2.1 Virgo (NGC 4636 and NGC 4808 fields)

WALLABY’s Phase 2 pilot programme observed two close fields, each centred on one of two Virgo groups, NGC 4636 (Lin et al. Reference Lin2023) and NGC 4808 (Murugeshan et al. submitted). NGC 4636 is a relatively close group at a distance of 16.2 Mpc (Kourkchi & Tully Reference Kourkchi and Tully2017) and a radius of 0.61 Mpc, based on ROSAT X-ray measurements (Reiprich & Böhringer Reference Reiprich and Böhringer2002). Two galaxies, NGC 6156 (in the Norma Field) and NGC 4632 (in this field), were studied in detail in Deg et al. (Reference Deg2023) as they show a polar ring structure in H 1. Lin et al. (Reference Lin2023) presents a catalogue of galaxies around the N4636 group centre with redshift measurements from several H 1 and optical catalogues. Lin et al. (Reference Lin2023) note that of the 19 galaxies detected by WALLABY belonging to this group, six galaxies are resolved enough for detailed moment-0 map study. They present flags for different types of interaction based on the combined WALLABY-FAST data, which include objects in the NGC 4808 field. This is the basis for our training sample (see Section 5.1). The second WALLABY pilot field is centred around NGC 4808 group. The Tully–Fisher (T-F) distances in this field are presented in Courtois et al. (Reference Courtois2023). This group is similarly close, at approximately $\sim$ 16 Mpc.

2.2 NGC 5044 mosaic

The third field, a mosaic of four fields centred on the NGC 5044 group, has been studied across wavelengths before in the optical, x-ray, and H 1 observations (Ferguson & Sandage Reference Ferguson and Sandage1990; Ferguson & Sandage Reference Ferguson and Sandage1991; Tamura et al. Reference Tamura, Kaastra, Makishima and Takahashi2003; Buote et al. Reference Buote, Lewis, Brighenti and Mathews2003; Buote, Brighenti, & Mathews Reference Buote, Brighenti and Mathews2004; Osmond & Ponman Reference Osmond and Ponman2004; McKay et al. Reference McKay2004; Forbes et al. Reference Forbes2006).

The WALLABY internal release on this field (DR3) covers 120 deg $^2$ of the NGC 5044 four-tile mosaic across a 21 cm H 1 line red shift range of $cz \sim 500$ to 25 400 km/s ( $z \unicode{x003C} 0.085$ ), which uses the full RFI-free bandwidth available to WALLABY. NGC 5044 DR3 includes 1 326 detections. The resulting catalogue is richest of the three in source counts with a large number of sources well behind the nearby group around NGC 5044 (Fig. 1).

Figure 1.

Distribution of distance for galaxies in the three WALLABY fields, centred on NGC 4808, NGC 4646, and NGC 5044. The vertical dashed line is the 60 Mpc cutoff for selection for the training sample in NGC 4808 and the application samples.

Fig. 1 shows the distribution of H 1 detections in all three catalogues. A majority of sources in the three fields is not associated with the groups themselves. In the NGC 5044 field especially, several groups and clusters can be identified in the background. There are full samples of these fields for which we compute H 1 morphometrics and assign stellar mass and star formation rates.

4.1 Concentration-Asymmetry-Smoothness (CAS) morphometrics

CAS refers to the commonly used Concentration-Asymmetry-Smoothness space (Conselice Reference Conselice2003) for stellar morphological analysis of distant galaxies. Concentration of the light, symmetry around the centre and smoothness is an indication of substructure.

Concentration is defined by Bershady, Jangren, & Conselice (Reference Bershady, Jangren and Conselice2000) as:

(1) \begin{equation}C = 5 \, \log (r_{80} / r_{20})\end{equation}

with $r_{f}$ as the radius containing percentage f of the light of the galaxy (see definitions of $r_f$ in Bertin & Arnouts Reference Bertin and Arnouts1996; Holwerda Reference Holwerda2005). In the optical regime (i.e. stellar component), typical values for the concentration index are $C=2-3$ for discs, $C\unicode{x003E}3.5$ for massive ellipticals, while peculiars span the entire range (Conselice Reference Conselice2003).

The asymmetry is defined as the level of point-, (or rotational-) symmetry around the centre of the galaxy (Abraham et al. Reference Abraham, Valdes, Yee and van den Bergh1994; Conselice Reference Conselice2003):

(2) \begin{equation}A = {\Sigma_{i,j} | I(i,j) - I_{180}(i,j) | \over \Sigma_{i,j} | I(i,j) | } - A_{bgr},\end{equation}

where I(i,j) is the value of the pixel at the position [i,j] in the image, and $I_{180}(i,j)$ is the pixel at position [i,j] in the galaxy’s image, after it was rotated $180^\circ$ around the centre of the galaxy. $A_{bgr}$ is an estimate of the contribution of the background to this value. This is the definition, without the background contribution, used in Holwerda et al. (Reference Holwerda, Pirzkal and Heiner2012) for H 1 as line emission does not have a clear background contribution to asymmetry. Because we use the postage stamps extracted by SoFiA for the calculation, we use the definition of asymmetry without the background computation.

