GRB Classification using Self Organizing Map (SOM)

Praveen Boinee Ph.D student

Udine university

Presentation outline 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 Importance of analysis

can be useful in understanding the physics of the gamma ray sources

can be helpful in finding the GRB sources But …

GRB data is one of the complex astronomical data sets High dimensionality

Analysis Techniques Statistical Artificial Neural Networks can be efficiently used in

data classification

GRB Classes

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 subclasses

Pre-Processed GRB Data

Classified data

Scientific and

Logical Assessment

GRB classification process

DataBase

Data Mining VisualizationData

Preparation

Neural Networks 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

Learning = Training = knowing information This information is stored on the links between the

neurons Also called weights Two types of learning

Supervised unsupervised

After Training Neural Network is ready to Classify the data Find hidden patterns / relations

Weights

Neural Network

OutputInput

Supervised vs. Unsupervised Learning

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

To find useful representations of the data, for example: finding clusters dimensionality reduction finding the hidden causes or sources of the data modelling the data density

Uses of Unsupervised Learning data compression outlier detection classification make other learning tasks easier a theory of human learning and perception

Self-Organisation

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 SOM produces the similarity

graph of the input data Converts non-linear

relationships between high dimensional data into simple geometric relationships

Illustration of the SOM model with a 7 X

7architecture

Input pattern

Weight

Updated Weight

Input space

Output space

SOM – Self organizing Map

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 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

Initialization Training Visualization

Initialization

Consider an n-dimensional dataset Each row in the data set is treated as a n-dimensional

vector For each neuron /classifier unit in the map assign a a

prototype vector from the data set Prototype vectors are initialized

Randomly Linearly

After training Prototype vectors serves as an exemplar for all the vector that associated with the neuron

Training – Best matching procedure

Let be a neuron in grid be the prototype vector associated to

be a arbitrary vector Now our task is to map this x to any one of

the neuron For each neuron compute the distance

Better statistic:

neuron satisfying the above statistic is the winner and denoted by b

iim

i nn

nRx

imxmin

iiD

ii

i mxmaxD

Topology Adjust – critical step The following update rule is used for each neuron i in

the the neighborhood of winner neuron b

tmxthttmtm ibiii 1

1at trtype vectois a prototim )1(

mapte of the earning rar valued lis a scalat )(

ernelbourhood kis a neight

rrth ib

bi 2

exp)(2

2

e coordinatcrete timeis the dist

kernel dth of the is the witσ

,i neuronsctors of b radius vei , rbr

with timeecreasing onically d are monott,αtσ

Training – Topology 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 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

Data Visualization using SOM

Representation forms

Component planes representation (Graphs,

scatter plots, ..)

Data distribution

Mesh visualizations SOM grid

Surface plot of distance matrix

Cell visualizations (Distances matrices e.g.

U-matrix, similarity coloring, map unit size) Clusters

(data structure)

Shape of clusters

Relationships

Shape

Color

Position

View (2D/3D

Object identifiers

(icons)

Connection lines

Coordinates control

Surface reflectance

Derived information

User interactions

Visual properties

Lighting

Transparency

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.

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

Data classification in Cube Points

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

PhD research seminar (Qualifying phase) - September 19, 2001- Etien Luc Koua

Data set has 39 indicators describing various quality-of-life factors, such as state of health, nutrition, educational services, etc,)

WEB SOM

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

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

SOM_PAK MS-DOS / UNIX Free, from the website. The "official" SOM implementation.

SOM Toolbox Matlab 5 Free, from the website.

Software

Geo-vista an open software development environment Java Bean component technology http://www.geovista.psu.edu/software/

software.jsp

Research Plan

Case studies: application to

multi dimensional data sets

Theoretical model of the SOM for

GRB data

Network training and

testing

Visualization system design

Modeling and preprocessing of

data

SOM algorithm adaptation and implementation

1

2

3

4 5

6

7

8

Evaluation results and conclusionsConceptual

framework

References 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/