标题： Co-SOM：使用自组织映射进行光度红移估计的协同训练 显示英文标题

标题： Co-SOM: Co-training for photometric redshift estimation using Self-Organizing Maps

摘要： 即将到来的星系大尺度调查，如维拉·C·鲁宾天文台的时空遗产巡天（LSST），将生成数十亿星系的测光数据。大规模弱引力透镜图的解释以及星系聚类的估计，需要多波段测光的高精度可靠红移。然而，对数十亿星系进行光谱观测是不切实际且复杂的；因此，拥有足够数量具有光谱观测的星系来训练监督算法以实现准确的红移估计是一个重大挑战和开放的研究领域。我们提出了一种称为Co-SOM的新方法，基于协同训练和自组织映射（SOM），在训练过程中整合标记数据（具有光谱红移的源）和未标记数据（仅具有测光观测的源），通过基于地图拓扑（SOM网格的连接结构）的选择方法，利用有限的光谱数据进行光子红移估计。我们使用斯隆数字天空勘测数据发布18（SDSS-DR18）的亮度和颜色来分析和评估性能，改变标记数据的比例并调整训练参数。对于标记数据占1%的训练集（$\approx 20{,}000$个星系），我们实现了偏差$\Delta z = 0.00007 \pm 0.00022$，精度$\sigma_{zp} = 0.00063 \pm 0.00032$，以及异常值比例$f_{\mathrm{out}} = 0.02083 \pm 0.00027$。此外，我们进行了改变标记数据量的实验，无论光谱或测光数据的大小如何，偏差始终低于$10^{-3}$。这些低红移结果展示了半监督学习在解决未来测光调查中光谱限制方面的潜力。 显示英文摘要

摘要： The upcoming galaxy large-scale surveys, such as the Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST), will generate photometry for billions of galaxies. The interpretation of large-scale weak lensing maps, as well as the estimation of galaxy clustering, requires reliable redshifts with high precision for multi-band photometry. However, obtaining spectroscopy for billions of galaxies is impractical and complex; therefore, having a sufficiently large number of galaxies with spectroscopic observations to train supervised algorithms for accurate redshift estimation is a significant challenge and an open research area. We propose a novel methodology called Co-SOM, based on Co-training and Self-Organizing Maps (SOM), integrating labeled (sources with spectroscopic redshifts) and unlabeled (sources with photometric observations only) data during the training process, through a selection method based on map topology (connectivity structure of the SOM lattice) to leverage the limited spectroscopy available for photo-z estimation. We utilized the magnitudes and colors of Sloan Digital Sky Survey data release 18 (SDSS-DR18) to analyze and evaluate the performance, varying the proportion of labeled data and adjusting the training parameters. For training sets of 1% of labeled data ($\approx 20{,}000$ galaxies) we achieved a performance of bias $\Delta z = 0.00007 \pm 0.00022$, precision $\sigma_{zp} = 0.00063 \pm 0.00032$, and outlier fraction $f_{\mathrm{out}} = 0.02083 \pm 0.00027$. Additionally, we conducted experiments varying the volume of labeled data, and the bias remains below $10^{-3}$, regardless of the size of the spectroscopic or photometric data. These low-redshift results demonstrate the potential of semi-supervised learning to address spectroscopic limitations in future photometric surveys.