In the statmorph implementation, the asymmetry is calculated in the inner 1.5 PetrosianFootnote ^b radii (typical size of the stellar disc), the background asymmetry is subtracted, and A is minimised by moving the centre of rotation. Note that the maximum value for the asymmetry is 2 (all pixels off-centre) and can be negative if the background asymmetry value is large. We note that we do not subtract a background when using the moment-0 H 1 maps as these are extracted from the field using a 3D source mask. A background subtraction makes more sense with continuum emission where a substantial contribution to morphometrics can be expected (i.e. optical or ultraviolet emission) as opposed to line emission maps as is the case here. Moreover, the subtraction has already happened in the radio continuum subtraction that was applied to the data-cube prior to H 1 line extraction. In our case, background subtraction is a separate step in the data reduction process. To obtain a background asymmetry contribution, one would have to combine continuum subtraction, source extraction, and asymmetry computation. Reynolds et al. (Reference Reynolds, Westmeier, Staveley-Smith, Chauhan and Lagos2020) compute this background component using an empty Section of the H 1 cube with the same shape as the mask. This was more useful for their comparison between different H 1 surveys. Here, the background contribution would be dominated by the H 1 mask shape but statmorph expects to compute it based on a sky background just outside the aperture.

Asymmetry in H 1 maps or profiles has shown a lot of promise in recent studies to identify perturbed or disrupted disc galaxies (e.g. Reynolds et al. Reference Reynolds, Westmeier, Staveley-Smith, Chauhan and Lagos2020; Glowacki et al. Reference Glowacki2022; Watts et al. Reference Watts2023; Holwerda et al. Reference Holwerda2023).

Inspired by the ‘unsharp masking’ technique (Malin Reference Malin1978), Smoothness is defined by Takamiya (Reference Takamiya1999) and Conselice (Reference Conselice2003) as:

(3) \begin{equation}S = {\Sigma_{i,j} | I(i,j) - I_{S}(i,j) | \over \Sigma_{i,j} | I(i,j) | }\end{equation}

where $I_{S}(i,j)$ is the same pixel in a smoothed image. What type of smoothing is used has changed over the years. Often a fixed Gaussian smoothing kernel is chosen for simplicity.

The fact that this Smoothness has another input parameter in the form of the size of the smoothing kernel, makes it highly ‘tunable’, meaning one gets out exactly what the parameter was optimised for. It is very difficult to reliably compare between catalogues and especially samples over different distances. The kernel employed here is a Gaussian with a width of 2.5 pixels in the moment0 map. This is less than the beam size of the instrument in question. Thanks to the lower dynamical range in H 1 maps, one does not expect the high-contrast areas such as HII regions in star-forming galaxies. The smoothing kernel choice is therefore a conservative choice (low amount of smoothing) for the Smoothness parameter. The Smoothness parameter is expected to be less useful in H 1 than in optical or ultraviolet imaging.

4.2 Gini and $M_{20}$

Abraham, van den Bergh, & Nair (Reference Abraham, van den Bergh and Nair2003) and Lotz et al. (Reference Lotz, Primack and Madau2004) introduce the Gini parameter to quantify the distribution of flux over the pixels in an image. They use the following definition:

(4) \begin{equation}G = {1\over \bar{I} n (n-1)} \Sigma_i (2i - n - 1) I_i, \end{equation}

$I_i$ is the value of pixel i in an ordered list of the pixels, n is the number of pixels in the image, and $\bar{I}$ is the mean pixel value in the image.

The Gini parameter is an indication of equality in a distribution (initially an economic indicator Gini Reference Gini1912; Yitzhaki Reference Yitzhaki1991), with $G=0$ the perfect equality (all pixels have the same fraction of the flux) and $G=1$ perfect inequality (all the intensity is in a single pixel). Its behaviour is therefore in between that of a structural measure and concentration. Gini appears quite sturdy as it does not require the centre of the object to be computed. It remains relatively unchanged, even when the object is lensed (Florian, Li, & Gladders Reference Florian, Li and Gladders2016), and it is popular for this reason. However, it depends strongly on the image’s signal-to-noise (Lisker Reference Lisker2008); noise forces the inclusion of a lot of low-signal pixels, throwing off the entire distribution. This issue is not noisy data but how it typically affects image segmentation. In essence, noise can add pixels with no fraction of the flux in them, artificially increasing the Gini value. However, with a less concentrated radial profile and choices of segmentation already made by SoFiA, Gini is a good fit for H 1 maps.

