Kernel PCA for type Ia supernovae photometric classification

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 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 \textit{Supernova Photometric Classification Challenge} (SNPCC) data set. Our method provide good purity results in all data sample analysed, when SNR$\geq$5. As a consequence, we can state that if a sample as the post-SNPCC was available today, we would be able to classify $\approx 15$ of the initial data set with purity $\gtrsim$ 90% (D$_{7}$+SNR3). Results from the original SNPCC sample, reported as a function of redshift, show that our method provides high purity (up to $\approx 97$), specially in the range of $0.2\leq z < 0.4$, when compared to results from the SNPCC, while maintaining a moderate figure of merit ($\approx 0.25$). We also present results for SNe photometric classification using only pre-maximum epochs, obtaining 63% purity and 77% successful classification rates (SNR$\geq$5). 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.