Source Clustering: Methods & Applications

• Source clustering is a family of clustering problems where the term 'source' denotes domain-specific entities such as astrophysical signals, software artifacts, or sensor data.
• It employs varied methodologies—from graph optimization and statistical models to pseudo-source guidance and hierarchical clustering—to preserve source characteristics while reducing ambiguity.
• Applications span astrophysics, weak lensing calibration, software code analysis, and multi-source integration, offering practical solutions for domain-driven data organization.

Searching arXiv for recent and foundational papers related to “source clustering” across its main technical senses.

{"^^^^^^^^4query4 clustering\"^^^^^^^^4 OR ti:\4^^^^^^^^"source clustering\"^^^^^^^^4 OR abs:\4^^^^^^^^"source clustering\"","max_results":^^^^4all:\4query4^^^^,"sort_by":"relevance"} {"^^^^^^^^4query4 OR id:(&&&^^^^4all:\4^^^^&&&) OR id:(&&&^^^^4 OR ti:\4^^^^&&&) OR id:(&&&^^^^4 OR abs:\4^^^^&&&) OR id:(Gatti et al., 2023) OR id:(Rogatch, 2012) OR id:(Misra et al., 2012) OR id:(0809.1330)","max_results":^^^^4 OR ti:\4query4^^^^,"sort_by":"relevance"} Source clustering denotes a family of clustering problems in which the noun “source” is domain-dependent. In astrophysics and cosmology, it can refer to the angular clustering of unresolved infrared point sources or to the source-lens clustering bias produced because source galaxies are not randomly distributed. In machine learning, it can denote the use of source-domain structure, source models, or pseudo-source anchors to guide target clustering under domain shift. In software engineering, it includes clustering source-code artifacts and source-code changes to recover architecture or classify modifications. In multi-source data integration, it includes clustering across partially aligned sources, sensor networks, or linked-data repositories. The shared motif is not a single algorithm, but the organization of source-related structure into clusters that preserve coherence, suppress ambiguity, or expose latent organization (&&&^^^^4query4^^^^&&&, Valageas, 2013, &&&^^^^4 OR abs:\4^^^^&&&, Gatti et al., 2023, &&&^^^^4 OR ti:\4^^^^&&&, &&&^^^^4all:\4^^^^&&&, &&&^^^^4all:\44^^^^&&&, Rogatch, 2012, &&&^^^^4all:\4^^^^6&&&).

^^^^4all:\4^^^^. Scope of the term

In the literature, “source clustering” is used for several distinct objects. In some settings the clustered objects are physical sources, such as unresolved infrared emitters or aeroacoustic source types. In others they are software artifacts, source-code edits, entities drawn from multiple data sources, or edges in infected subnetworks. In yet others, “source” denotes a privileged distribution or model whose structure is transferred to a target domain without exposing the original data.

Setting	Meaning of “source”	Representative formulation
CMB foregrounds	Unresolved IR point sources	PRESERVED_PLACEHOLDER_^^^^4query4^^^^
Weak lensing	Source galaxies	PRESERVED_PLACEHOLDER_^^^^4all:\4^^^^
Domain adaptation	Source classifier or source domains	Pseudo-source banks, prototype alignment, distillation
Software engineering	Source code or source-code changes	Metric vectors, dependency graphs, architectural hierarchies
Multi-source integration	Distinct data repositories or sensor sources	Consensus embeddings, KLD-based clustering, holistic clusters

The mathematical encodings vary accordingly. Some works cluster metric vectors, some construct weighted graphs and optimize graph objectives, some cluster by discrepancy penalties across partially observed mappings, and some build hierarchical decompositions constrained by domain-specific structure. A plausible implication is that “source clustering” functions as a cross-domain umbrella for clustering problems in which provenance, generating mechanism, or source-side structure is part of the inferential target rather than merely background metadata.

