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UPMASK: unsupervised photometric membership assignment in stellar clusters

A. Krone-Martins, A. Moitinho

arXiv:1309.4471v1astro-ph.IMastro-ph.GA

TL;DR

Recognizing cluster members in fields contaminated by field stars is difficult, and accurate distances or other discriminators are not always available. UPMASK identifies members from photometry and positions using a data-driven, model-free approach. Tests on simulated and real cluster fields showed good membership results across a broad range of conditions.

  • Problem

    Identifying cluster members is difficult when field stars obscure their signatures, and accurate parallactic distances are generally unavailable except for nearby stars.

    Source: §1 · p. 1

  • Method

    UPMASK identifies cluster members from photometry and projected positions in a purely data-driven framework without relying on models.

    Source: §1 · p. 2

  • Results

    Tests on simulated and real fields showed good true positive and member recovery rates across a broad range of cluster ages, masses, distances, and field-star contamination.

    Source: §6 · p. 12

  • Takeaways & Limitations

    Although tested here with photometry and positions, the framework can be adapted to other data types and potentially to clustering objects of a different nature.

    Source: §6 · p. 12

    Missing-data handling currently uses a crude uniform distribution over a specified range and was not enabled in the tests.

    Source: §5 · p. 11

Abstract

from arXiv · show

We develop a method for membership assignment in stellar clusters using only photometry and positions. The method, UPMASK, is aimed to be unsupervised, data driven, model free, and to rely on as few assumptions as possible. It is based on an iterative process, principal component analysis, clustering algorithm, and kernel density estimations. Moreover, it is able to take into account arbitrary error models. An implementation in R was tested on simulated clusters that covered a broad range of ages, masses, distances, reddenings, and also on real data of cluster fields. Running UPMASK on simulations showed that it effectively separates cluster and field populations. The overall spatial structure and distribution of cluster member stars in the colour-magnitude diagram were recovered under a broad variety of conditions. For a set of 360 simulations, the resulting true positive rates (a measurement of purity) and member recovery rates (a measurement of completeness) at the 90% membership probability level reached high values for a range of open cluster ages ($10^{7.1}-10^{9.5}$ yr), initial masses ($0.5-10\times10^3$M$_{\sun}$) and heliocentric distances ($0.5-4.0$ kpc). UPMASK was also tested on real data from the fields of the open cluster Haffner~16 and of the closely projected clusters Haffner~10 and Czernik~29. These tests showed that even for moderate variable extinction and cluster superposition, the method yielded useful cluster membership probabilities and provided some insight into their stellar contents. The UPMASK implementation will be available at the CRAN archive.

1. Introduction

Identifying cluster members in fields crowded with field stars is difficult, while distance, proper-motion, and spectroscopic approaches have practical limits. UPMASK addresses this challenge with data-driven membership identification using photometry and positions, without relying on models.

1. Introduction

  • Accurate parallactic distances are generally unavailable beyond nearby stars, while proper-motion methods require precise motions and spectroscopy is telescope-time-intensive.Proper-motion and spectroscopic approaches also face constraints from stellar brightness and directions dominated by solar motion.Source: §1 · p. 1
  • Multi-band imaging provides large, deep catalogues over wide areas, but the resulting star counts also bring strong field-star contamination.When contamination is heavy, visual techniques break down and cluster over-densities can become marginal against field-star fluctuations.Source: §1 · p. 2
  • Heavy field-star contamination can obscure cluster signatures and make visual identification, classical parameter estimates, and simple statistical approaches uncertain or even useless.This is especially consequential when studies need individual memberships, such as searches for specific stellar types or analyses of clusters projected along the same line of sight.Source: §1 · pp. 1–2
  • Photometric stellar-parameter and cluster-parameter determinations rely on models such as isochrones and reddening laws, and may be sensitive to passband mismatches.Individual reddenings and classifications can help distinguish members, but the related parameter solutions are model-dependent.Source: §1 · p. 2
  • UPMASK aims to identify cluster members in contaminated fields using photometry and projected sky positions in a purely data-driven way, without models.The paper presents this as a special case of a framework that could also be applied to spectrophotometry, radial velocities, and proper motions.Source: §1 · p. 2

2. The UPMASK method

UPMASK identifies cluster members by looking for stellar groups that are concentrated in positional space, without prescribing distributions for the observables. PCA, clustering, and spatial-density tests form an iterative kernel, while an outer loop accounts for measurement errors and assigns membership probabilities.

