Capturing the Physics of MaNGA Galaxies with Self-supervised Machine Learning

We use the Simple framework for Contrastive Learning of visual Representations (SimCLR; Chen et al. 2020a). SimCLR is a contrastive-learning framework to extract meaningful representations of the data. More precisely, we use the model in Tensorflow (Abadi et al. 2015) and follow the findings on optimization by Chen et al. (2020a) with minor changes in the architecture.

This algorithm optimizes representations that keep the semantic, or physical, information of the data by maximizing the agreement between the representations of a data object and its transformed pair ( x , x ^T). This is particularly beneficial when similar objects appear to be different due to observational biases. By selecting transformations that simulate these observational biases, the model is encouraged to neglect these differences while capturing the common remaining features, which correspond solely to the galaxy. Likewise, agreement is minimized when representations originate in different galaxy maps. This way, the program is self-taught to recognize meaningful patterns present in the data.

More specifically, the model consists of a CNN block followed by a set of fully connected layers, after which the contrastive loss l is computed. The CNN block acts as a base encoder that outputs the representations, while the fully connected layers project the representations to the comparison space. We will refer to these last fully connected layers as the head projection function. While both components are trained together, the head projection is removed to obtain the final galaxy representations. Chen et al. (2020a) found that this configuration yields better representations in the previous layers.

The CNN base encoder consists of four convolutional layers with kernel sizes of 5, 3, 3, and 3 and 128, 256, 512, and 1024 filters each. Max-pooling layers and exponential linear unit activation functions (Clevert et al. 2016) are used between the convolutional layers. The output of this set of layers encodes the array-like representations of the galaxies of 1024 features each.

The projection head is composed of three fully connected layers (512, 128, and 64 neurons each). This nonlinear function takes the galaxy representations to a latent space where the contrastive loss is computed.

The contrastive loss is calculated for each L²-normalized representation z _i in the contrastive space with the following equation:

$$\begin{eqnarray}&&{l}_{i,j}=-\mathrm{log}\displaystyle \frac{\exp (\langle {{\boldsymbol{z}}}_{i},{{\boldsymbol{z}}}_{j}\rangle /h)}{{{\rm{\Sigma }}}_{k=1,k\ne i}^{2N}\,\exp (\langle {{\boldsymbol{z}}}_{i},{{\boldsymbol{z}}}_{k}\rangle /h)},\end{eqnarray} \tag{ 1 }$$

where 〈, 〉 is the dot product, and h is a temperature factor that regulates the distribution of the output representations by decreasing or increasing its concentration (Hinton et al. 2015; Wu et al. 2018); in our case, h is set to 0.5. Here z _j denotes the representation of the augmented view of x _i , while k sweeps the other 2N − 1 representations in the batch.

This loss, first introduced in Sohn (2016), does not assume a prior distribution of the representation space and therefore can be used to learn representations of both continuous or discrete data sets. The model benefits from a large number of negative examples and long training times (Chen et al. 2020a). Our model was trained using a batch size of 1024 during 500 epochs, which represents 40 minutes of computing time on one GeForce RTX 2080 Ti GPU with NVIDIA V- 450.102.04.

Data augmentation is a common practice in machine learning that consists of applying transformations to the input data during the training step. The goal is to create different views of the objects while keeping their semantic information. In a supervised approach, data augmentation can be used to enlarge the training sample, since the different views of the data will have the same labels. In the contrastive-learning framework, augmentations are essential to create positive pairs of objects; these are the transformed images that originate from the same image.

When generating meaningful representations of the data in our machine-learning approach, we aim that galaxies that are similar in intrinsic physical parameters will appear close to each other in the representation space. A standard but nonoptimal feature decomposition of the data may reproduce features that are intrinsic to the data but not representative of the galaxies. The possible origin of such features is diverse and may be related to the survey design, instrumental effects, the pipeline used to process the data, or top observational constraints, such as orientation or apparent size of the target. Therefore, the augmentation functions we used during the training of the CNN were designed for the MaNGA data set and with the purpose of mitigating nonphysical dependencies as detailed below and illustrated in Figure 1.