^^^^4 OR ti:\4^^^^. Astrophysical and cosmological meanings

In CMB foreground modeling, unresolved infrared source clustering is treated as an angular-power-spectrum component that must be separated from Poisson shot noise. A combined fit to ^^^^4all:\4^^^^6 spectra from Planck, BLAST, and BLASTPRESERVED_PLACEHOLDER_^^^^4 OR ti:\4^^^^ACT models the anisotropy power as

PRESERVED_PLACEHOLDER_^^^^4 OR abs:\4^^^^

with

$C_\ell^{\rm clust}\propto \ell^{-n},$

pivoted at $\ell_0=3000$. Over the angular scales and frequencies considered, the clustered power is well fit by a single power law with $n=1.25\pm 0.06$, and the clustered SED is described phenomenologically by the square of a modified blackbody, $\left[\nu^\beta B(\nu,T_{\rm eff})\right]^2$, with $\beta=2.20\pm 0.07$ and $T_{\rm eff}=9.7\,{\rm K}$. The fit quality is PRESERVED_PLACEHOLDER_^^^^4all:\4query4^^^^, the predicted effective clustered dust spectral index between ^^^^4all:\4max_results4query4^^^^ and ^^^^4 OR ti:\4 OR ti:\4query4^^^^ GHz is PRESERVED_PLACEHOLDER_^^^^4all:\4all:\4^^^^, and the combined Planck and BLAST data rule out a linear bias clustering model; a broken power law yields only marginal improvement over the single-index form (&&&^^^^4query4^^^^&&&).

In weak gravitational lensing, source clustering has a different meaning: source galaxies trace the same underlying density field that lenses them. This couples the sampling of the shear or convergence field to the signal itself and biases estimators built from galaxy pairs, triplets, or map-level summaries. In one formulation, galaxy density is written as PRESERVED_PLACEHOLDER_^^^^4all:\4 OR ti:\4^^^^, and for tomography the observed source overdensity is decomposed as

PRESERVED_PLACEHOLDER_^^^^4all:\4 OR abs:\4^^^^

where intrinsic source clustering and cosmic magnification/size bias are the two distinct origins of the effect. For two-point statistics, source-lens clustering is typically several orders of magnitude below the weak-lensing signal, except in extreme low/high-redshift pairings; for three-point statistics, the bias is typically of order PRESERVED_PLACEHOLDER_^^^^4all:\44^^^^ of the signal as soon as the source redshifts are not identical, so it becomes a leading systematic for better-than-PRESERVED_PLACEHOLDER_^^^^4all:\4^^^^5 accuracy (Valageas, 2013).

Tomographic estimators do not suppress the two SLC contributions equally. For the standard estimator, SLC induced by both intrinsic clustering and cosmic magnification can bias the lensing power spectrum by PRESERVED_PLACEHOLDER_^^^^4all:\4^^^^6–PRESERVED_PLACEHOLDER_^^^^4all:\4 although the standard estimator suppresses intrinsic source clustering in the cross-spectrum. By contrast, the pixel-based estimator suppresses SLC through cosmic magnification but fails to suppress SLC through intrinsic source clustering and can bias the measured power spectrum low by PRESERVED_PLACEHOLDER_^^^^4all:\4^^^^8–PRESERVED_PLACEHOLDER_^^^^4all:\4 For typical photo-PRESERVED_PLACEHOLDER_^^^^4 OR ti:\4query4^^^^ errors PRESERVED_PLACEHOLDER_^^^^4 OR ti:\4all:\4^^^^ and photo-PRESERVED_PLACEHOLDER_^^^^4 OR ti:\4 OR ti:\4^^^^ bin sizes PRESERVED_PLACEHOLDER_^^^^4 OR ti:\4 OR abs:\4^^^^, the lensing E-mode power spectrum is altered by PRESERVED_PLACEHOLDER_^^^^4 OR ti:\44^^^^–PRESERVED_PLACEHOLDER_^^^^4 OR ti:\4^^^^5, with PRESERVED_PLACEHOLDER_^^^^4 OR ti:\4^^^^6 and PRESERVED_PLACEHOLDER_^^^^4 OR ti:\4^^^^7 especially relevant (&&&^^^^4 OR abs:\4^^^^&&&).

