisation
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The brain cells are self organizing themselves in
groups, according to incoming information.
This incoming information is not only received by a
single neural cell, but also influences other cells in its
neighbourhood. This organisation results in some
kind of map, where Neural cells with similar functions
are arranged close together.
SOM mechanism is also based on this principle
SOM working
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SOM produces the similarity
graph of the input data
Converts non-linear
relationships between high
dimensional data into simple
geometric relationships
Input
pattern
Weight
Updated
Weight
Output
space
Input
space
Illustration of the SOM model with a
7 X 7architecture
SOM – Self organizing Map
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Valuable tool in data mining and KDD
Neural network algorithm for Data Mining
Based on Unsupervised learning
Vector quantisation + vector projection
Used in clustering and visualization of high
dimensional data sets
Very effective in information visualizations
Introduced by Teuvo Kohonen in 1984
Used in many fields
 But little done in astronomy area!!
SOM Architecture
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Set of neurons / cluster units
Each neuron is assigned with a prototype vector that is taken from the
input data set
The neurons of the map can be arranged either on a rectangular or a
hexagonal lattice
Every neuron has a neighborhood as shown in the figure
Hexagonal
Rectangular
SOM in Classification
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Initialization
Training
Visualization
Initialization
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Consider an n-dimensional dataset
Each row in the data set is treated as a ndimensional vector
For each neuron /classifier unit in the map assign a
a prototype vector from the data set
Prototype vectors are initialized
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Randomly
Linearly
After training Prototype vectors serves as an
exemplar for all the vector that associated with the
neuron
Training – Best matching procedure
Let i be a neuron in n n grid
mi be the prototype vector associated to i
x  R n be a arbitrary vector
 Now our task is to map this x to any one of the
neuron
 For each neuron compute the distance
D  min  x  m 
i
i 
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Better statistic: i
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Di  max x  mi 
i
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neuron satisfying the above statistic is the winner
and denoted by b
Topology Adjust – critical step
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The following update rule is used for each neuron i in the the
neighborhood of winner neuron b
mi t  1  mi t    t  hbi t  x  mi t 
t is the discrete time coordinate
mi (t  1) is a prototype vector at t  1
2
 rb  ri
hbi (t )  exp 
2
t 
2
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 is a neigh bourhood kernel
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rb , ri radius vectors of b,i neurons
  is the width of the kernel
σ t
 (t ) is a scala r valued learning ra te of the map
σ  t  ,α t  are monotonically decreasing with time
Training – Topology
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Training and Topology
adjustments are made
iteratively until a sufficiently
accurate map is obtained
After training the prototype
vectors contain the cluster
means for the classification
Neurons can be labeled
with the cluster means or
classes of the associated
prototype vectors
Data Visualization using SOM
Data visualization techniques using the SOM can be divided to
three categories based on their goal:
1. visualization of clusters and shape of the data:
projections, U-matrices and other distance matrices
2. visualization of components / variables:
component planes, scatter plots
3. visualization of data projections:
hit histograms, response surfaces
Data Visualization using SOM
The idea is to visually present many variables
together offering a degree of control over a
number of different visual properties
High dimensionality of data set and visual
properties such as color, size can be added to
the position property for proper visualization
purposes.
Multiple views can be used by linking all
separate views together when the use of these
properties makes it difficult.
Representation forms
Cell visualizations
(Distances matrices e.g.
U-matrix, similarity
coloring, map unit size)
Component planes
representation (Graphs,
scatter plots, ..)
Visual properties
Color
Position
Shape
Lighting
Surface
reflectance
Transparency
Derived
information
User interactions
Clusters
(data structure)
View (2D/3D
Shape of
Data
clusters
distribution
Relationships
Object
identifiers
(icons)
Mesh visualizations
SOM grid
Connection
lines
Surface plot of distance
matrix
Coordinates
control
Data classification
in Cube Points
The data set constructed for this demo
consists of random vectors taken from
a cube in 3D space
The data is plotted using 'o's of different
colors and the map prototype vectors
with black '+'s.
From the visualization we can see there are three
clusters, some prototype vectors between the
clusters
3 – xy points
2 – yz points
1 – zx points
Similar vectors are coded with same color
Clusters are coded with different colors
in interpolated form
XY plane points
YZ plane points
ZX plane points
Data distributions for each vector component
World Poverty Map
Data set has 39 indicators describing various quality-of-life
factors, such as state of health, nutrition, educational services,
etc,)
PhD research seminar (Qualifying phase) - September 19, 2001- Etien Luc Koua
WEB SOM
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SOM analysis
technique to map
thousands of articles
posted on Usenet
newsgroups
Lagus et al. (1996);
Honkela et al. (1998)
- HUT NN Research
Centre)
GRB classification - Choice of
Parameters
Three variables have been identified by Bagoly study on Batse 3B
catalog using principle components and factor analysis
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Burst duration Parameter (T90 ): Time it takes for 90% of the total
burst flux to arrive, taken from duration table of BATSE catalog
Total flux in the channels : The rate of flow of particles or energy
through a given surface
Weighted fluence : the sum of the energies of the photons passing
through a unit area.
Batse 3B Data
U-matrix of an SOM trained with 100 random GRBs from classes
1b and 2b (mukherjee classification).Distances increasing from
gray to black color codes
Landscape Plot
Classes 1 and 2 are separated by clear
boundary( mountain range )
Software Packages
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SOM_PAK
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MS-DOS / UNIX
Free, from the website.
The "official" SOM implementation.
SOM Toolbox
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Matlab 5
Free, from the website.
Software
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Geo-vista
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an open software development environment
Java Bean component technology
http://www.geovista.psu.edu/software/software.
jsp
Research Plan
1
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Conceptual
framework
Theoretical model of
the SOM for GRB
data
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Modeling and
preprocessing of
data
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SOM algorithm
adaptation and
implementation
Evaluation results and
conclusions
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Case studies:
application to
multi dimensional
data sets
Visualization
system design
Network training
and testing
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6
5
References
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T. Kohonen :Self – organizing Maps (second edition)
H.J Rajaneimi , P.Mahonen : Classifying GRB using SOM ,APJ566:202-209
2002 February 10
J.Hakkila ,A.Meegan : AI Gamma-Ray Burst Classification:
Methodology/Preliminary Results arXiv:astro-ph/9712077 4 Dec 1997
Juha Vesanto :SOM-Based Data visualization Methods in Intelligent Data
Analysis journal, 1999:
S.Kaski:Data exploration using SOM ,Espoo 1997 :
T.Kohonen : Exploration of very large data bases by SOM , ICNN’97
Piscataway,NJ
S.Mukherjee : Three types of Gamma Ray Bursts ,APJ 508:314-327,1998
M.Koskela , J. Laaksonen : Self Organizing Image retrieval with MPEG-7
Descriptors
http://www.batse.msfc.nasa.gov/batse/grb/