Kernel PCA for Type Ia supernovae photometric classification

The problem of supernova photometric identification will be extremely important for large surveys in the next decade. In this work, we propose the use of kernel principal component analysis (KPCA) combined with k = 1 nearest neighbour algorithm (1NN) as a framework for supernovae (SNe) photometric classification. The method does not rely on information about redshift or local environmental variables, so it is less sensitive to bias than its template fitting counterparts. The classification is entirely based on information within the spectroscopic confirmed sample and each new light curve is classified one at a time. This allows us to update the principal component (PC) parameter space if a new spectroscopic light curve is available while also avoids the need of re-determining it for each individual new classification. We applied the method to different instances of the Supernova Photometric Classification Challenge (SNPCC) data set. Our method provides good purity results in all data sample analysed, when signal-to-noise ratio (SNR) >= 5. Therefore, we can state that if a sample as the post-SNPCC was available today, we would be able to classify approximate to 15 per cent of the initial data set with purity greater than or similar to 90 per cent (D-7+SNR3). Results from the original SNPCC sample, reported as a function of redshift, show that our method provides high purity (up to approximate to 97 per cent), especially in the range of 0.2 <= z < 0.4, when compared to results from the SNPCC, while maintaining a moderate figure of merit (approximate to 0.25). This makes our algorithm ideal for a first approach to an unlabelled data set or to be used as a complement in increasing the training sample for other algorithms. We also present results for SNe photometric classification using only pre-maximum epochs, obtaining 63 per cent purity and 77 per cent successful classification rates (SNR >= 5). In a tougher scenario, considering only SNe with MLCS2k2 fit probability >0.1, we demonstrate that KPCA+1NN is able to improve the classification results up to >95 per cent (SNR >= 3) purity without the need of redshift information. Results are sensitive to the information contained in each light curve, as a consequence, higher quality data points lead to higher successful classification rates. The method is flexible enough to be applied to other astrophysical transients, as long as a training and a test sample are provided.