2.1. Conceptual approach

  • UPMASK defines a stellar cluster as a spatial over-density of stars with a common origin, and assumes members cluster in positional space while field stars do not.Members may cluster in other parameter spaces too, but their photometric indexes need not be concentrated around a common colour.Source: §2.1 · p. 2
  • UPMASK is data-driven: apart from spatial uniformity of field stars, it assumes no prior parametrizations such as isochrones or King profiles.Tidal interactions can reshape cluster density profiles, and current stellar-evolution models do not describe all stages, mass ranges, or colour-magnitude combinations equally well; young clusters' pre-main-sequence stars, especially low-mass stars, remain a particular challenge.Source: §2.1 · pp. 2–3

2.2. Dimensional transformation

  • PCA reduces redundancy among correlated observables; the UBVRI examples also add colours and a nearly reddening-free index because band interdependencies are nonlinear.The authors describe linear PCA as a useful heuristic with physical motivation, rather than a prescribed physical model.Source: §2.2 · p. 3
  • The first three principal components account for 99% of data variance; for Haffner 16, the four leading components contribute 58.8%, 31.3%, 9.0%, and 0.9%.The authors interpret the leading components as encoding distance, reddening, temperature, and, to a lesser degree, metallicity or surface gravity; they treat linear PCA as a physically motivated heuristic.Source: §2.2 · p. 3

2.3. Implementation of the method

  • The implementation uses two iterative processes: the UPMASK kernel performs the core classification, and an outer loop incorporates measurement errors and relaxes dependence on clustering initialization.The outer loop repeatedly runs the kernel on perturbed data and uses the fraction of runs classifying each star as a member as its membership probability.Source: §2.3 · p. 3, §2.3.3 · p. 4

2.3.1. Main iterative process: UPMASK kernel

  • Each kernel iteration scales non-positional observables, selects four principal components, clusters with k-means, then retains groups that are spatially clustered; tests favored 10–25 stars per cluster.Groups failing the positional-clustering test are catalogued as field stars, although some true members may be misclassified at this stage.Source: §2.3.1 · p. 3

2.3.2. Detection of spatial clustering

  • UPMASK compares positional kernel-density scores with uniform-position realizations matched to the observed star count and region; compatible distributions are classified as field.The method uses the separation between peak and mean density, measured in standard deviations, to assess spatial concentration.Source: §2.3.2 · p. 4

2.3.3. Outer loop

  • The outer loop replaces each observable with a random draw from its error model, reruns the kernel, and estimates membership probability from the fraction of runs assigning a star to the cluster.Gaussian draws use the measured value as the mean and measurement error as σ; other error models can be used for manifestly non-Gaussian errors.Source: §2.3.3 · p. 4

3. Application to simulated data

UPMASK was assessed on synthetic cluster fields spanning varied conditions, using high-probability membership assignments to evaluate purity and completeness. Across 360 simulations and focused case studies, it recovered cluster members and spatial or colour–magnitude structure, with performance depending on cluster and analysis settings.

3.1. Simulated data

  • Synthetic UBVRI cluster fields were generated across initial mass, age, and distance, with a TRILEGAL Galactic field and magnitude-dependent photometric noise.The simulated field of view was 12′ × 12′, with limits of U, B, V, R, I ∼19.5, 20.5, 21.5, 22, 22 mag.Source: §3.1 · p. 5, §3 · p. 5

3.2.1. Global analysis

  • Purity was measured as TPR in the subset above a membership-probability cutoff, while MRR measured the fraction of all members recovered; the global analysis used a 90% cutoff.At that cutoff, the high-purity list can omit cluster stars; lowering the cutoff can improve completeness at the cost of purity.Source: §3.2.1 · pp. 5–6
  • More than 63% of 360 simulated clusters had TPR90 ≥80%; high-mass clusters retained MRR90 ∼50% at 3.5 kpc, while poorer clusters yielded useful high-purity recovery beyond 1 kpc for most ages.TPR90 was generally fairly high even under heavy contamination.Source: §3.2.1 · pp. 5–6, Figure 3 · p. 6, Figure 4 · p. 6

3.2.2. Case studies

  • CMD gaps can arise because UPMASK does not require continuity between k-means clusters classified as members or non-members; non-parametric post-processing could fill them.An alternative described is fitting an isochrone to identified members and selecting stars near it.Source: §3.2.2 · p. 6
  • Across the case studies, larger n can reduce TPR90 and contaminate assignments; n≈10–25 was considered broadly usable, with n=15 suggested as a default and lower n for less-dense clusters.For less-dense clusters, n=7–10 gave high TPR50 and MRR50 within their observed ranges.Source: §3.2.2 · pp. 7–8, Figure 7 · p. 8
  • The field-size test found fairly constant 10–20% MRR90 for the lighter cluster, while the current implementation does not disentangle fields much smaller than the cluster radius.For the more massive, distant cluster, purity stayed above ∼85%, and more extended fields could raise MRR90 up to ∼10%.Source: §3.2.2 · p. 8, Figure 8 · p. 8
  • In two non-favourable simulated cases, UPMASK separated field and cluster populations and recovered overall spatial structure, including disconnected main-sequence and red-clump stars.The first cluster’s members were mostly assigned probabilities ≫0.5; the second case was highly contaminated and its cluster was barely distinguishable in the CMD.Source: §3.2.2 · pp. 6–8, Figure 5 · p. 7, Figure 6 · p. 7