• 1.  
  Model variation. To prevent the model from learning modeling systematics that could be introduced by the pipeline, a transformation that replaces the input set of maps by a set of differently modeled maps is included. With this transformation, the kinematic maps are replaced by those obtained from the MaNGA Data Analysis Pipeline (DAP), which uses Voronoi binning to ensure S/N = 10 in the g-band (Cappellari & Copin 2003) and MILES template library for the stellar continuum fitting (Sánchez-Blázquez et al. 2006; Falcón-Barroso et al. 2011). The luminosity-weighted age and metallicity maps are replaced by the FIREFLY catalog (Goddard et al. 2017; Neumann et al. 2021) analogs. The V-band reconstructed image is replaced by the scale-matched SDSS r-band photometric image, ⁸ which represents a change of view of the galaxy morphological features rather than a modeling variation.
• 2.  
  Random flip and rotation (0°, 90°, 180°, 270°). Since there is no preference in the orientation of the galaxies, the model should be invariant to the galaxy position. We quantify this dependence with the galaxy's position angle (PA) and rotation angle (RA). While the first is used as listed in the DR15Pipe3D catalog, the second was estimated from each velocity map as the perpendicular angle to the direction defined by the mean positions of the negative and positive pixels separately.
• 3.  
  Noise perturbation. The data are affected by errors inherent to the instrument and the postprocessing of the observations. This transformation aims to compensate for measurement uncertainties by shifting the values of the map pixels. The transformation consists of multiplying each value by a random normal factor ${ \mathcal N }(1,\sigma$), with σ adjusted to the expected error for each pixel of each map. The σ maps are calculated as the averaged S/N maps for each channel. ⁹
• 4.  
  Resize. Since the model uses a fixed size for the input, IFUs with a smaller number of fibers will be more intensively zero-padded than IFUs with more fibers. Even though the IFU size used for each galaxy is linked to its apparent size, the MaNGA survey has an uneven sampling of galaxy angular sizes to IFU size. The IFU size is chosen for each galaxy by optimizing 1.5R_e angular coverage of the target object in the primary sample and 2.5R_e in the secondary sample (Bundy et al. 2015), which means that the ratio ${D}_{\mathrm{IFU}}[\mathrm{arcsec}]/{R}_{{\rm{e}}}[\mathrm{arcsec}]$ ranges from 1.5 to 2.5 when combining the primary and secondary samples. To prevent the algorithm from considering the IFU size and resolution as relevant features, the resize transformation randomly enlarges or reduces the image size to up to 25% of the side size of the original frame. Cubic interpolation is used.
• 5.  
  Gaussian blur. A 2D Gaussian kernel of 3 × 3 pixels² and σ [pixels] from ${ \mathcal U }[0.1,2)$ is convolved with each layer of the data input. This encourages the model to become invariant to different resolutions and sharp artificial features in the data maps.

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While the noise perturbation, resize, and Gaussian blur transformations have a 50% probability of being applied to the raw data input copy, random flip and rotation is always applied for a better performance. The model variation augmentation is applied with a lower probability, since the Voronoi tessellation of the stellar maps could affect the performance of the kernels of the CNN. Therefore, this augmentation randomly replaces 25% of the copies.

In order to easily visualize the representation space, we perform a dimensionality reduction of the representations of dimension 1024 to a 2D space using Uniform Manifold Approximation and Projection (UMAP; McInnes et al. 2018) and color-code using different physical and instrumental properties. This is shown in Figure 2. We emphasize that the UMAP representation is only used here for visualization purposes. The actual dimensionality of the representation space is higher than these two dimensions. Our goal is to understand how galaxies are organized in the representation space and, more precisely, whether nonphysical dependencies have been properly removed. We therefore include, on the one hand, the parameters related to instrumental effects (two left panels in Figure 2), which are (top to bottom) the number of fibers in the IFU, galaxy angular size (${R}_{{\rm{e}}}[\mathrm{arcsec}]$), number of zero pixels, PA and RA of the galaxy, angular coverage (${D}_{\mathrm{IFU}}[\mathrm{arcsec}]/{R}_{{\rm{e}}}[\mathrm{arcsec}]$), and redshift z, to account for physical resolution. On the other hand, we include a set of integrated physical properties derived from the input maps (two right panels), namely (top to bottom), the effective radius (R_e [kpc]), specific angular momentum within 1.5R_e (${\lambda }_{{R}_{{\rm{e}}}}$), radial velocity dispersion at the center of the frame (σ_cen), luminosity-weighted age at R_e, and luminosity-weighted metallicity at R_e normalized by the solar metallicity (${[{\rm{Z}}/{\rm{H}}]}_{{R}_{{\rm{e}}}}$). We also include the slopes of the gradients within 0.5–2R_e of the last two parameters (${\rm{\nabla }}{\mathrm{age}}_{{R}_{{\rm{e}}}}$ and ${\rm{\nabla }}{[{\rm{Z}}/{\rm{H}}]}_{{R}_{{\rm{e}}}}$).

