ULEDS-SVMs: Upper/Lower Limits and Error Data Supposted Support Vector Machines

Abstract

A Support Vector Machine, ULEDS-SVMs, was developed for classification in data domain which contains limits or errors.

Data with upper or lower limits are different from missing data. They provide constraints at a certain level in data classification and modeling. Data with errors may be recognized as the special case of an upper and a lower limit existing at the two boundaries at an attribute. Such kind of data quality exists widely, from scientific data measurement, to databases resulted from integration and emerge with different quality. Including these data in training rather than dropping them or arbitrarily filling with some value is very desired to provide useful constraints in machine learning.

A simple enhanced 1R algorithm is described which may be able to handle data in such a domain, and which principle may be extendable to other machine learning methods. But this is not favored because of its time complicity. Support Vector Machines (SVMs) treatment of the data in such a domain is, however, very promising. We provided the mathematical foundation to treat this kind of problem by recognizing the concepts of feasibilities for training, testing and predicting in SVMs. Algorithms were described by utilizing the theorems.

For applying ULEDS-SVMs, we made an integration of a data set in astronomy (CHDF-N) based on Chandra Deep Field (CDF) and Hubble Deep Field (HDF) North observations. Classification of the astronomical objects is interesting for the study of formation and evolution of galaxies in the deep universe. This direction contains the deepest observations made with the largest astronomical facilities currently available.

We used CHDF-N as a test bed for the ULEDS-SVMs algorithms application implemented via Matlab.

The separation between stars and extragalactic objects gets a 100% accuracy, which would be otherwise more ambiguous in determining the separation plane if limit data in extragalactic class were not included. Training and testing using leave-one-out partition achieved 82% accuracy for separation of galaxies and active galactic nuclei (AGNs). This is better than 72.4% accuracy by using conventional R-log(F_x) plot separation method commonly used in the astronomical community. Prediction rate increased from 49.6% by using conventional SVMs to 75.5% by using ULEDS-SVMs.