Morphological Classification of Galaxies based on Computer Vision features using CBR and Rule Based Systems

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1 Morphological Classification of Galaxies based on Computer Vision features using CBR and Rule Based Systems Devendra Singh Dhami Tasneem Alowaisheq Graduate Candidate School of Informatics and Computing Graduate Candidate School of Informatics and Computing Masters in Computer Science PhD in Computer Science 3801 S. Sharon Dr. 1227, S. Fenbrook Lane Bloomington, Indiana Bloomington, Indiana Abstract There are 10^11 galaxies in the universe and many more are getting discovered at a very fast rate. It becomes really necessary to classify these heavenly bodies into some appropriate classes to help them study further. There have been several approach taken to classify these galaxies with varying degrees of success. In this paper we present two systems: a Case Based Reasoning system and a rule based system designed to perform the classification task. We make use of the morphological features i.e. features describing the structure of the galaxy like its shape, central characteristics (has a bar or bulge at its center) etc., we extract from our Computer Vision System and try to classify the galaxies according to the extracted features. 1. History and Motivation The problem we are tackling is a really interesting one and goes back to the advent of Astronomy. When the first galaxies were discovered, they were very few in number and thus a need of their classification was not a demanding task. But then with the advancement of technology there was a burst in the number of galaxies that were being found and the need of their classification arose. Edwin Hubble classified the galaxies into something called the Hubble sequence in 1936 [1]. This was purely done in a manual way relying on the images that were seen through the telescopes. There were few other systems like the De Vaucoulers syetem and the Yerkes (or Morgan) schemes that were invented to classify the galaxies [1]. Then in 2007, a citizen science project called the Galaxy Zoo was launched, in which millions of volunteers around the world were asked to classify the galaxies based on the images from the Sloan Digital Sky Survey (SDSS) database. The project was successful but with new galaxies being discovered at a really rapid pace, a need was felt to automate the classification process. Some works used Machine learning techniques for the process like the one by Gauci, Adami and Abela [3] that and the one by Banerji [4] were instrumental in introducing the world of Artificial Intelligence to this problem. 2. The Problem We tried to apply the Case Based Reasoning technique to this problem as we figured that it can be very relevant to the problem domain. As the number of galaxies increase we can use the already classified galaxies to classify them. This approach will require the morphological features of the galaxies that can be extracted using Computer Vision techniques. The problem proved to be very interesting and challenging at the same time. Interesting because the Case based reasoning and the rule based method had not been applied before to this domain and to this problem. Challenging because the images of the galaxies were very noisy and small (Figure 1) and the extraction of features was difficult and time-consuming. As the CBR and Rule based system were completely dependent on the extracted features the classification proved to be a hard task. Another problem that was faced was the comparison metric between the old and the new cases. Several approaches were tried some of which performed poorly and some performed satisfactorily. Another challenge was the staggering size of the database. We had around 283 Thousand images and we tested the systems on only 32 images but it can be scaled up to any number of images with none or minor modification. The related work on the area has mainly been on Machine learning classification algorithms and Neural Network systems which proved to be quite effective but were still

2 dependent heavily on the Computer Vision technique. Our system suffers from the same flaw but the results shows that the CBR systems performs relatively well. The CBR approach makes its contribution as this classification process based on morphological features can be made simpler and relatively faster if old examples of the classification can be used as cases for the new galaxies being found. This can reduce the need for a new classification algorithm to be applied every time and although will need a staggering database for the cases will prove to be less costly than other techniques in the long run. This approach will also give us the luxury of having the old data at our disposal and thus the possibility of wrong classification can be significantly reduced. Figure 1. Example of a Galaxy Image. belong to a single class. The class to which they belong will depend on the probabilities of their subclasses. Figure 2. Example of the Human Classified data We build the cases by reading the data from the excel sheet and putting it into the proper case format. We would like to mention here that another challenge we faced during this project was the decision on the case format. A case format for CBR system for human data did not perform well with the CBR system for extracted features and thus we went for two case formats, which although are different but are same in their basic design. We first try to find the class for which the probabilities of the subclasses sum up to 1, as this indicates a 100% probability that the galaxy will belong to that said class. If we don t find such a class then we search for a sum of 0.99 as we feel that this is a big enough probability to safely assume that the galaxy will belong to the class in question. If both the above conditions are not met then we take the nearest neighbor approach. We find out the case for which the distance between the new case and the case is lowest. Then we take the class for which the distance is lowest. This gives us a good enough measure of the class to which the galaxy belongs. Figure 3 shows an example output: 3. Our Approach We implemented 3 systems for this project, 2 Case based reasoning systems and a rule based system. One of the Case Based systems was made for the human data available. By human data we mean the data we obtained from the galaxy Zoo project [2] in which the human volunteers classified the galaxies into various classes. The other Case base and the rule based system were implemented for the features obtained from the computer vision systems. 3.1 CBR system for the human data The format of the human classified data is static. (Figure 2) The data provides us with the galaxy id and the class names with the probabilities as stated by humans of each galaxy belonging to the certain class. We take a very simple approach in this CBR system. We take the liberty of assuming that the galaxies classified by the humans will Figure 3. Output for Classification of Human data