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To better quantify the efficiency of the removal of instrumental dependencies, we contrast representations obtained by a PCA with those obtained with the SimCLR algorithm. For the first set, the five MaNGA maps are decomposed to 1024 principal components to match the SimCLR representation dimensions. In all panels, the distribution of the 2D projection of the PCA feature decomposition, is displayed on the left (labeled with "a" in the top right corner), while the representations learned by contrastive learning, are on the right (labeled with "b" in the top right corner). These projections are simply obtained by applying the UMAP to the features obtained with PCA on the one hand and SimCLR on the other.

The principal components directly projected via UMAP are primarily organized based on instrumental and observational parameters (Figure 2). The main features that drive the organization of the PCA space are indeed the number of zero pixels, the number of fibers on the IFU, and the angular sizes of the galaxies (panels (a1)–(a3)). Although some slight dependencies on these parameters are recognizable in the SimCLR representation space, they are remarkably reduced (panels (b1)–(b3)). More precisely, we find that the principal components are locally organized according to the orientation parameters (PA and RA) in panels (a4) and (a5), while the representations learned through the contrastive algorithm remove these orientation dependencies efficiently (panels (b4) and (b5)). We notice, however, that the angular coverage dependencies were not completely removed (panel (b6)); an overdensity of the MaNGA secondary sample is visible in the representation space. Panel (b7) also shows a dependence of the representations with redshift; this could be due to the fact that the MaNGA survey has an overpopulation of massive galaxies toward higher z (Wake et al. 2017). When not considering a volume-limited sample, using z to quantify nonphysical dependencies could lead to the conclusion that representations depend on spatial resolution, whereas the features learned actually reflect physical properties. Therefore, even if redshift indicates a physical resolution dependency, it is not a reliable indicator for this particular data set.

The rightmost column of Figure 2 shows that the SimCLR representation space smoothly transitions as a function of physical properties: age, metallicity, and central velocity dispersion (panels (b11), (b12), and (b10)). Furthermore, parameters that are less trivial to obtain from the maps, such as ${\lambda }_{{R}_{{\rm{e}}}}$ (b9) and ${\rm{\nabla }}{\mathrm{age}}_{{R}_{{\rm{e}}}}$ (b13), are also learned by the model and show smooth transitions in the SimCLR representations. In general, the distribution of the principal components also shows a clear dependence on these parameters, but in this space, galaxies that share the same properties tend to appear in separate areas of the diagram due to instrumental biases.

These results confirm that the SimCLR representations efficiently remove the complex instrumental and observational biases present in the MaNGA survey data and primarily organize galaxies based on physical parameters.

Based on the encouraging results of the previous subsection, we further investigate how the sample of galaxies is clustered in the representation space by dividing the sample into groups using the K-means clustering algorithm (MacQueen 1967; Pedregosa et al. 2011) on the 1024 dimensions of the representation space. The K-means is a standard iterative algorithm to cluster unlabeled data by minimizing the sum of the squared euclidean distances of the data points within each cluster to their average position, or centroid. The number of clusters provided by the user will determine the number of centroids that will be initialized. We assume the same distance metric in the representation space as the one used to calculate the contrastive loss in the head projection space and, therefore, normalize the representations with L² norm such that the euclidean and cosine (as [1 − 〈 a , b 〉], where a , b are two array-like representations) distances between representations are equivalent.

The resulting clusters represent a first-order division of representation space and will allow further understanding of the underlying astrophysical properties that drive the space distribution by studying the galaxy groups. Since our representation space is continuous in nature, this exercise will not lead to a sharply defined, discrete classification. Nevertheless, we define a criterion to obtain a repeatable and physically driven classification, allowing further study of the galaxy groups thus identified. To define the number of clusters, we require the division to be robust; i.e., it should be independent from the training run and initialization parameters. Additionally, the clusters must be independent of features that are not physically relevant.

