The storage capacity of digital databases overcomes our ability to analyze data, so the need to narrow this gap as much as possible is imperative. In astronomy, telescopes can perform automatic surveys of the sky gathering a huge amount of data that are waiting to be analyzed in more detail. The deeper is the analysis the more elaborated and slower are the procedures. Computer science is facing the challenge of creating e cient algorithms . Machine learning (ML), a branch of computer science, is an option for many problems where there is no a simple de nition of the relation input-ouput. ML techniques have been successively used in several astronomical and storage knowlege problems. We focus the research on various branches of machine learning by solving a practical problem: estimation of stellar population parameters (SPP) and kinematics of galactic spectra. The SPP have been tackled in multiple ways, but as the complexity and number of spectra grows, the techniques of ML gain importance. We de ne the stellar populations and we survey some of the most common methods for their estimating. We concentrate on a special type of spectra, called 3D spectra.
Nowadays, technologies of storage and instrumentation are producing huge databases in several sciences, astronomy is a good example of this situation. Modern telescopes and instruments daily record spectra and images, these data have a lot of valuable implicit information which needs to be analyzed by e cient algorithms. Sophisticated computational algorithms have already been used for classifying astronomical objects from images and for estimating physical parameters from spectra. The complexity of the techniques changes according to the size and intrinsic di culty of the data. However, the astronomical observational techniques evolve and now they are producing more complex data each time. A relatively new technique for obtaining spectra is the Integral Field Spectroscopy (IFS) that can produce thousands of spectra of only one object. The collected data by this kind of instruments require e cient methods of analysis. Examples of the type of information that can be retrieved from an IFS spectrum of one galaxy are the distribution of ages of the component stars in each region of the galaxy, the kinematics of stars and gases. In principle, with these data, one can form the history of the galaxy, a very important problem in Astrophysics. Surely the study of the problems set by IFS spectroscopy will require to develop new algorithms that will contribute to computer science and to other disciplines. The main methods for estimating stellar populations are introduced section 2, two new strategies for improving e ciency are are presented in section 3, the experimental results are discussed in section 4. 2
The stellar populations in galaxies are characterized for an age distribution, the
chemical composition (metallicity) and the amount of gas that obscures star light
(extintion). These properties can be directly inferred from the charactetization
of the absorption and emission lines of their spectra [
3D spectra of galaxies allow to know the stellar populations in greater spatial
detail. 3D spectra are formed by a grid of spaxles, where each spaxel contains
a spectrum that samples a region of the galaxy providing the necessary spatial
resolution to synthesize stellar populations kinematics maps [
We believe that a machine learning approach will be successful in addressing our problem, this claim is based on both the state of the art review and in our own experience. The problem could be posed as an optimization problem, therefore we must review the available optimization algorithms, mainly those in the machine learning area. We also explore the preprocessing of data as a medium to improve the system performance. The research will lead us to design algorithms that hopefully would be of wide application.
Our problem of stellar population parameters is non-linear with constraints, the di erent objectives functions that model galactic spectra contain several independent variables, so we have a high dimensional problem, for instance, the objective function 2 based on the model 1. On the other hand, the data have certain degree of noise. Therefore, we have selected stochastic and heuristic methods to start our experiments, in particular Simulated Annealing (SA) and Evolution Strategies (ES). f (P ) = X jo
In any machine learning system the preprocessing stage has particular
relevance on the nal performance, even more in cases where the data are of high
dimension [
One way of accelerating the convergence of an optimization algorithm is start with an initial guess solution that near us to an acceptable solution. The guess can be produced by another algorithm. We test this strategy by designing two architectures. The rst architecture sort the 3D spectra by means of a similarity metric. This ordering will allow us to estimate the parameters of a given spectrum and then use them as an initial solution for a similar spectra, then the optimization algorithm will re ne this initial solution, see Figure 1. The second one, a neural network whose training set are the ordered pairs (spectral features, stellar population parameters) gives the initial guess, see Figure 2.