Lotz et al. (Reference Lotz, Primack and Madau2004) also introduced a way to parameterise the extent of the light in a galaxy image. They define the spatial second order moment as the product of the intensity with the square of the projected distance to the centre of the galaxy. This gives more weight to emission further out in the disc. It is sensitive to substructures such as spiral arms and star-forming regions but insensitive to whether these are distributed symmetrically or not. The second order moment of a pixel i is defined as:

(5) \begin{equation}M_i = I_i \times [(x-x_c)^2 + (y-y_c)^2 ],\end{equation}

where [x, y] is the position of a pixel with intensity value $I_i$ in the image and $[x_c, y_c]$ is the central pixel position of the galaxy in the image.

The total second order moment of the image is given by:

(6) \begin{equation}M_{tot} = \Sigma_i M_i = \Sigma I_i [(x_i - x_c)^2 + (y_i - y_c)^2].\end{equation}

Lotz et al. (Reference Lotz, Primack and Madau2004) use the relative contribution of the brightest 20% of the pixels to the second order moment as a measure of disturbance of a galaxy after sorting the list of pixels by intensity ( $I_i$ ):

(7) \begin{equation}M_{20} = \log \left( {\Sigma_i M_i \over M_{tot}}\right),\ {\rm for}\ \Sigma_i I_i \unicode{x003C} 0.2 I_{tot}. \\\end{equation}

The $M_{20}$ parameter is sensitive to bright regions in the outskirts of discs and higher values can be expected in galaxy images (in the optical and UV) with star-forming outer regions as well as those images of strongly interacting discs. Due to a lack of high contrast clumps at higher radii, the $M_{20}$ parameter is not expected to show as much of a range in H 1 compared to star formation dominated wavelengths where it was first employed.

4.3 Multimode–Intensity–Deviation (MID) morphometrics

The MID morphometrics (Freeman et al. Reference Freeman2013; Peth et al. Reference Peth2016) were introduced as an alternative to the Gini–M20 and CAS morphometrics to be more sensitive to recent mergers. However, these new morphometrics have not been tested as extensively as the Gini–M20 and CAS statistics, especially using hydrodynamic simulations (Lotz et al. Reference Lotz, Jonsson, Cox and Primack2008; Lotz et al. Reference Lotz, Jonsson, Cox and Primack2010; Lotz et al. Reference Lotz2011; Bignone et al. Reference Bignone2017), see also the discussion in the implementation in statmorph (Rodriguez-Gomez et al. Reference Rodriguez-Gomez2019). In the case of H 1 data for the Hydra cluster, these parameters did not contribute new information (Holwerda et al. Reference Holwerda2023).

The multimode statistic (M) measures the ratio between the areas of the two most ‘prominent’ clumps within a galaxy. The implicit assumption is that the galaxy is well resolved and has at least two well-defined clumps. Its calculation mostly consists in finding such substructures. First, all pixels within the MID segmentation map are sorted by brightness. Then, for a given quintile q (between 0 and 1), the set of all pixels with flux values above the qth quintile will generally consist of n groups of contiguous pixels, which are sorted by area (largest first). Finally, M is defined as the quintile q that maximises the area ratio between the two largest groups (Peth et al. Reference Peth2016):

(8) \begin{equation} M = \max\left({A_{q,2} \over A_{q,1}}\right)\end{equation}

where $A_{q,1}$ is the largest quintile and $A_{q,2}$ is the second-to-largest quintile area.

The intensity statistic (I) measures the ratio between the two brightest subregions of a galaxy. To calculate it, the galaxy image is first slightly smoothed using a Gaussian kernel with $\sigma = 1$ pixel. Then, the image is partitioned into pixel groups according to the watershed algorithm: each distinct subregion consists of all the pixels such that their maximum gradient paths lead to the same local maximum. Once the pixel groups are defined, their summed intensities are sorted into descending order: I1, I2, etc. The intensity statistic is then defined as Freeman et al. (Reference Freeman2013):

(9) \begin{equation} I = {I_2 \over I_1}\end{equation}

The same issue that can be raised for M can be raised here. There is a built-in assumption of resolved structure, and that this structure has not fractured the segmentation map into separate catalogue entries.