To ensure a robust division, we train the SimCLR framework 10 independent times such that the input maps are perturbed differently in each run. By construction, the features obtained in each run are not exactly the same, since the training has some inherent stochastic behavior. Nevertheless, our assumption is that the representation spaces must encode the same information irrespective of the initialization, such that neighboring galaxies in one run should remain neighbors in the other resulting spaces. We set the first run as the reference run and maximize the matching clusters of the remaining runs with the linear assignment algorithm implemented in SciPy (Crouse 2016; Virtanen et al. 2020). As the clusters of each run will not necessarily be identified under the same labels by the clustering algorithm, the linear assignment algorithm provides a new set of cluster labels such that the number of galaxies that fall in the same groups as the reference run is maximized. An agreement score is defined as the fraction of objects that are consistently placed in the same group in at least 90% of the runs. Although this score might appear too restrictive when a large number of clusters is considered, it shows how reproducible the resulting groups are. We consider the divisions to have good agreement when the agreement score is over 85%.

Finally, to account for undesired dependencies, e.g., on instrumental parameters, we compute the linear contribution of the nonphysical parameters to the classifications found. We perform a linear regression fit of the parameters to a binary classification for each cluster. One class contains galaxies that belong to the given cluster, while the other class is a random selection of nonmember galaxies. The fit is presented with the same number of examples of both classes, while a spare 20% of the sample is used to obtain the validation accuracy. The resulting coefficient associated with each parameter is then normalized to indicate its contribution percentage to the classification. We reject clusters when the accuracy of this fit is higher than 65%, in which case, we assume that the cluster is the result of instrumental and/or nonphysical effects.

For comparison purposes, we also perform a K-means clustering on a representation space derived through PCA on the five MaNGA maps. We note that the metrics chosen are compatible with the SimCLR framework, while this might not be the case for PCA. Therefore, a more favorable additional test is performed for the PCA decomposition. In this case, only the first 10 PCA parameters are selected, and each parameter is scaled to have a zero mean and a standard deviation of 1.

The agreement score and the most accurate fit to the parameters that are not physically relevant are shown in Table 1 for 14 divisions of the SimCLR representations and four divisions of the 1024 and 10 most relevant PCA features. For comparison, the relevance of the physical and nonphysical parameters in each cluster—computed through linear regression—are also listed in the last two columns.

Table 1. Cluster Division Performance

SimCLR
N Clusters	% Agree	${\mathrm{Acc}}_{\max }$Nonphys	AccmeanPhys
2	89.419 ± 0.006	64 ± 2	93.1 ± 0.5
3	93.63 ± 0.03	60.5 ± 0.5	89.3 ± 0.5
4	62.5 ± 0.1	63 ± 2	86.4 ± 0.3
5	84.43 ± 0.08	68 ± 1	85.5 ± 0.6
6	85.04 ± 0.09	68 ± 1	84.1 ± 0.5
7	60 ± 1	70 ± 1	83.1 ± 0.5
8	58 ± 5	72 ± 1	82.4 ± 0.3
9	56 ± 2	72.9 ± 0.7	82.6 ± 0.5
10	58 ± 2	71 ± 1	81.9 ± 0.5
11	65 ± 3	71 ± 2	81.5 ± 0.9
12	47 ± 2	71 ± 2	80.9 ± 0.7
13	50 ± 3	72 ± 3	80.1 ± 0.7
14	51 ± 5	73 ± 3	79.1 ± 0.8
15	64 ± 8	75 ± 4	78.7 ± 0.9
PCA 1024
N clusters		${\mathrm{Acc}}_{\max }$Nonphys	AccmeanPhys
2		92.13 ± 0.09	72.28 ± 0.07
3		94.9 ± 0.8	71.3 ± 0.2
4		92.7 ± 0.7	64.7 ± 0.2
5		91.9 ± 0.3	69.5 ± 0.5
PCA 10
N clusters		${\mathrm{Acc}}_{\max }$Nonphys	AccmeanPhys
2		95 ± 3	72 ± 2
3		93 ± 2	67.4 ± 0.6
4		92 ± 1	68 ± 1
5		94.1 ± 0.5	64.2 ± 0.5

Note. For each division into N clusters, an agreement score is calculated from 10 different runs of the contrastive algorithm. The third column indicates the most accurate fit to the nonphysical parameters among the N clusters, while the fourth column shows the average accuracy of the fit to the integrated astrophysical parameters. The uncertainty for the agreement score is estimated as the standard deviation due to K-means initialization with 10 different seeds, while accuracy uncertainties were estimated as the standard deviation corresponding to five SimCLR independent runs with five different seeds each in the clustering step. The values that are within the agreement score or accuracy required are incated in bold.