We start our work by taking both simulated annealing and evolution
strategies [
The rst experiments are focused on stellar population, the issue of kinematics will be treated later. 4.1
The Graphical User Interface We have designed a simple graphical user interface (GUI), because given the amount of data graphical results can help us in debbuging the approach, besides of integrating the system parts in an ordered way. Figure 3 shows the GUI, it has a menu bar, a central window that shows a test spectrum and its corresponding estimation, the upper right group galaxy components displays the selected options for data set and model, nally, the lower group model parameters shows the parameter values for both test and estimated spectrum, the number and type of parameters will depend on the chosen model.
The GUI contains already menus for the following tasks:
Fig. 2. Estimation architecture based on an classi er.
{ Select data and models: menu Model. The data are simple stellar
populations spectra and the model speci es how to combine these data in order to
form a synthetic galaxy.
{ Create training and test sets: menu Samples. The training set is used to
train a neural network that can be used to make a rst estimation of
parameters.
{ Calculate features and train a neural network: menu Preprocessing. The
multiple metric option extracts from the training and test sets features as
inputs of a backpropagation neural network.
{ Select the optimization algorithm: menu Estimation. Here, we can choose
between Simulated Annealing and Evolution Strategies as estimation
algorithm.
We can choose from several models of synthetic galaxy spectra, they basically
make linear combinations of spectra of di erent ages, and then they include
a non-linear factor for taking into account the extinction. We test the model
reported in [
f kjg) vu m deuc(f 0; f k) = utX(f 0
f k)2 =1 m X(f 0 =1 dsqreuc =
k 2 f )
We divide the spectrum into j intervals of the same length and we measure their means, the intervals are designated by [jlow; jup] meanjk =
1 (jup jlow + 1) jup X f k =jlow
j = 1 : : : 10 dmeanj (f 0; f k) = jmeanj0 meanjkj (4) (5) (6) (7) (8) (9) In order to assess the relevance of the selected features in the estimation process, we prepared a training set of 100 spectra, this set is the input to the neural network that will predict the population parameters. The prediction done by the network is the starting point of the optimization algorithms SA-NN and ES-NN.
Another way of generating a rst guess is to order the spectra by a similarity metric, so in the estimation of a given spectrum we can use the solution of a neighboring spectrum as the starting point of the optimization algorithms SA-PCA and ES-PCA. The proximity in the feature space should re ect the proximity in the parameter space. We project the features on the principal components instead of calculating the distances over all the pairs of spectra, and we use rst component as criterion of nearness.
The better results were obtained using a neural network (see gure 4). The PCAs did not work better than neural networks, a explanation of this result could be that the test set is randomly sparse and probably the mean distance between set of parameters is not suitable for this technique. In addition, in SA and ES algorithms, the rate of change of the actual solution is high at the beginning, so we must try to choose appropriately the parameters of the algorithms to control the rate when a starting guess is used.
The real spectra of galaxies cover only certain regions of the parameter space, so we do not discard the use of PCA until dealing with real 3D spectra. The gure 5 shows that a set of parameters over a given direction, could be ordered by the PCA of the features. The distribution of the parameters over a direction was formed by sampling uniformly from minor to major each parameter range (coordinates). The 100 sets of parameters were integrated by combining the sampled values in this form: the rst point is formed by the rst elements of each coordinate, the second point by the second elements of each coordinate, and so on.
The stop criterion was the number of evaluations of the objective function: 2000. The training of the backpropagation network lasted three minutes with a training set of 100 spectra and the stop criterion was the prediction accuracy: sum of squared di erences <= to 0.01. 5
From these preliminary results, we conclude that the selected features used as inputs to a neural network can increase the accuracy of the optimization algorithms, at the same time the features can be useful in the de nition of a measure of the nearness in the parameter space that can be exploited in optimization of multiple instances, under certain restrictions, i.e. the data should be clustered and no distributed over all parameter space. Furthermore, the parameters of the optimization algorithms must be initialized in a non standard way for taking advantage of the rst guess.