The deviation statistic (D) measures the distance between the image centroid, ( $x_c,y_c$ ), calculated for the pixels identified by the MID segmentation map, and the brightest peak found during the computation of the I statistic, ( $x_I$ , $y_I$ ). This distance is normalised by $\sqrt{n_{seg}/\pi}$ , where $n_{seg}$ is the number of pixels in the segmentation map, which represents an approximate galaxy ‘radius’ Freeman et al. (Reference Freeman2013):

(10) \begin{equation} D = \sqrt{\pi \over n_{seg}} \sqrt{ (x_c - x_I)^2 + (y_c - y_I)^2}\end{equation}

This is a metric that can be calculated from Source Extractor (Bertin & Arnouts Reference Bertin and Arnouts1996; Holwerda Reference Holwerda2005) output by using the image centroid and the peak location, albeit again that this makes assumptions on the number of substructures in the galaxy image.

Figure 2.

A corner plot of the H 1 morphometrics of galaxies in the NGC 4636 pointing based on the SoFiA segmentation maps.

4.4 Patchiness

A recent addition to the morphometric parameter space is a ‘patchiness’ parameter (Fetherolf et al. Reference Fetherolf2023) defines as:

(11) \begin{equation}P = -\log_{10} \left\{ \Pi^N_i {1 \over \sqrt{2\pi\sigma_i}} \exp \left[ - {(X_i-\bar{X_w})^2 \over 2\sigma_i^2} \right] \right\}\end{equation}

where $N_i$ is the number of pixels, $X_i$ is the value of pixel i. The Gaussian probability that all the pixels equal the weighted average is lower when the image is ‘patchier’. Here, $X_w$ is the weighted (or not) average of the distribution of pixels that make up the object and $\sigma_i$ is the pixel uncertainty. The benefits are that this measure is sensitive to deviations above and below the average. It is also notable that this parameter, like the Gini parameter, does not depend on the central position, unlike $M_{20}$ or Asymmetry, which relies on a bright subset of pixels and the object’s central position. Fetherolf et al. (Reference Fetherolf2023) use their parameter for Voronoi tesselations of their objects and not individual pixels. However, we implement a pixel-based definition here. The implementation in Fetherolf et al. (Reference Fetherolf2023) focused on their reddening maps, that is, the dust distribution. Therefore, this seemed a likely H 1 morphometric. Upon implementation however, it became clear that the values computed from SoFiA maps are often infinite. For completeness, we include the values in our final catalogue, but not use it in the kNN training below.

4.5 Sérsic profile

The final step by STATMORPH is to fit a single Sérsic profile with the effective radius ( $r_{50}$ ) and index (n) to the pixel collection constituting each object. This is not the optimal description of the H 1 disc which is usually described with a $R_{1 M_\odot}$ , the radius where the profile reaches 1 M $_\odot$ /pc $^2$ in H 1 mass. However, this alternate morphometric, very commonly used in optical studies, is available for use here, and we include the Sérsic index for consideration.

4.6 STATMORPH

Calculating catalogues for these WALLABY data is straightforward for the cutouts provided by the WALLABY data-release. One can run through all the entries made by the SoFiA source detection and run statmorph (Rodriguez-Gomez et al. Reference Rodriguez-Gomez2019). These catalogues are our starting point for the machine learning approach described in the following sections.

Part of the parameter space of H 1 morphometrics are presented in Figs. 2 through 4, colour-coded by the inferred H 1 mass from the SoFiA catalogue. The H 1 masses are derived after application of the H 1 flux correction as described in Westmeier et al. (Reference Westmeier2022). This flux correction is a critical step to match the H 1 size-mass relation. Concentration, Asymmetry, Gini and $M_{20}$ are the most commonly used parameters.

Figure 3.

A corner plot of the H 1 morphometrics of galaxies in the NGC 4808 pointing based on the SoFiA segmentation maps.

Figure 4.

A corner plot of the H 1 morphometrics of galaxies in the NGC 5044 pointing based on the SoFiA segmentation maps.

These are full morphometric catalogues for each field, that is, all galaxies at all redshifts. This approach gives us a sense of the range of values expected. For the subsequent analysis, we apply a cut of $D \unicode{x003C} 60$ Mpc to select galaxies at mostly similar distances (similar to the samples in Reynolds et al. Reference Reynolds, Westmeier, Staveley-Smith, Chauhan and Lagos2020; Holwerda et al. Reference Holwerda2011d). This distance cutoff ensures the larger features in the H 1 discs are included in the morphometric calculation; WALLABY’s spatial resolution of 30” $\simeq 10$ kpc at this distance. We intentionally do not select known group members because eventually we hope to apply this technique on WALLABY blindly, without prior knowledge of group membership.

Because we do not have full intuition which morphometrics are the optimal feature space to train a machine learning algorithm on –even after the initial work in Holwerda et al. (Reference Holwerda2023) – we start with the full morphometric space provided by statmorph. We do know that Smoothness and Intensity are likely too dependent on the smoothing kernel to be of use in this lower spatial resolution data (see Section 4). This in a way is limiting since there could be other morphometrics much better suited for the identification of perturbed H 1 discs. It could be possible to define entirely new ones, perhaps including kinematic information as well (cf Deg et al. Reference Deg2023). For now, we adopt the morphometric space provided by statmorph with our addition of Patchiness.

