Nonparametric Transient Classification using Adaptive Wavelets

Classifying transients based on the multi band light curves is a challenging but crucial problem in the era of GAIA and LSST since the sheer volume of transients will make spectroscopic classification unfeasible. Here we present a nonparametric classier that uses the transient's light curve measurements to predict its class given training data. It implements two novel components: the first is the use of the BAGIDIS wavelet methodology - a method of characterizing functional data using hierarchical wavelet coefficients. The second novelty is the introduction of a ranked probability classier on the wavelet coefficients which handles both the variable size of measurement errors (heteroscedasticity) of the data in addition to the potential non-representativity of the training set. The ranked classier is simple and quick to implement while a major advantage of the BAGIDIS wavelets is that they are translation invariant, hence they do not need the light curves to be aligned to extract features. Further, the BAGIDIS methodology is nonparametric so it can be used for blind searches for new objects. We demonstrate the effectiveness of our ranked wavelet classier against the well- tested Supernova Photometric Classification Challenge (SNPCC) dataset in which the challenge is to correctly classify light curves as belonging to Type Ia or non- Ia supernovae. We train our ranked probability classier on the spectroscopically- confirmed subsample (which is not representative) and show that it gives good results for all supernova with observed light curve timespans greater than 100 days (roughly 55% of the dataset). For such data, we obtain a Ia efficiency (recall) of 80.5% and a purity (precision) of 82.4% yielding a highly competitive score of 0.49 averaged over all redshifts whilst implementing a truly \model-blind" approach to supernova classification. The classier compares favourably to standard algorithms such as k- Nearest Neighbours (kNN) and Support Vector Machines (SVM), which obtain scores of 0.45 and 0.41 respectively. Consequently this approach may be particularly suitable for the classification of astronomical transients in the era of large synoptic sky surveys.