Map-based higher-order weak-lensing summaries show the effect directly in data. Simulations that compare galaxies that trace or do not trace the density field show stronger source-clustering effects at small scales, for mixed low/high-redshift combinations, and for lower-redshift samples. In DES Year ^^^^4 OR abs:\4^^^^ data, null tests against the source-clustering-free case give PRESERVED_PLACEHOLDER_^^^^4 OR ti:\4^^^^8 (PRESERVED_PLACEHOLDER_^^^^4 OR ti:\4^^^^9) using third-order map moments and PRESERVED_PLACEHOLDER_^^^^4 OR abs:\4query4^^^^ (PRESERVED_PLACEHOLDER_^^^^4 OR abs:\4all:\4^^^^) using wavelet phase harmonics. Existing DES Y^^^^4 OR abs:\4^^^^ moments and peaks analyses remained safe because of scale cuts and de-noising procedures, but the broader conclusion is that higher-order map statistics, N-point functions, wavelet-moment observables, scattering transforms, and field-level summaries require explicit modeling or mitigation of source clustering (Gatti et al., 2023).

^^^^4 OR abs:\4^^^^. Source-guided clustering under domain shift

In fully test-time adaptation, source clustering often means injecting source semantics without retaining source data. pSTarC performs pseudo source-guided target clustering by synthesizing a pseudo-source feature bank from the source classifier head PRESERVED_PLACEHOLDER_^^^^4 OR abs:\4 OR ti:\4^^^^ itself. Pseudo-features are initialized as PRESERVED_PLACEHOLDER_^^^^4 OR abs:\4 OR abs:\4^^^^ and optimized for 5^^^^4query4^^^^ Adam steps with an entropy term and a diversity term,

PRESERVED_PLACEHOLDER_^^^^4 OR abs:\44^^^^

so that the bank is both confident and class-balanced. The bank size is set as PRESERVED_PLACEHOLDER_^^^^4 OR abs:\4^^^^5 with PRESERVED_PLACEHOLDER_^^^^4 OR abs:\4^^^^6 features per class, and top-PRESERVED_PLACEHOLDER_^^^^4 OR abs:\4^^^^7 retrieval uses PRESERVED_PLACEHOLDER_^^^^4 OR abs:\4^^^^8. During adaptation, low-entropy target samples align to retrieved pseudo-source neighbors, high-entropy samples self-anchor through their own detached predictions, and the full objective combines augmentation consistency, pseudo-source-guided attraction, and dispersion:

PRESERVED_PLACEHOLDER_^^^^4 OR abs:\4^^^^9

This is source-guided clustering without actual source examples; the class structure is inherited from the source-trained classifier and imposed on unlabeled target data at test time (&&&^^^^4 OR ti:\4^^^^&&&).

Prototype-oriented Clustering with Distillation addresses unsupervised clustering under domain shift when both source-domain data and source model parameters must remain private. The source model is learned by aligning prototype distributions and source-domain feature distributions using entropic optimal transport with cosine dissimilarity costs, while also maximizing mutual information and applying CutMix regularization. Knowledge transfer then occurs only through source-provided cluster labels returned by an API, using KL-divergence distillation, label smoothing, and temporal self-ensembling, followed by a target-only refinement stage. The method is explicitly data-private and model-private: no source data are shared, no source parameters are exposed, and only cluster labels are queried. Reported average gains over ACIDS in the standard setting are about $C_\ell^{\rm clust}\propto \ell^{-n},$^^^^4query4^^^^ on Office-^^^^4 OR abs:\4all:\4^^^^, $C_\ell^{\rm clust}\propto \ell^{-n},$^^^^4all:\4^^^^ on Office-Home, and $C_\ell^{\rm clust}\propto \ell^{-n},$^^^^4 OR ti:\4^^^^ on PACS (&&&^^^^4all:\4^^^^&&&).