Figs. 2 through 4 show corner plots of the most commonly used morphometrics (modelled after the corner plot in Scarlata et al. Reference Scarlata2007). There are some correlations between Concentration and Gini or Concentration and $M_{20}$ evident, something noted by Conselice (Reference Conselice, Knapen, Mahoney and Vazdekis2008) and Lotz et al. (Reference Lotz, Jonsson, Cox and Primack2008). This morphometric space is not an orthogonal one, especially not with lower resolution data. An orthogonal space would be the easiest to train a machine learning algorithm on and engineer the feature space. Thanks to a large body of work applying these morphometrics to data from ultraviolet through radio wavelengths, the morphometric space is a familiar one to astronomy.

5.1 Training sample

To construct a training sample, we require WALLABY H 1 morphometrics and a label. For the labelling, we use the sample from Lin et al. (Reference Lin2023) who classified galaxies in this field using FAST and WALLABY information. We crosscorrelated the catalogue of Lin et al. (Reference Lin2023) with both the NGC 4636 and NGC 4808 fields using an arcsecond. We found an overlap with the 63 sources from Lin et al. (Reference Lin2023) with the WALLABY catalogues of 21 and 15 sources in the NGC 4636 and NGC 4808 fields, respectively. We impose our distance limit of 60 Mpc, arriving at a training sample with Lin et al. (Reference Lin2023) labels of 29 sources and 57 WALLABY sources without a label but within that distance and the area of the catalogue (the green circle in Fig. 5). These unlabelled WALLABY sources are considered to be ‘non-perturbed’. Combined, these form our training sample.

Figure 5.

The WALLABY detections for both the NGC 4808 and NGC 4636 fields within (60 Mpc) in grey. Superimposed is the catalogue from Lin et al. (Reference Lin2023) with the perturbed (red circles) and unperturbed (white circles). Not every source in Lin et al. (Reference Lin2023) has a counterpart in the two WALLABY catalogues but a sufficient number is available for training. Because the Lin et al. (Reference Lin2023) catalogue is based on different data, we select all the sources within the green circle to be used as the WALLABY training sample with those without a Lin et al. (Reference Lin2023) classification deemed ‘unperturbed’.

The final training sample is 29 WALLABY sources with some sort of perturbance and 57 WALLABY sources without the perturbed label. This is a reasonably size and balanced training/test sample which can be complemented using smote Footnote ^c (Synthetic Minority Oversampling Technique, Kegelmeyer Reference Kegelmeyer2002) to fully balance the training sample. The galaxies outside the green circle in Fig. 5 as well as all the objects in the NGC 5044 catalogue are our ‘deployment’ sample: the sources the trained algorithm will be deployed on for independent classification.

Fig. 6 shows the H 1 morphometric feature space with the label from Lin et al. (Reference Lin2023) for the galaxies that are undergoing ram-pressure stripping (flag=1), a tidal interaction (flag=2), or a gravitational merger (flag=3). The perturbed sample is spread throughout the full H 1 morphometric space, preempting any possibility to simple cuts in parameter space to separate the two labels. As noted above, the morphometric feature space is degenerate.

Figure 6.

The processing flag for WALLABY objects according to Lin et al. (Reference Lin2023): ram-pressure (1), tidal interaction (2) or merger (3). We train kNN to distinguish between an undisturbed (0) and processing (1) label which includes all three here (1-3).

With a limited size training sample, a feature set that is degenerate and no good preset hyperparameter for the ML algorithm (the number of neighbours in this case), we will explore the feature engineering and hyperparameter settings, first separately and then combined.

For the metrics on performance, we will use precision, recall, and F1. Starting with True Positive (TP), True Negative (TN), False Positives (FP), and False Negatives (FN), precision is defined as: $precision = {TP \over TP+FP}$ and recall as: $recall = {TP \over TP+FN}$ . F1 is a combination of these: $F1 = 2 \times {Precision \times Recall \over Precision + Recall }$ .

5.2 Feature engineering

Because of the size of the training set, we must be extra careful to select a feature space from the H 1 morphometrics available. Because the undisturbed and perturbed galaxies lie well mixed in the H 1 feature space, kNN or a random forest (RF) make the most sense to test on this feature space. Each iteration, before we train on this set, we apply smote to balance and then the built-in StandardScaler in sk-learn to whiten (normalise) the data.

