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.