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In all cases, the SimCLR representations yield group divisions that are more dependent on physical features than on those that are not physically relevant, thus confirming the qualitative results of the previous section. In contrast, the divisions derived from the PCA are highly dependent on nonphysical features (>90% correlation). In particular, the number of fibers in the IFU and the number of zeros in the maps show the strongest correlation with the group divisions in the PCA features.

The maximum number of clusters that fulfills our agreement and nonphysical accuracy requirements is three. This number also corresponds with the natural divisions of the UMAP maps of Figure 2, which clearly show a large cluster in the bottom left corner and a strong age trend in the right blob.

In the following, we only consider these three clusters and analyze their physical properties. Table 2 shows the correlation of the clusters with several integrated physical parameters. The strongest correlations are with velocity dispersion, age, physical size, and ${\lambda }_{{R}_{{\rm{e}}}}$. For better visualization, we show in Figure 3 four well-studied planes for galaxies: $\mathrm{log}\,{M}_{* }\mbox{--}\mathrm{log}\,\mathrm{SFR}$, –λ_R , $\mathrm{log}\,{M}_{* }\mbox{--}[{\rm{Z}}/{\rm{H}}]$, and $\mathrm{log}\,\sigma \mbox{--}\mathrm{log}\,\mathrm{age}$.

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Table 2. Cluster Dependence with Integrated Parameters

Cluster	$\mathrm{log}(\sigma )$	LW ${\mathrm{Age}}_{{R}_{{\rm{e}}}}$	$\mathrm{log}({R}_{{\rm{e}}}[\mathrm{kpc}])$	${\lambda }_{{R}_{{\rm{e}}}}$	log(${\mathrm{SFR}}_{{{\rm{H}}}_{\alpha }}$)	LW ${\mathrm{ZH}}_{{R}_{{\rm{e}}}}$	∇LW ${\mathrm{ZH}}_{{R}_{{\rm{e}}}}$	∇LW ${\mathrm{Age}}_{{R}_{{\rm{e}}}}$
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)
1	13.4% ± 3.7%	35.2% ± 1.6%	14.6% ± 1.4%	17.9% ± 1.9%	6.8% ± 0.6%	4.5% ± 0.8%	6.4% ± 0.3%	1.1% ± 0.3%
2	3.7% ± 2.2%	61.5% ± 3.1%	8.9% ± 0.4%	4.5% ± 1.1%	10.9% ± 1.2%	7.4% ± 1.4%	1.9% ± 0.8%	0.9% ± 0.5%
3	43.6% ± 1.6%	14.2% ± 1.6%	11.2% ± 1.2%	16.7% ± 1.5%	1.3% ± 0.5%	4.9% ± 0.7%	3.9% ± 0.4%	4.0% ± 0.3%

Note. Dependence with integrated parameters of the three groups found with the K-means clustering in the SimCLR representation space.

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We clearly observe that the three different clusters identified in a purely unsupervised way populate different regions in the different planes. While star-forming disks (with $\langle \mathrm{log}\,\mathrm{age}\ [\mathrm{yr}]\rangle =9.9$ and 〈〉 = 0.36) with low metallicity (〈Z/H〉 = − 0.25) group in cluster 2, quenched fast-rotating galaxies with low-to-intermediate masses ($\mathrm{log}\,{M}_{* }/{M}_{\odot }\lesssim 10.9$) can be found in cluster 1. Lastly, cluster 3 includes the massive ($\mathrm{log}\,{M}_{* }/{M}_{\odot }\gtrsim 10.4$) slow-rotating galaxies. We emphasize that the star formation rate is not included in the maps used for the representation. Nevertheless, most of the main-sequence galaxies are associated with one unique cluster, which naturally suggests that star-forming galaxies share similar kinematic and stellar population properties over several decades of stellar mass. We will discuss this further in Section 6. For comparison, the bottom row of Figure 3 shows the same four physical planes obtained through clustering on the PCA space. Interestingly, we see that there is very little dependence on physical properties, which again highlights the effectiveness in extracting physical information of the SimCLR representations when compared to those of the PCA.