First, we examine how many features we will need. Naively, one would use the full H 1 morphometric space but there is a point of limited return as this is a known degenerate parameter space (see Scarlata et al. Reference Scarlata2007). At some point, one would no longer provide new information, just artificially weigh in on features already provided in another format. If we use the built-in function SelectKBest in sklearn, and ask for the 6 highest performing features for the interaction label, we arrive at Concentration, Gini, $M_{20}$ , Multimode, Deviation, and Sérsic index (n). This validates our initial suspicion that Smoothness and Intensity do not hold much additional information in this data and are too dependent on the smoothing kernel size.

5.3 Hyperparameter optimisation

Fig. 7 shows the number of neighbours used and the different metrics. There is a notable interSection at $k=2$ and $k=6$ when using the full parameter space. Here, the metrics are very similar, while at $k=1$ ,3,4, and 5, the trade-off between recall and precision is overly skewed in favour of recall. This is not clearly reflected in $F1 = 2 \times {Precision \times Recall \over Precision + Recall }$ . Ideally we would keep the number of neighbours low since we are dealing with a small training set. The high number of neighbours $(k=6)$ would average over a large fraction of the training set every time. A single neighbour suffers from high variance in the classification and affect reliability, essentially over-fitting.

We examine the kNN mean and variance of all the metrics by running multiple iterations with a number of features, randomly selected and a setting for the hyper-parameter (k), the number of neighbours (Fig. 8).

Optimisation of both the hyperparameter (k, number of neighbors) and the feature space, specifically how many features to use, depends on which metric is considered more valuable. Does one want high precision (accurate classifications) or a high recall (reliable classifications) and the F1 metric is meant to reflect a balance between the two. Historically, for merger statistics using morphometrics and other techniques, a high precision was valued since the merger fraction was the aim of the study. However, with more detailed individual galaxy studies, recall may be of higher value for observational follow-up. We therefore aim to strike a balance.

To map out the balance between precision and recall here, we map both the mean value and variance as a function of the number of neighbours (k) and the number of features in Fig. 8 for each metric. The key here is not that the number of features is increased but that which are used is chosen randomly. So the training set does not automatically start with concentration and moves on from there. The mean value for a combination of neighbours and features tells us how well the kNN algorithm is performing but the variance for that combination (the right side panels in Fig. 8) informs us how reliable that performance is. This is missing in a simpler diagnostic plot such as Figs. 7 or 9 which concentrate on just one aspect.

Given the size of the training sample and feature space (large but not orthogonal), we opt for $k=2$ neighbours and more than 4 features for optimal performance. This is partly motivated by Figs. 7 and 9 but validated when inspecting Fig. 8 for low variance in performance. We select those listed in Table 2 based on the experience with Hydra, Fig. 8, and which parameters are reported with high F1 scores and close precision/recall scores.

Figure 7.

Hyperparameter choice for a set feature space with metrics as a function of the number of neighbours (k). This is the performance for the full of morphometric space.

Figure 8.

The mean (left row) and variance (right row) map of the precision, recall and F1. Mean and variance are determined by drawing a random set of features in the H 1 morphometric space and running the kNN on it. Variance tends to be high for $k=1$ or $n=2$ features.

To illustrate the importance of the choice of feature space, Fig. 9 shows the metrics for the six features selected by SelectKBest in sklearn. Interestingly, this feature space performs better than the full morphometric space, and it is more consistent with metrics. The choice of $k=2$ is still well motivated as Recall and the other metrics diverge at $k=3$ and higher.

Similarly, one can argue which six morphometrics are preferred. For example, asymmetry is better understood and more widely adopted than the MID parameters. This could be an argument to include asymmetry instead of the multimode parameter. To ascertain the effectiveness of the kNN on this data-set, we evaluate the average of a series training-test runs, where the training/test sample split is 80%. We do this ten times. This approach is very similar to bootstrapping a simple fit. Fig. 10 shows the average confusion matrix for the test sample after training on 80% of total sample. The average metrics of this configuration (the features in Table 2 and $k=2$ ) are listed in Table 3. Thanks to the repeat in kNN training/test instances, the metrics also come with a standard deviation around the mean performance. These mean performance metrics are proficient for a simple machine learning algorithm.

However, for application to other data-sets, it can be beneficial to use the entire labelled sample as the training sample. If we do this, the metrics become those in Table 4 and the confusion matrix in Fig. 11. Performance is quite good considering the size of the training sample. We will now employ this kNN (trained on the full labelled sample) on the other catalogue, the one for the NGC 5044 mosaic.

