SOMz: Photometric redshift PDFs with self-organizing maps and random atlas

In this paper, we explore the applicability of the unsupervised machine learning technique of self-organizing maps (SOM) to estimate galaxy photometric redshift probability density functions (PDFs). This technique takes a spectroscopic training set, and maps the photometric attributes, but not the redshifts, to a two-dimensional surface by using a process of competitive learning where neurons compete to more closely resemble the training data multidimensional space. The key feature of a SOM is that it retains the topology of the input set, revealing correlations between the attributes that are not easily identified. We test three different 2D topological mapping: rectangular, hexagonal and spherical, by using data from the Deep Extragalactic Evolutionary Probe 2 survey. We also explore different implementations and boundary conditions on the map and also introduce the idea of a random atlas, where a large number of different maps are created and their individual predictions are aggregated to produce a more robust photometric redshift PDF. We also introduced a new metric, the I-score, which efficiently incorporates different metrics, making it easier to compare different results (from different parameters or different photometric redshift codes). We find that by using a spherical topology mapping we obtain a better representation of the underlying multidimensional topology, which provides more accurate results that are comparable to other, state-of-the-art machine learning algorithms. Our results illustrate that unsupervised approaches have great potential for many astronomical problems, and in particular for the computation of photometric redshifts.