Photometric redshift estimation for quasars by integration of KNN and SVM

The massive photometric data collected from multiple large-scale sky surveys offer significant opportunities for measuring distances of celestial objects by photometric redshifts. However, catastrophic failure is an unsolved problem with a long history and it still exists in the current photometric redshift estimation approaches (such as the k -nearest neighbor (KNN) algorithm). In this paper, we propose a novel two-stage approach by integration of KNN and support vector machine (SVM) methods together. In the first stage, we apply the KNN algorithm to photometric data and estimate their corresponding z _phot. Our analysis has found two dense regions with catastrophic failure, one in the range of z _phot ϵ [0.3, 1.2] and the other in the range of z_phot ϵ [1.2, 2.1]. In the second stage, we map the photometric input pattern of points falling into the two ranges from their original attribute space into a high dimensional feature space by using a Gaussian kernel function from an SVM. In the high dimensional feature space, many outliers resulting from catastrophic failure by simple Euclidean distance computation in KNN can be identified by a classification hyperplane of SVM and can be further corrected. Experimental results based on the Sloan Digital Sky Survey (SDSS) quasar data show that the two-stage fusion approach can significantly mitigate catastrophic failure and improve the estimation accuracy of photometric redshifts of quasars. The percents in different | δz| ranges and root mean square (rms) error by the integrated method are 83.47%, 89.83%, 90.90% and 0.192, respectively, compared to the results by KNN (71.96%, 83.78%, 89.73% and 0.204). (paper)