3 3.2 Rule Based System for extracted features The input data we use for the rule based system is the features we output from the Computer vision system. Figure 4 shows an example of the format of the excel sheet we output from the CV system. We also implement a conflict resolution strategy in the rule based system which was required so that a false rule does not fire. Here we check the rule that needs to be fired, which we obtained from the consequent, with the antecedent of the matched rule. We also check whether there is a consequent rule that needs to be fired because not all rules are connected to other rules. We write the classified output in a text file whose snippet is shown below in Figure 7. The first element is the galaxy id and the rest are the classes to which the galaxy belongs to. Figure 4. Example of feature output by CV system for rule based system. This serves as input to the rule based system i.e. goes into the working memory. Figure 6. Running the Rule-Based System The topmost rows is the feature to be detected and the values show the features detected. We have taken care to keep the formats of the rules (Figure 5) in a way that made the task of generating the working memory from the feature output and its comparison with the rules easier. Figure 7. Output of the rule based system 3.3 CBR system for extracted feature Figure 5. Examples of rules in our system The rules consist of the complete rule number as its first part (Rule-1, Rule-2 etc.). This was done because the rule 1 is related to the Rule 2 and Rule 3 to Rule 9 and so on. The second part of the rule gives the antecedent which is the feature of the galaxies in that subclass and the consequent which gives the class number and the Rule which needs to fired next for that galaxy. The CBR system differs with the rule based system in the way the extracted features from the Computer Vision system are sent as input to the system. As shown in Figure 4, for rule based systems we directly send the extracted features to be compared with the rules. In CBR system, we take a little different approach. Here we send the numerical values we received for the parameters of every feature. We do this to test whether the CBR system can find out the features along with the class for each galaxy. Thus we push the CBR system a step further. The CBR system does not disappoint us and is able to search and output the correct feature along with the classes in a greater number of instances. Figure 8 below shows the input file for the CBR system as received from the CV system. The 1 st row indicates the parameters names for different features and their values are indicated in the rows below. ID denotes the galaxy ID.

4 base. Then we normalize all the values for that feature by dividing the feature values with the minimum value. We then find out the nearest case to the normalized value to obtain the feature. A classifier is then used to classify the feature into its class. We write the features obtained for a galaxy in an excel sheet (Figure 11) and the class obtained in a text file (Figure 12). Figure 10. Running the CBR system for features Figure 8. Example of feature output by CV system for CBR system. This serves as input to the CBR system i.e. comprises of the new cases We train our CBR system with selected cases (not among the input cases). Some of the rules are shown in Figure 9 below. Figure 9. Examples of training rules for CBR system We take 2 approaches for the different features, namely case retrieval for the first 3 features is done in one way and that for the last 3 features is done another way. For the first 3 features we use something we call the weight matrix. This is actually a list of lists that consists of weights that are assigned for each features for each case. These weights are assigned according to the concept that the new case should be near to the one of the training cases. The weights are either 1(very near to a case in the knowledge base), 0.5(neither very near nor very far to a case in the knowledge base) or -1(very far from a case in the knowledge base) Then we get the best case according to the weights to get the feature. Then we use a classifier to classify that feature to a class. For the last 3 features we find the minimum value for a feature from the new case and all cases in the knowledge Figure 11. The features as obtained by the CBR system. First row represents the feature name and the values obtained are in the below rows Figure 12. Output of the CBR system In Figure 12, the 1 st column represents the galaxy id and the classes it belongs to are shown after the id.