Nearest-neighborhood-based deep clustering for source data-absent UDA replaces isolated target samples with nearest-neighborhood structures. The fundamental unit is a nearest neighborhood $C_\ell^{\rm clust}\propto \ell^{-n},$^^^^4 OR abs:\4^^^^, and the method imposes semantic consistency on the nearest neighborhood (SCNNH). It then extends this to semantic hyper-nearest neighborhood (SHNNH), which restricts guidance to a confident set defined by entropy and centroid distance and finds a “home sample” by chain search. The training objective combines an information-maximization term with a self-supervised term. Reported averages are $C_\ell^{\rm clust}\propto \ell^{-n},$4 and $C_\ell^{\rm clust}\propto \ell^{-n},$5 on Office-^^^^4 OR abs:\4all:\4^^^^ for N^^^^4 OR ti:\4^^^^DC and N^^^^4 OR ti:\4^^^^DC-EX, $C_\ell^{\rm clust}\propto \ell^{-n},$6 and $C_\ell^{\rm clust}\propto \ell^{-n},$7 on Office-Home, and $C_\ell^{\rm clust}\propto \ell^{-n},$8 and $C_\ell^{\rm clust}\propto \ell^{-n},$9 on VisDA-C, with the paper emphasizing that SHNNH gives particularly strong gains on the larger VisDA-C dataset (&&&^^^^4 OR ti:\4 OR abs:\4^^^^&&&).

4. Source-code and software-engineering variants

A direct software-engineering use of source clustering is the classification of source-code changes. One method represents each change $\ell_0=3000$^^^^4query4^^^^ by an ^^^^4all:\4all:\4^^^^-dimensional metric vector

$\ell_0=3000$^^^^4all:\4^^^^

with metrics for added, deleted, and modified lines of code, cyclomatic complexity, modified files, interfaces, and classes/structures. Clustering is performed by k-means with cosine similarity,

$\ell_0=3000$^^^^4 OR ti:\4^^^^

and an expert then maps clusters to semantic change classes such as bug fixing, refactoring, or new functionality. The pipeline begins with $\ell_0=3000$^^^^4 OR abs:\4^^^^, checks a clustering quality functional $\ell_0=3000$4, increases $\ell_0=3000$5 if needed, and evaluates the final mapping by purity and entropy. On five software systems, including Subversion and NHibernate, the reported quality is $\ell_0=3000$6 and $\ell_0=3000$7 at significance level $\ell_0=3000$8; in the NHibernate example, only 7^^^^4 OR abs:\4^^^^ out of ^^^^4 OR ti:\4query4^^^^69 changes required manual classification during expert mapping (&&&^^^^4all:\44^^^^&&&).

At architectural scale, source clustering is used to recover subsystem structure from dependency graphs. InSoAr models software artifacts as vertices in an undirected weighted graph and applies hierarchical Flake-Tarjan clustering based on minimum cuts with a parameter $\ell_0=3000$9. Smaller $n=1.25\pm 0.06$^^^^4query4^^^^ values yield fewer, larger clusters, while larger $n=1.25\pm 0.06$^^^^4all:\4^^^^ values yield more, smaller clusters. The method uses directed-to-undirected normalization to control utility artifacts, a priority-driven search over $n=1.25\pm 0.06$^^^^4 OR ti:\4^^^^-space, arbitrary-order merge into a global tree, distributed computation, and a post-processing step called perfectization to repair overly flat hierarchies caused by the “alpha-threshold” phenomenon. Reported experiments reach ^^^^4all:\4all:\4^^^^,^^^^4all:\4 Java classes, ^^^^4all:\4sort_by4 OR abs:\4^^^^,^^^^4all:\4query4 OR abs:\4^^^^ class members, and ^^^^4 OR ti:\4^^^^.^^^^4query4^^^^7 million graph edges, with the output interpreted as a nested software decomposition for reverse engineering and maintenance (Rogatch, 2012).

A related Java source-code clustering framework unifies syntactic and semantic evidence into a single weighted graph. Textual features are extracted from comments and identifiers and weighted by TF-IDF; class-name and method-name similarities use weighted Jaccard variants; packaging and inheritance similarities use Jaccard coefficients; and structural similarity is derived from byte-code-based method-call dependencies. The combined similarity is

$n=1.25\pm 0.06$^^^^4 OR abs:\4^^^^

with default significance factors summing to ^^^^4all:\4^^^^. Clustering then searches for a partition maximizing

$n=1.25\pm 0.06$4

using multiple seed populations and hill climbing with simulated annealing. The same framework is extended to cluster interfaces, inter-cluster interactions, auto-labeling, borderline-class handling, ^^^^^^^^4query4 mapping, and recursive cluster hierarchy construction (Misra et al., 2012).

