This work is focused on the morphological classification of galaxies
following the Hubble sequence in which the different classes are arranged in a
hierarchy. The proposed method, BCNN, is composed of two main modules. First, a
convolutional neural network (CNN) is trained with images of the different
classes of galaxies (image augmentation is carried out to balance some
classes); the CNN outputs the probability for each class of the hierarchy, and
its outputs/predictions feed the second module. The second module consists of a
Bayesian network that represents the hierarchy and helps to improve the
prediction accuracy by combining the predictions of the first phase while
maintaining the hierarchical constraint (in a hierarchy, an instance associated
with a node must be associated to all its ancestors), through probabilistic
inference over the Bayesian network so that a consistent prediction is
obtained. Different images from the Hubble telescope have been collected and
labeled by experts, which are used to perform the experiments. The results show
that BCNN performed better than several CNNs in multiple evaluation measures,
reaching the next scores: 67% in exact match, 78% in accuracy, and 83% in
hierarchical F-measure.

本研究主要使用 BCNN 方法对星系进行形态分类，通过卷积神经网络（CNN）训练不同类别的星系图像，并结合贝叶斯网络进行预测，结果显示 BCNN 在多个评估指标上表现优于其他 CNN 模型。

贝叶斯和卷积网络用于星系的层次形态分类

Bayesian and Convolutional Networks for Hierarchical Morphological  Classification of Galaxies

We report an integral-field spectroscopic (IFS) observation of a
gravitationally lensed spiral galaxy A1689B11 at redshift $z=2.54$. It is the
most ancient spiral galaxy discovered to date and the second kinematically
confirmed spiral at $z\gtrsim2$. Thanks to gravitational lensing, this is also
by far the deepest IFS observation with the highest spatial resolution ($\sim$
400 pc) on a spiral galaxy at a cosmic time when the Hubble sequence is about
to emerge. After correcting for a lensing magnification of 7.2 $\pm$ 0.8, this
primitive spiral disk has an intrinsic star formation rate of 22 $\pm$ 2
$M_{\odot}$ yr$^{-1}$, a stellar mass of 10$^{9.8 \pm 0.3}$$M_{\odot}$ and a
half-light radius of $r_{1/2}=2.6 \pm 0.7$ kpc, typical of a main-sequence
star-forming (SF) galaxy at $z\sim2$. However, the H\alpha\ kinematics show a
surprisingly tranquil velocity field with an ordered rotation ($V_{\rm c}$ =
200 $\pm$ 12 km/s) and uniformly small velocity dispersions ($V_{\rm \sigma,
mean}$ = 23 $\pm$ 4 km/s and $V_{\rm \sigma, outer-disk}$ = 15 $\pm$ 2 km/s).
The low gas velocity dispersion is similar to local spiral galaxies and is
consistent with the classic density wave theory where spiral arms form in
dynamically cold and thin disks. We speculate that A1689B11 belongs to a
population of rare spiral galaxies at $z\gtrsim2$ that mark the formation epoch
of thin disks. Future observations with JWST will greatly increase the sample
of these rare galaxies and unveil the earliest onset of spiral arms.

利用重力透镜技术，我们使用整个视场光谱观测了一个位于红移 $z = 2.54$ 的 A1689B11 螺旋星系。通过观测我们发现它是迄今为止发现的最古老的螺旋星系之一，通过捕捉到螺旋臂接近形成时期的它，我们可以推断这个星系属于一种罕见的在 $z>2$ 时期标志着薄盘形成的星系群体。