5 4. Strengths and Weaknesses We feel that our approach has the following strengths: 1. The system is simple in design but efficient. 2. CBR system and the Rule based system give a good estimation of the galaxy classes. 3. System is domain-independent. 4. CBR System is expert knowledge independent. The weaknesses are as follows: 1. Case and rule format is rigid. 2. System not yet tested on a large dataset. The results we obtained so far are not a sufficient measure for accuracy but they provided a good performance indictor 3. Stricter heuristic required for CBR systems. 5. Relation to other works The closest related works we found was by Kasivajhula, Raghavan, and Shah[5]. Other related works were by Gauci, Adami and Abela [3] and Banerji [4] that used Machine learning classification algorithms to classify the galaxies. In [3] decision tree learning algorithms and fuzzy inferencing systems are applied to the problem. The main aim here was to develop distinct models for spiral, elliptical galaxies and stars or unknown space artifacts. For decision tree learning algorithms they use the Classification and Regression Tree (CART) scheme and random forests and for the fuzzy systems they define ifthen rules that deal with fuzzy consequents and antecedants, which is like a rule based system but yet different in a way that they define a degree of membership from 0 to 1 for each class and classify them into bands, namely i and r bands. Their approach is quite different from our approach in this project as they try to find which parameters are important for galaxy classification whereas we use the morphological features for the classification assuming all are important and also look at how similar and distinct each galaxy is to another galaxy. For their Machine learning algorithms they get a 81% accuracy whereas for fuzzy systems they get a 75% accuracy. In [4] an artificial neural network is trained on space objects classified by the human eye (they use the SDSS dataset, which we have also used in this project) and test whether the machine-learning algorithm can reproduce the human results. For classification they use different sets of parameters. One set of input parameters are based on colors and profile fitting. Another set is based on shape and texture as well as the concentration. Their third and final set is a combination of 12 parameters. They classify the galaxies into 3 categories, early types, spirals and artifacts. Using the 1 st set they have a high accuracy of about 87%, 84% and 95% accuracy for the 3 categories. The second set gives around 84%, 87% and 28% accuracy for the 3 categories. The third set gives the highest accuracy, 92%, 92% and 96% for the 3 categories. In [5] they compare 3 classic Machine learning algorithms, Support vector machines, Random Forests and Naïve Bayes in the task of galaxy classification. They follow the same approach as us in extracting the various features of the galaxies. They classify the galaxies into 3 categories, Elliptical, Spiral and Irregular and then subdivide these into 7 classifications, namely, E0, E7, Sa, Sc, SBa, SBc and I. They used 119 images from Zsolt Frei s galaxy catalog[6]. The below Figure 13 (obtained from [5]) shows their classification results. Figure 13. Classification results of [5] Another work was by Godreya and Lolling[7] who described a computational scheme to develop an automatic galaxy classifier. They presented two types of classifiers. One used geometric shape features (which is our approach) and the other used pixel images of galaxies and artificial neural networks. They used the SDSS database. Figure14 below (adopted from 7) shows their computational scheme flowchart.

6 Here is another example for galaxy id The case based system classifies it into ['Class 1.2', 'Class 3.2', 'Class 4.1', 'Class 9.2', 'Class 10.3', 'Class 11.1'] Whereas the rule based system outputs [' Class-4.1 Class-10.3 Class-11.1 Class-1.2 Class-2.2 Class-3.2 Class-9.2'] Again the results are very close to each other but case based system fares better. 7. Future work We feel that our future work consists of expanding our system for a large dataset. Also changes to heuristics for case based system are required for better performance. Another region where we think our system lags is the rigidity of rules and cases. We would want to remove this rigidness. Figure 14. Computational Scheme Flowchart of [7] Their Feature extractor is a bit wider than ours and the classification technique used is Neural Networks. For their Shape feature classifier they used shape properties like elongation, Convexity and area to name among a few. For their direct image based classifier they trained a NN on 215 galaxies and then tested their network on unknown galaxies. For this method their learning probability was 97.16% but the correct identification/classification rate was only 51.35%. 6. Results The results from rule based systems and the case based system go neck to neck in our project. For example for the galaxy id case based system gives the following classes: ['Class 1.1', 'Class 3.2', 'Class 4.2', 'Class 9.2', 'Class 10.2', 'Class 11.6'] The rule based system for the same galaxy gives the following result: [' Class-4.2 Class-11.6 Class-1.1 Class-2.2 Class- 3.2 Class-9.2'] As we can see the results are fairly close to each other with only the Class 10.2 missing from the rule based system and Class 2.2 missing from the case based system. The human data says that the case based system is closer to the human classification. 8. Conclusion We conclude that the case based system fares better than the rule based system in most of the cases we encountered. Though we did not test our systems for a very large number of images but we do get a certain idea of as to how the systems might perform when tested on a large dataset with a few modifications. Case based systems are an interesting application to this domain which we feel is quite relevant for the CBR systems but not much work has been done on this domain. We believe that with a better feature extractor the CBR and rule based systems can prove to be handy tolls for this classification tasks. 9. References [1] ion [2] [3] Gauci, Adam, Kristian Zarb Adami, and John Abela. "Machine Learning for Galaxy Morphology Classification." arxiv preprint arxiv: (2010) [4] Banerji, Manda, Ofer Lahav, Chris J. Lintott, Filipe B. Abdalla, Kevin Schawinski, Steven P. Bamford, Dan Andreescu et al. "Galaxy Zoo: reproducing galaxy morphologies via machine learning." Monthly Notices of the Royal Astronomical Society 406, no. 1 (2010): [5] Kasivajhula, Siddhartha, Naren Raghavan, and Hemal Shah. "Morphological galaxy classification using machine learning." Monthly Notices of the Royal Astronomical Society 8 (2007): 1-8.

7 [6] Frei, Zsolt, Puragra Guhathakurta, James E. Gunn, and J. Anthony Tyson. "A catalog of digital images of 113 nearby galaxies." arxiv preprint astro-ph/ (1995). [7] [7] Goderya, Shaukat N., and Shawn M. Lolling. "Morphological classification of galaxies using computer vision and artificial neural networks: A computational scheme." Astrophysics and Space Science 279, no. 4 (2002): [8] SDSS database