5. Physical sources, networked sources, and multi-source integration

In aeroacoustics, clustering is used as expert decision support for source type identification rather than as a fully autonomous classifier. The EDSS pipeline first extracts interpretable features from deconvolved beamforming data, including self-similarity over Strouhal or Helmholtz normalizations, power scaling with Mach number, tonality, source motion, compactness, shape, and spectral slope. The features are designed to be independent of the absolute Mach number. Clustering is then performed with HDBSCAN after log transformation, normalization, and KPCA with an RBF kernel, yielding cluster labels, confidences, cluster hierarchy, and mean feature values. For the Do7^^^^4 OR ti:\4^^^^8 data, the paper reports ^^^^4all:\4^^^^5 clusters, 9^^^^4 OR ti:\4^^^^8 source predictions, and about $n=1.25\pm 0.06$5 accuracy by the authors’ assessment; for the A^^^^4 OR abs:\4 OR ti:\4query4^^^^ case, the reported accuracy is about $n=1.25\pm 0.06$6 (&&&^^^^4 OR ti:\4^^^^7&&&).

In large-scale sensor networks, clustering is introduced because direct distributed source coding over hundreds of correlated sensors is computationally intractable. The sensors observe correlated Gaussian source samples $n=1.25\pm 0.06$7, and the network is partitioned by source-optimized hierarchical clustering that minimizes the Kullback-Leibler distance between the true joint density and an approximating factorized density. Merges are selected using the differential KLD benefit

$n=1.25\pm 0.06$8

and the final hierarchy is pruned to clusters of bounded size $n=1.25\pm 0.06$9. The clusters are then linked by a minimum-cost directed spanning tree for factor-graph decoding. Reported complexity estimates are $\left[\nu^\beta B(\nu,T_{\rm eff})\right]^2$^^^^4query4^^^^ for source-optimized clustering, $\left[\nu^\beta B(\nu,T_{\rm eff})\right]^2$^^^^4all:\4^^^^ for source-optimized linking, and $\left[\nu^\beta B(\nu,T_{\rm eff})\right]^2$^^^^4 OR ti:\4^^^^ or $\left[\nu^\beta B(\nu,T_{\rm eff})\right]^2$^^^^4 OR abs:\4^^^^ for sum-product decoding, depending on whether the factor graph is cycle-free or iterative (0809.1330).

In linked data, clustering replaces a purely pairwise link-discovery view with holistic clusters of entities that represent the same real-world object across many sources. The pipeline preprocesses input mappings, computes connected components as initial clusters, decomposes them by semantic type and similarity, constructs cluster representatives, and then iteratively merges similar clusters in Apache Flink/Gelly. The result is both a fused representation and a mechanism for identifying erroneous links and many new links. On a manually curated geographic benchmark, the paper reports $\left[\nu^\beta B(\nu,T_{\rm eff})\right]^2$4 recall, $\left[\nu^\beta B(\nu,T_{\rm eff})\right]^2$5 precision, and $\left[\nu^\beta B(\nu,T_{\rm eff})\right]^2$6 F^^^^4all:\4^^^^ for the benchmark setting; in the music domain, holistic clustering improves from $\left[\nu^\beta B(\nu,T_{\rm eff})\right]^2$7, $\left[\nu^\beta B(\nu,T_{\rm eff})\right]^2$8, $\left[\nu^\beta B(\nu,T_{\rm eff})\right]^2$9 on input links to $\beta=2.20\pm 0.07$^^^^4query4^^^^, $\beta=2.20\pm 0.07$^^^^4all:\4^^^^, $\beta=2.20\pm 0.07$^^^^4 OR ti:\4^^^^ (&&&^^^^4 OR ti:\4^^^^9&&&).