5.4 Biases

There remains the possibility of biases applying a training sample on a new data-set. The objects in the NGC 5044 mosaic are biased towards greater distances, the signal-to-noise in the different data-cubes varies due to RFI or other factors, etc. The parameterisation of morphology through the above morphometrics is meant to be mostly invariant to small changes. Aside from familiarity, this is a prominent reason to convert to morphometrics first before attempting a machine learning algorithm. Our cut in distance to just those galaxies closer than 60 Mpc is also meant to remove biases in the training and application set (e.g. there are many sources in the wide field behind the NGC 5044 group that would skew our results). Fig. 12 shows the position of the galaxies in each field closer than 60 Mpc with the kNN classification marked. That said, small differences and thus biases between data-sets may well be present. Based on the distribution of sources in the parameter space, we estimate the issue to be small. However, moving from one sample to another with a (small) fundamental difference is a known issue in machine learning known as ‘transfer learning’.

5.5 Application on NGC 5044

We cut down the samples to only those galaxies below 60 Mpc for the training sample in the NGC 4808/4636 fields. The NGC 5044 field is a little further away on average but richer and well within this distance limit. The rationale for the distance limit is that it generously includes all labelled galaxies while removing the majority of unresolved background objects (Fig. 1). The resulting sample is 258 galaxies (within $D\unicode{x003C}60$ Mpc) for the NGC 5044 field. In the comparisons in scaling relations, we will compare the training sample scaling relation to this deployment sample of NGC 5044 mosaic.

6.1 Fraction of perturbed galaxies

Table 5 lists the fraction of the galaxies below 60 Mpc. in each of the three groups that the kNN trained on the Lin et al. (Reference Lin2023) classifications as perturbed somehow (i.e. ram-pressure stripping, tidally disturbed or merging). We compare these to ‘perturbed’ criteria from the literature, similar to Holwerda et al. (Reference Holwerda2011d).

The fraction of perturbed galaxies in the catalogue of Lin et al. (Reference Lin2023) is slightly lower than what we find using kNN. In general, the kNN finds a similar fraction of galaxies perturbed in each field. Based on the metrics listed as listed in Table 4, one would expect these fractions to be accurate to within a few percentage points. The difference of $\sim$ 1% in NGC 4808 is therefore illustrative of what the uncertainty should be.

Previous uses of morphometrics used a simple criterion to separate perturbed from unperturbed galaxies. Holwerda et al. (Reference Holwerda2011d) reviews these in the context of their use on H 1 surveys. H 1 morphology is expected to be perturbed earlier and longer during a gravitational interaction. Table 5 lists the fractions of galaxies that meet the various criteria as well. It is notable that a the basic asymmetry criterion ( $A\unicode{x003E}0.35$ ) identifies a similar percentage as the kNN classifier. Once compared however, that Asymmetry criterion is biased towards false negatives. Since in the past, the goal of morphometric identification of mergers was to identify the merger fractions at different epochs or environments, the kNN approach works certainly well enough on a population.

Table 2.

The features selected for the final iteration of the kNN.

Figure 9.

Hyperparameter choice for a set feature space with metrics as a function of the number of neighbours (k). This is for the optimal set of features in Table 2.

Figure 10.

The average confusion matrix for the kNN ( $k=2$ , trained on subsamples of 80%, tested on the remaining 20% shown here) with the optimised feature space listed in Table 2 for all the members of the NGC 4636 and NGC 4636 groups. We repeated the training/test ten times and these are the averages of all ten split-train-test iterations.

Table 3.

The performance metrics of the WALLABY training catalogue $(D \unicode{x003C} 60$ Mpc within the green circle in Fig. 5) split into subsections using the features listed in Table 2. By iterating ten times over this sample and splitting off 20% for testing, these are the mean and variance of the kNN performance.

Table 4.

The performance metrics of in the full WALLABY training catalogue ( $D \unicode{x003C} 60$ Mpc within the green circle in Fig. 5) using the features listed in Table 2.

Figure 11.

The confusion matrix for the kNN ( $k=2$ , trained on a subsample of 80%) with the optimised feature space listed in Table 2 for all the objects in the combined catalogue of the NGC 4808 and NGC 4636 fields ( $D \unicode{x003C} 60$ Mpc within the green circle in Fig. 5).

Table 5.

The fraction of galaxies that were perturbed as reported by Lin et al. (Reference Lin2023) and the kNN trained on NGC 4808+4636 (WALLABY training sample). For comparison, the morphometric criteria for merging or perturbed galaxies from Conselice (Reference Conselice2003), Lotz et al. (2004, (Reference Lotz, Jonsson, Cox and Primack2008), and Holwerda et al. (Reference Holwerda2011d) are listed as well.

Figure 12.

The kNN labelling in both the training sample (left) and the deployment field, NGC 5044. Compare to the labels in Fig. 5.

6.2 Galaxy scaling relations

One application of a ML classifier is to rapidly classify galaxies to then examine the galaxy scaling relations for those galaxies undergoing some interaction to those that are not. Here we examine three: the star-forming galaxy main sequence, the H 1 and stellar mass relation, and the Baryonic Tully-Fisher relation. We also looked at the H 1 size-mass relation but there is little difference between galaxies marked perturbed and not. The lack of an H 1 size-mass relation can be attributed to the still relatively low spatial resolution of the WALLABY pilot observations, expected to improve, and relatively simple size measures.

