# Clustering Algorithms for Single-Cell Proteomics: A Comparison of PhenoGraph, FlowSOM, and k-Means

Single-cell proteomics generates high-dimensional measurements of protein expression across thousands to millions of individual cells. Analysts must partition these cells into biologically meaningful populations to identify cell types, states, and rare subsets. This article compares three widely used clustering algorithms, PhenoGraph, FlowSOM, and k-Means, for single-cell proteomics datasets derived from CyTOF and single-cell mass spectrometry platforms. The practical outcome is a decision framework for selecting an algorithm based on dataset size, expected population structure, computational resources, and downstream analysis requirements.

## Scope and Reader Context

This comparison targets biology students, researchers, laboratory professionals, and life-science practitioners who generate or analyze single-cell proteomics data. The term single-cell proteomics here covers two measurement modalities. CyTOF, also called mass cytometry, uses metal-tagged antibodies to measure 30 to 50 protein targets per cell. Single-cell mass spectrometry measures peptides or proteins directly, typically with lower cell throughput but higher molecular specificity. Both modalities produce data matrices where rows are cells and columns are measured protein features. Clustering assigns each cell to a group, and the resulting cluster labels become the basis for population identification, differential abundance testing, and trajectory inference.

The three algorithms compared here represent distinct families. k-Means is a centroid-based partitional method that has been used for decades in cytometry analysis. FlowSOM uses self-organizing maps followed by consensus clustering and is designed for high-throughput flow and mass cytometry data. PhenoGraph constructs a nearest-neighbor graph and applies community detection to find populations. Each algorithm makes different assumptions about cluster shape, density, and separability, and these assumptions matter when applied to real proteomics data.

A systematic benchmark of 28 clustering algorithms on 10 paired transcriptomic and proteomic datasets found that no single method performs best across all scenarios. The benchmark identified FlowSOM as a top performer across both omics types with excellent robustness, while community detection methods such as PhenoGraph showed strengths in specific contexts. These findings support a practical approach where analysts match algorithm choice to data characteristics instead of defaulting to one method.

## Data Characteristics That Influence Clustering Performance

Single-cell proteomics data differ from transcriptomic data in ways that directly affect clustering algorithm behavior. Protein measurements are bounded, often transformed, and subject to different noise structures than RNA counts. Understanding these characteristics is necessary before selecting an algorithm.

### Dimensionality and Feature Count

CyTOF panels typically measure 30 to 50 proteins per cell. Single-cell mass spectrometry experiments may quantify hundreds of proteins but often with substantial missing values. The benchmark study noted that differences in feature dimensions and data quality between single-cell modalities pose challenges for clustering. High-dimensional spaces create problems for distance-based algorithms because the concept of nearest neighbors becomes less meaningful as dimensions increase. k-Means is particularly sensitive to this issue because it relies on Euclidean distance to assign cells to centroids. FlowSOM mitigates this through self-organizing map training, which projects high-dimensional data onto a lower-dimensional grid before clustering. PhenoGraph computes pairwise similarities between cells and therefore also faces computational challenges as dimensionality grows, though the graph structure can capture local relationships that global distance metrics miss.

### Data Distribution and Transformation

Protein expression data from CyTOF are typically transformed using arcsinh or similar variance-stabilizing transformations before analysis. The choice of transformation changes the data distribution and therefore affects clustering results. The benchmark study emphasized that differences in data distribution between modalities require careful method selection. k-Means assumes roughly spherical clusters with similar variance across features. FlowSOM and PhenoGraph make fewer distributional assumptions because they operate on topological relationships instead of parametric models. For single-cell mass spectrometry data, where protein measurements may span several orders of magnitude and include zeros from missing detection, transformation choices become even more consequential.

### Sparse and Missing Data

Single-cell mass spectrometry frequently produces sparse data matrices where many protein measurements are missing or below detection limits. The scMNMF study noted that high-dimensional and sparse characteristics of single-cell multi-omics data lead to generally poor clustering performance with many algorithms. k-Means cannot handle missing values directly and requires imputation or feature filtering before clustering. FlowSOM also requires a complete data matrix. PhenoGraph can be adapted to handle missingness through appropriate distance calculations, but the choice of distance metric becomes critical. Analysts working with sparse proteomics data should evaluate whether their chosen algorithm can accommodate missing values or whether preprocessing must include imputation.

### Cell Type Granularity

The benchmark study discussed the impact of cell type granularity on clustering performance. Granularity refers to the level of detail in population structure, from broad lineages to fine subtypes. Some algorithms resolve rare populations better than others. PhenoGraph is known for identifying rare cell types because community detection on a nearest-neighbor graph can isolate small, dense groups. FlowSOM with appropriate meta-cluster settings can also resolve fine populations, but the number of meta-clusters must be specified or optimized. k-Means tends to split large populations and merge rare ones because it optimizes global variance instead of local density. Analysts studying rare cell populations should prioritize algorithms with demonstrated sensitivity to small clusters.

## Algorithm Descriptions and Operational Principles

Each algorithm implements a distinct mathematical strategy for partitioning cells. This section describes the operational principles of k-Means, FlowSOM, and PhenoGraph in the context of single-cell proteomics analysis.

### k-Means Clustering

k-Means partitions cells into k clusters by minimizing the within-cluster sum of squares. The algorithm initializes k centroids, assigns each cell to the nearest centroid, recomputes centroids as the mean of assigned cells, and repeats until convergence. The analyst must specify k in advance, which is a major limitation for exploratory analysis where the number of cell populations is unknown.