3.2.3. Fields with lower counts

  • In low-count tests, n=7 yielded TPR90 values of ∼97.5%, ∼94.4%, and ∼100%; with 916 field stars, MRR90 was only 12%.Testing n=25 produced lower purity but higher completeness, while n=15 remained acceptable in the analysed simulations.Source: §3.2.3 · p. 9

4. Application to real data

UPMASK produced useful membership probabilities on real cluster fields, including a field containing two closely projected clusters. The tests also show that field selection can affect probabilities, while the method reveals CMD features and possible complications in interpreting them.

4.1. Haffner 16

  • For Haffner 16, high-probability members define a main sequence at V < 17, while a fainter group may indicate an older cluster or thick-disc stars.The faint group coincides with a blue bump and stars off the cluster centre; the authors leave its interpretation open.Source: §4.1 · p. 9, Figure 9 · p. 9
  • UPMASK avoided holes in the field-star CMD and positional distributions, although some likely cluster members remained concentrated in the field-assigned sample.The authors suggest those stars received low membership probabilities.Source: §4.1 · p. 9, Figure 9 · p. 9
  • Restricting Haffner 16 to the central 34% of the field changed membership probabilities and removed the faint high-probability clump.The reduced-field analysis also showed a redder sequence below V ∼17.Source: §4.1 · p. 10, Figure 11 · p. 10

4.2. Haffner 10 and Czernik 29

  • Haffner 10’s probable members show a broad-colour main sequence and red clump, whose spread could reflect variable reddening.The red-clump branch is reported to parallel the reddening/extinction vector.Source: §4.2 · p. 11
  • UPMASK automatically assigned membership probabilities to two overlapping clusters in one field, identifying separate high-probability regions with Czernik 29 and Haffner 10.The regions occupy different CMD loci, with Czernik 29 in the upper right and Haffner 10 in the lower left.Source: §4.2 · p. 11

4.3. Remarks on the application of UPMASK to real data

  • The real-data tests approached the distances where simulations indicated performance limits, yet still yielded useful probabilities and insights into the studied clusters.Haffner 16 and Haffner 10 are reported at ∼3.7 kpc, and Czernik 29 at ∼3.0 kpc.Source: §4.3 · p. 11

5. Present caveats and possible developments

The discussion outlines possible extensions to other data and photometric parameter spaces, while noting that missing-data treatment was crude and unused in the tests, and that the implementation is compute-intensive.

5. Present caveats and possible developments

  • The missing-data option was not used in the tests because it currently imputes missing magnitudes with a crude uniform distribution.The authors propose using constraints from available measurements and identify missing-data treatment as future work.Source: §5 · p. 11
  • UPMASK can be adapted to use parallaxes and proper motions alongside photometry and positions.Parallaxes could join positions in the spatial veto, while proper motions could enter an intermediate step or the k-means variables.Source: §5 · p. 11
  • A possible development is to run UPMASK separately on photometric-space cells, optimizing the PCA for dominant spectral types in member-rich cells.The proposal addresses the fact that one linear PCA transformation is applied to a nonlinear problem.Source: §5 · pp. 11–12
  • UPMASK is compute-intensive, though its R implementation parallelizes the outer loop and the authors report almost linear speed-up with core count.A run of 120 kernels on 2,096 Haffner stars took about 7 minutes using 12 cores.Source: §5 · p. 12

6. Summary and conclusions

UPMASK identifies cluster members in contaminated fields by finding shared structure in observable spaces with few assumptions. Tests on simulated and real data report good recovery across a broad range of conditions, and the framework may extend beyond photometry and positions.

6. Summary and conclusions

  • UPMASK was designed to identify cluster members in highly contaminated fields with minimal assumptions, using clustering in spaces of observables related to shared member properties.The paper tested it with UBVRI photometry and positions on simulated and real cluster fields.Source: §6 · p. 12
  • PCA reduces overweighting of observables and separates physical parameters, especially when photometric colours carry redundant correlated information.For UBVRI photometry, the parameters include reddening, distance, and temperature, and sometimes metallicity and surface gravity.Source: §6 · p. 12
  • Tests on simulated clusters found good true positive and member recovery rates across a broad range of ages, masses, distances, and field-star contamination.Real-data applications also produced good results when pushed to the limits indicated by the simulations.Source: §6 · p. 12
  • The framework may be adapted to other data or object types when members share a favored positional region and common characteristics, while non-members are not significantly clustered in those spaces.The paper mentions extragalactic data as one possible application.Source: §6 · p. 12
  • The implementation was intended for open-source distribution through the CRAN archive as the UPMASK package.The simulated data could be requested from the authors.Source: §6 · p. 12
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