6.2.1 Star-forming main sequence

The star-forming galaxies main sequence (e.g. Noeske et al. Reference Noeske2007) is an important relation between the stellar mass of galaxies and their (relative) growth rate.

Fig. 13 shows the stellar mass and star formation relation for the WALLABY training sample and the deployment data in the NGC 5044 mosaic. The kNN-identified perturbed galaxies are mixed in with the main sequence of star-forming galaxies. A linear fit to the stellar mass and star formation relation for these galaxies, all of whom are on the star-forming main sequence, is essentially the same for perturbed and non-perturbed sets (Table 6). We note there is a normalisation difference between the training and deployment sample for the SFR estimate from WISE. It is unclear if this is a distance effect, or additional flux in WISE W3 due to Galactic Cirrus. The training and NGC5044 samples show the same slope and intercept within their respective bootstrap errors (Table 6).

There is no functional difference in the slope and intercepts between perturbed and unperturbed galaxies. There is a difference between training and deployment samples but that is to be expected when moving to a sample with a difference mass range.

Table 6.

The linear fits to the stellar mass and star formation relation for the training sample and the deployment sample of NGC 5044 for all the galaxies in the sample, the unperturbed and perturbed ones. Qualitatively the fits are similar but the deployment fits have lower slopes and higher intercepts than the training sample.

Figure 13.

The stellar mass and star formation relation for the WALLABY training sample (left) and the NGC 5044 deployment sample (right). Qualitatively, the results are similar for the star-forming galaxy main sequence: similar slopes for all three populations, unperturbed, perturbed, and all galaxies, but there are quantitative differences in the SFGMS slope and interecept between the training and the deployement samples.

Figure 14.

The stellar mass and H 1 mass relation for the training sample (left) and the deployment sample, the NGC 5044 mosaic. Both the combined and the unperturbed samples show very similar fits and the galaxies indicated as perturbed in the training sample as well as in the NGC 5044 mosaic both show less H 1 mass for a given stellar mass.

6.2.2 Stellar and HI mass

Fig. 14 shows the stellar mass, as derived from the WISE W1 flux, and the H 1 mass from the WALLABY catalogue for the training sample and the deployment data of the NGC 5044 mosaic. We note that a quantitative comparison with existing relations (e.g. Catinella et al. Reference Catinella2018) is not done here because stellar mass estimates are based on catalogue photometry on a single filter from WISE. Qualitatively, the correlations for this relation are similar for training and deployment samples; unperturbed galaxy relation has a higher slope, the perturbed ones a lower slope than the whole sample fit. Table 7 quantifies this with bootstrapped errors. We note here that the training set skews a little lower mass than the deployment sample.

Figure 15.

The Baryonic Tully–Fisher relation for the WALLABY training sample (left) and the deployment sample on NGC 5044 (right). The velocity is computed according to equation 12 with the unit in m/s.

6.2.3 Baryonic Tully–Fisher relation

Fig. 15 shows the Baryonic Tully–Fisher relation for all three groups combined. We used the WISE W1 based stellar mass and a factor 1.33 to convert the H 1 mass into a total gas mass including Helium. The H 1 velocity is the W50 measurement corrected for inclination from the SoFiA measurements:

(12) \begin{equation} V_{HI} = { w50 \over \sqrt{1 - \left({b \over a}\right)^2 }}\end{equation}

Table 7.

The linear fits to the stellar and H 1 mass relation for the training sample and the deployment sample of NGC 5044 for all the galaxies in the sample, the unperturbed and perturbed ones. Qualitatively the fits are similar but the deployment fits have lower slopes and higher intercepts than the training sample.

The slope and the intercept were fit with a standard linear regression. Because the uncertainty in the Baryonic mass is under-estimated with the formal uncertainties, we estimate the variance in the slope and intercept using a bootstrapping of the fits. The BTF linear fit through all the galaxies and those labelled unperturbed are very similar but the kNN-identified perturbed population shows a flatter BTF relation. The uncertainties reported in Table 8 are a standard deviation. The discrepancy is therefore significant.

Table 8.

The linear fits to the Baryonic Tully–Fisher relation for the training sample and the deployment sample of NGC 5044 for all the galaxies in the sample, the unperturbed and perturbed ones.

The measurements for individual galaxies can have some uncertainties due to model fits. For example, the conversion from WISE W1 flux to a stellar mass and the correction for inclination using the SoFiA measured major and minor axes. Especially in recently perturbed galaxies, this axis ratio may not be indicative of the disc’s inherent inclination.