Additionally, we analyze the morphological features of the galaxies in each cluster using the MaNGA deep-learning DR-17 morphological catalog (MDLM-VAC; private communication, H. Domínguez Sánchez et al. 2021, in preparation). This catalog is an extension of the deep-learning DR-15 catalog presented in Fischer et al. (2019), and it was obtained with deep-learning models trained on SDSS-DR7 images (see Domínguez Sánchez et al. 2018 for more details on the methodology and model performance). Figure 4 shows how the galaxies distribute in each cluster according to the morphological parameter T type.

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We find that galaxies that have been classified as early types (T type < 0) belong predominantly to the cluster containing high-mass slow-rotating galaxies, while a smaller fraction belongs to the intermediate-mass quenched galaxy cluster. Galaxies with T types > 0 distribute in the clusters that include less massive galaxies, with the latest T types belonging to the star-forming cluster.

As in Section 4.1, the SimCLR representations obtained after training the model are projected to a 2D space with UMAP (McInnes et al. 2018) to visualize how the representation space correlates with known physical parameters. For comparison, the projections of both sets of normalized maps are presented together in Figure 5.

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While the relative norm representations show smoother transitions for central velocity dispersion, projected angular momentum, age, and metallicity (panels (R2)–(R5)), the correlation between these parameters and the individual norm representation space is not negligible. Furthermore, panels (I3)–(I5) show that young and metal-poor galaxies with low velocity dispersion tend to populate the left side of the maps, while old metal-rich galaxies with higher velocity dispersion primarily locate on the right-hand side.

As the representation space distribution changes when applying different norms to the input data, we analyze the dominant drivers of the new space by performing an unsupervised clustering.

In this representation space, we find that only a division into two clusters fulfills the agreement requirement defined in Section 4.2 with an agreement score of 90.89 ± 0.03, while more partitions yield scores of <78%. The nonphysical parameter fits have comparable accuracy to the ones obtained with the relative norm. Specifically for the two-cluster division, this value is 67.6 ± 1.3, which is only slightly larger than the 65% threshold imposed in the previous section. To avoid confusion with the clusters of the previous section, we refer to the new groups as clusters A and B.

The distribution of the two clusters in the physical planes $\mathrm{log}\,{M}_{* }\mbox{--}\mathrm{log}\,\mathrm{SFR}$, –λ_R , $\mathrm{log}\,{M}_{* }\mbox{--}[{\rm{Z}}/{\rm{H}}]$, and $\mathrm{log}\,\sigma \mbox{--}\mathrm{log}\,\mathrm{age}$ is shown in the bottom row of Figure 3. While cluster A is constrained in the planes toward higher-mass, older, and more metal-rich regions (with average values $\langle \mathrm{log}\,{M}_{* }/{M}_{\odot }\rangle =10.6$, $\langle \mathrm{log}\,\mathrm{age}[\mathrm{yr}]\rangle =9.5$, and 〈Z/H〉 = −0.11), cluster B spreads across all of the planes with a lower concentration in the overlapping regions (with average values $\langle \mathrm{log}\,{M}_{* }/{M}_{\odot }\rangle =10$, $\langle \mathrm{log}\,\mathrm{age}[\mathrm{yr}]\rangle =9$, and 〈Z/H〉 = − 0.23). The low-mass and star-forming galaxies are contained primarily in the last cluster. Although there is overlap between the two groups, a physical difference is captured and clearly visible in age, mass, and metallicity. This is interesting because the information about the absolute values has been removed; however, we still see that the main clusters found correlate with integrated properties such as stellar mass and velocity dispersion.

To further visualize the typical spatial features found in each group, we select the five galaxies whose representations are closer to the centroid of each cluster. The example galaxies of each cluster are shown in Figure 6. While the example galaxies from cluster A show an early-type morphology and negative gradients in velocity dispersion and metallicity maps, galaxies in cluster B tend to have gradients that are inverted compared to those in cluster A, and their V-band reconstructed images show structure and disk features compatible with later-type morphology.

