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Bringer, M. & Boër, M. 2000, in ASP Conf. Ser., Vol. 216, Astronomical Data Analysis Software and Systems IX, eds. N. Manset, C. Veillet, D. Crabtree (San Francisco: ASP), 640

An Automatic Astronomical Classifier Based on Topological Neural Networks

M. Bringer, M. Boër
Centre d'Etudes Spatiales des Rayonnements (CESR/CNRS), 9 av du Colonel Roche, 31028 Toulouse cedex 04, France

Abstract:

We report progress in the development of an automatic classifier for astronomical objects. The described method is adaptive. It is trained by examples and doesn't need any training rules. The map is used later as a code book by the TAROT (Télescope à Action Rapide pour les Objets Transitoires, Rapid Action Telescope for Transient Objects) data processing pipeline. It is a general method which may be used for other purposes starting with large surveys. In this paper, we describe the method, as well as the results from test and general astronomical images taken by TAROT.

1. Introduction

The setting up of new automatic observatories, essential in order to understand rapid event such as gamma ray bursts, has shown the need to develop fully automated software able to detect and classify sources in a short time. There are now few good softwares able to detect and measure sources even in crowded areas, but still resist the problem of classification. The game consists of being able to attribute a nature to every object detected on the frame, even though it is not a common object. One of the solution may lie in the use of neural networks (NN). Multilayers perceptron (Bertin & Arnouts 1996) and Self Organizing Map (SOM) (Mahonen & Hakala 1995) seem able to separate stars and galaxies. We will at first expose the foundations of SOM in order to present our Topological Neural Networks (TNN) that gives us our first good results of classification.

2. Basics Facts about NN

2.1. Generality

It is quite difficult for a newcomer in the NN area to have a precise idea of what is a NN. The definition proposed by Haykin (Haykin 1999) to approach a NN as an adaptive machine is quite general:
A neural network is a massively parallel distributed processor made up of simple processing units, which has a natural propensity for storing experiential knowledge and making available for use.
A NN is just a group of connected units called neurons that perform useful computations through a process of learning.

2.2. Model of a Single Unit

The neuron is an information processing unit that is fundamental to the operation of NN. It can be modeled by Figure 1.

**Figure 1:** Model of an artificial neuron.

Where:

are the inputs,
is the bias,
is the activation function. Different functions are commonly in use. We have chosen the sigmoid function:

$\begin{displaymath}f(x)=\frac{1}{1+e^{-x}}\end{displaymath}$

2.3. Topology of a NN

Principles: Neural Maps are a a group of connected neurons. From that point, we can create lots of different NN depending on ordering of neurons, relations between neurons and training inputs.
Multilayer Perceptron is characterized by the way neurons are linked to each other. Typically, the input vector is connected to an input layer. Each neuron of the input layer is connected to neurons of another layer (which is called hidden layer if there are further layers), and so on till the output layer. Neurons of a same layer are usually independent one to each other. The connection between a neuron from a layer to a neuron of another layer is done through a synaptic weight which is used to store a knowledge. This knowledge is acquired thanks to the learning process. Topology of a TNN: A TNN is a network that preserve the topology of inputs. In order terms, two vectors close in the input space will be close in the output space. This NN is a single layer network. The power of the network is primaryly that neurons are dependant each other, in order to preserve the topology, and secondly that the training process is done with no a priori information on the inputs data.

3. Our TNN

3.1. The Map

We use

(dim p) neurons arranged in a two dimensional array. Each neuron is associated with a weight vector

. In our case, the input data consists of objects detected on the frame by our data processing software TAITAR as a two-dimensional array of

(dim n) pixels. The network is presented on Figure 2.

**Figure 2:** Left: Configuration of a Topological Neural Network, Right: The Topological Map after training.
$\begin{figure} \epsscale{0.3} \plottwo{P3-09b.ps}{P3-09c.ps} \end{figure}$

3.2. Initialization

Before the training phase, initial values are given to the weight vectors. We have adopted a linear initialization (Kohonen 1997) where the weight vectors are initialized in an orderly fashion along the linear subspace spanned by the two principal eigenvectors of the input data used for the training procedure.

3.3. Training

In each training step, the network will compute for every new input,

for each neurons:

$\begin{displaymath} D_j=\sum_{i=0}^{p}\vert\vert I_i-W_{ij}\vert\vert \end{displaymath}$

(1)

We then select the Best Match Unit (BMU) and update the weight vectors of the map according to Equation 2.

$\begin{displaymath} W_i(t+1) = W_i + h_{ci}(t)*(I(t)-W_i(t)) \end{displaymath}$

(2)

where denotes the time and $h_{ci}$ is the neighborhood kernel around the BMU.

3.4. The BMU

For every input data, the Network will compute for every neuron Equation 1. The BMU will be the neuron

according to

$\begin{displaymath} D_c = min_j(D_j) \end{displaymath}$

(3)

This means that the weight vector of neuron

most closely resembles to the input vector

3.5. Neighborhood Kernel

In order to preserve the topology of data, neurons are connected to adjacent neurons by a neighborhood relation dictating the structure of the map. The neighborhood kernel is an non-increasing function of time and of the distance of unit

to the BMU. It defines the region of influence that the input sample has on the map. In this work, we use the Gaussian Kernel.

4. Results - Application to TAROT

In order to train the net, we have used both simulated and original CCD subframes of

pixels containing either a point source, an extended object, a blended object or a sky background. The images were then mean subtracted and normalized to the unit length. Figure 2 shows the result after training. We clearly see 3 different areas that represent the point source area, the extended source area and the sky background area. It is then possible to use the map in the TAROT pipeline (Bringer et al. 2000). The idea is to calculate for every objects detected as a subframe of

pixels, the BMU of the map. If the BMU falls in the point source area, it means that our object is a point source. If the BMU is a neuron on the frontier area, we can't give more than a probability of being a point source.

5. Conclusion

We have introduced a Topological Feature Map which is capable to learn through experience and to discriminate between astronomical objects. One of the particularity of the map is that we don't calculate any parameters, and thus we do not introduce any subjective opinions about the object. The input data are raw objects. We are now looking forward to improving our map in order to deal with other types of astronomical objects. One will have notice that the map doesn't show any blended object area whereas we had some blended object in our training data. We probably need fine tuning during the training phase as well as a better training data set in order to classify the blended object. When this map will be strengthen, we will try to consider the temporal variability of objects. This is probably the next challenge of astronomical classification.

References

Bringer, M. et al. 2000, this volume, 445

Bertin, E., & Arnouts, S. 1996, A&AS, 117, 393

Haykin, S. 1999, in Prentice Hall International Editions, ISBN 0-13-908385-5

Kohonen, T. 1997, in Springer-Verlag Berlin Heidelberg New York Editions

Mahonen, P. H., & Hakala, P. J. 1995, ApJ, 452, 77

adass@cfht.hawaii.edu