In multiple-source detection on networks, source clustering refers to partitioning infected subnetworks so that multiple origins of diffusion can be identified. The proposed method replaces node clustering with edge clustering inside Community-based Label Propagation. The infected graph $\beta=2.20\pm 0.07$^^^^4 OR abs:\4^^^^ is extended with uninfected boundary nodes to form $\beta=2.20\pm 0.07$4, edges are clustered by automated Latent Space Edge Clustering, and an initial label matrix is propagated by

$\beta=2.20\pm 0.07$5

with $\beta=2.20\pm 0.07$6. Candidate sources are then selected cluster-by-cluster from the converged labels. On ADD HEALTH social networks, the method achieves superior F^^^^4all:\4^^^^-Measure relative to Louvain and Leading Eigenvector clustering, especially in overlapping source regions where node clustering overestimates the number of clusters (&&&^^^^4 OR abs:\4query4^^^^&&&).

6. Recurring formulations and methodological contrasts

Several works cast source clustering as a graph optimization problem. Dominant Set clustering represents data as an edge-weighted graph $\beta=2.20\pm 0.07$7 with affinity matrix $\beta=2.20\pm 0.07$8 and solves

$\beta=2.20\pm 0.07$9

typically by replicator dynamics

$T_{\rm eff}=9.7\,{\rm K}$^^^^4query4^^^^

The support of the converged probability vector is interpreted as one cluster, removed, and the procedure repeats. The method is rooted in evolutionary game theory and is presented as generalizing maximal cliques to the edge-weighted case (&&&^^^^4 OR abs:\4all:\4^^^^&&&).

A different graph-based formulation appears in crowdsourced clustering from relative distance comparisons. Here the primitive datum is a triplet $T_{\rm eff}=9.7\,{\rm K}$^^^^4all:\4^^^^ interpreted as

$T_{\rm eff}=9.7\,{\rm K}$^^^^4 OR ti:\4^^^^

with $T_{\rm eff}=9.7\,{\rm K}$^^^^4 OR abs:\4^^^^ the outlier. The objective is to find a clustering function $T_{\rm eff}=9.7\,{\rm K}$4 minimizing the number of unsatisfied triplets,

$T_{\rm eff}=9.7\,{\rm K}$5

After removing a vertex cover of the inconsistency graph, the cleaned triplets can be mapped to a standard weighted correlation-clustering instance, yielding an $T_{\rm eff}=9.7\,{\rm K}$6 approximation algorithm. The paper also gives a practical local-search heuristic, with Ls-AD-VC as the emphasized variant (&&&^^^^4 OR abs:\4 OR ti:\4^^^^&&&).

When multiple data sources measure the same objects, consensus rather than direct merging becomes central. Bayesian Consensus Clustering introduces an overall clustering $T_{\rm eff}=9.7\,{\rm K}$7 and source-specific clusterings $T_{\rm eff}=9.7\,{\rm K}$8, linked through adherence parameters $T_{\rm eff}=9.7\,{\rm K}$9 by

PRESERVED_PLACEHOLDER_^^^^4all:\4query4query4^^^^

and performs Gibbs sampling with per-iteration cost PRESERVED_PLACEHOLDER_^^^^4all:\4query4all:\4^^^^. Multi-source Multi-view Clustering treats the views within a source as a cohesive unit, learns source-level consensus embeddings PRESERVED_PLACEHOLDER_^^^^4all:\4query4 OR ti:\4^^^^, penalizes cross-source discrepancy through partial mappings PRESERVED_PLACEHOLDER_^^^^4all:\4query4 OR abs:\4^^^^, and iteratively infers unknown cross-source similarities; the reported experiments converge in fewer than ^^^^4 OR ti:\4query4^^^^ outer iterations (&&&^^^^4 OR abs:\4 OR abs:\4^^^^&&&, &&&^^^^4all:\4^^^^6&&&).

Taken together, these works suggest that source clustering problems are organized by a small set of recurring design choices. One choice is whether the source is itself an object to be clustered, as in source-code changes, linked-data entities, or aeroacoustic sources, or whether source structure acts as guidance, as in source-private or source-data-absent adaptation. A second choice is the similarity primitive: power spectra, cosine profiles, optimal-transport costs, call-graph weights, KLD merge costs, triplet constraints, or affinity graphs. A third choice is the intended output: a contaminant template, a bias calibration, a consensus partition, a subsystem tree, a fused linked-data cluster, or a ranked set of candidate diffusion sources. The term is therefore best understood as a family resemblance across domains rather than a single standardized clustering doctrine.