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As this division roughly separates early-type galaxies from late types, the morphological features encoded in the V-band reconstructed images could be driving the clustering. Therefore, in Appendix A, we evaluate the influence of the kinematic and composition maps in the division. When the V-band reconstructed images are excluded from the input maps, we find that the division can be recovered with good agreement (88.621% ± 0.007% overlap with the previous clusters), indicating that the information of the four remaining maps is enough to find the two groups.

A key property of contrastive learning–based dimensionality reduction, in contrast with other techniques, is that representations are encouraged to become invariant to a set of transformations. We have shown that this feature has a lot of potential when the data set is nonhomogeneous and affected by known biases, since these can be tackled with convenient transformations in the contrastive framework.

We confirm that the representations obtained in this work efficiently reduce their impact and focus on physical properties, even though MaNGA maps include important instrumental effects. This allows one to explore the physical correlations existing in the high-dimensional space.

Therefore, the presented framework might constitute an important tool to explore and discover patterns in future data sets. We have illustrated in this work how the representations organize based on five kinematics and stellar population maps. However, the method has no limit on the number of channels in the input data; thus, it is possible to extend the analysis to a larger number of maps, including, for example, gas properties or even complete IFU data cubes without postprocessing.

Additionally, because transformations included in the training procedure can be tuned, one could eventually combine data sets of different origins and selection effects. A natural extension of this work is thus the combination of IFU data from different surveys (i.e., MUSE, Henault et al. 2003; CALIFA, Sánchez et al. 2012; MaNGA, Bundy et al. 2015; SAMI, Croom et al. 2012) represented in a unique low-dimension space. Combining observations and predictions from recent hydrodynamic cosmological simulations is also a promising avenue to identify possible discrepancies between the physical properties of observed and simulated galaxies.

In addition to visualization, the representations learned can be used in a variety of downstream tasks. Abul Hayat et al. (2021) and Chen et al. (2020b) found that this framework can obtain the same levels of accuracy for classification as a supervised approach but reduce the number of training labels. We present in this work one application that makes use of the representation space as a tool to explore the data set.

Since contrastive learning locates objects with similar physical properties in nearby regions of the representation space, it can be used to identify groups of objects with shared physical properties in a purely data-driven manner. In Sections 3 and 5, we illustrated this procedure with two different normalizations of the MaNGA maps: with and without information about the absolute values of the physical properties. This allows us to study the interplay between the integrated properties of galaxies and their resolved internal structure.

6.2.1. Absolute Physical Properties

6.2.2. Internal Structure

We have repeated the cluster analysis with a different normalization that removes information about the absolute values of the physical properties. This allows us to quantify the relation between the integrated and resolved internal structure of nearby galaxies. Although the previous clusters cannot be completely recovered with this new normalization, it is possible to find two clusters with good agreement that are separated primarily by the spatial features present in the maps. These clusters correlate with the mean and integrated physical values derived from the maps, suggesting that the internal structure of galaxies serves as a footprint that is tightly related to the observed integrated properties. It suggests that these two galaxy types are different not only because they differ in absolute values but also because their internal structure is different, pointing toward distinct assembly histories, as highlighted in previous works.

The first cluster found when only spatial features are considered contains intermediate- to high-mass quenched galaxies. These galaxies show, in general, early-type morphologies and present negative slopes in the velocity dispersion and metallicity maps (Figure 6). The second cluster primarily includes the star-forming main sequence of galaxies. Figure 6 shows that galaxies in this cluster tend to present flat metallicity and velocity dispersion distributions and more disky stellar structure.

The comparison between the clusters obtained with the different normalizations reveals interesting trends. Figure 7 shows that ∼80% and ∼70% of the galaxies that were in different clusters when including the information about the absolute values are also separated by internal structure. It confirms that the distinction between high and low velocity dispersion systems reveals different assembly histories and is not only a reflection of a stellar mass bimodality. Interestingly, the third cluster found in the relative normalization run is distributed among the two main ones, with ∼35% being closer to the star-forming rotating disks and ∼65% being more similar to the massive slow-rotating systems. It suggests that this intermediate-mass quenched population is formed through a mixture of smooth and more violent assembly processes, but there is no particular signature in the internal kinematics of the galaxies that clearly distinguishes them from the two other groups. A fraction of the objects also change cluster when the normalization is modified. We will study these systems in more detail in future work.

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