For single-cell proteomics, k-Means has several practical considerations. The algorithm is computationally efficient and scales to millions of cells. It works well when populations are roughly spherical and well separated. However, it struggles with populations of different sizes, elongated shapes, or overlapping distributions. The benchmark study found that k-Means and similar centroid-based methods were generally outperformed by graph-based and self-organizing map approaches for proteomics data. The requirement to specify k makes k-Means less suitable for discovery-oriented analysis, though it can be useful when the expected number of populations is known from prior experiments or biological knowledge.

### FlowSOM

FlowSOM uses a two-stage approach. First, a self-organizing map trains on the data to produce a grid of nodes that represent the data distribution. Second, the nodes are clustered using hierarchical consensus clustering to produce meta-clusters that correspond to cell populations. The self-organizing map preserves topological relationships in the data, which helps maintain population structure even when clusters overlap.

FlowSOM was designed specifically for flow cytometry and mass cytometry data, and the benchmark study identified it as a top performer across both transcriptomic and proteomic datasets with excellent robustness. The algorithm handles large datasets efficiently because the self-organizing map reduces the effective number of data points before clustering. FlowSOM requires the analyst to specify the grid size and the number of meta-clusters, though the latter can be estimated using the elbow method on the consensus clustering results. The algorithm is available through the [Bioconductor project](https://bioconductor.org/), which provides documented workflows for cytometry analysis.

### PhenoGraph

PhenoGraph constructs a k-nearest-neighbor graph where each cell is connected to its nearest neighbors based on a chosen distance metric. The algorithm then applies community detection, typically using the Louvain method, to partition the graph into clusters. This approach identifies groups of cells that are more densely connected to each other than to the rest of the graph.

PhenoGraph does not require the analyst to specify the number of clusters, which is a significant advantage for exploratory analysis. The algorithm is sensitive to the choice of k for the nearest-neighbor graph and to the distance metric used. The benchmark study noted that community detection-based methods offer specific strengths, particularly for identifying populations with complex shapes or rare cell types. PhenoGraph can be computationally intensive for very large datasets because the graph construction step scales quadratically with cell number, though approximate nearest-neighbor methods can reduce this burden.

## At a Glance: Algorithm Comparison for Single-Cell Proteomics

The following table summarizes key operational characteristics of the three algorithms for single-cell proteomics analysis.

| Feature | k-Means | FlowSOM | PhenoGraph |
|---------|---------|---------|------------|
| Cluster number specification | Required in advance | Meta-cluster count specified or optimized | Not required, determined by community detection |
| Computational scaling | Efficient for millions of cells | Efficient, self-organizing map reduces data before clustering | Graph construction can be intensive for large datasets |
| Handling of rare populations | Poor, tends to merge small clusters | Good with appropriate meta-cluster settings | Excellent, isolates dense local groups |
| Sensitivity to data distribution | Assumes spherical clusters with similar variance | Robust to distributional differences, topology-based | Robust, graph structure captures local relationships |
| Missing data handling | Requires complete matrix or imputation | Requires complete matrix or imputation | Can adapt with appropriate distance metrics |
| Benchmark performance on proteomics | Generally outperformed by other methods | Top performer with excellent robustness | Strong for specific contexts, community detection strengths |
| Typical use case | Known population count, well-separated groups | High-throughput cytometry, large datasets | Exploratory analysis, rare cell discovery |

## Practical Workflow for Algorithm Selection

Selecting a clustering algorithm requires a structured workflow that accounts for data characteristics, analysis goals, and computational resources. The following steps provide a practical framework for single-cell proteomics analysis.

### Step 1: Assess Data Quality and Completeness

Before clustering, evaluate the data matrix for missing values, batch effects, and technical variation. For CyTOF data, check antibody panel design and signal stability across acquisition runs. For single-cell mass spectrometry data, assess the proportion of missing protein measurements and decide whether to filter features, impute values, or use algorithms that tolerate missingness. The [NCBI Data Resources](https://www.ncbi.nlm.nih.gov/) provide access to public single-cell datasets that can be used to test preprocessing decisions before applying them to experimental data.

### Step 2: Define Population Structure Expectations

Determine whether the analysis aims to identify known cell populations, discover novel subsets, or characterize rare cells. If the expected number of populations is known from prior experiments, k-Means may be sufficient. If the goal is discovery, PhenoGraph or FlowSOM with optimized meta-cluster counts is more appropriate. The benchmark study found that cell type granularity affects clustering performance, so the expected level of detail should inform algorithm choice.

### Step 3: Apply Appropriate Transformations and Scaling

Transform protein expression values using variance-stabilizing transformations appropriate for the platform. For CyTOF, arcsinh transformation with a cofactor of 5 is standard practice. For single-cell mass spectrometry, consider log transformation or other approaches that handle the dynamic range of protein measurements. Scale features to comparable ranges when using distance-based algorithms such as k-Means. The [EMBL-EBI Training](https://www.ebi.ac.uk/training) program offers practical guidance on data preprocessing for single-cell analysis.

### Step 4: Run Multiple Algorithms and Compare Results

Do not rely on a single algorithm. Run at least two clustering methods and compare the resulting population assignments. The benchmark study emphasized that existing methods have complementary strengths and limitations, and that integrating results from multiple approaches provides more reliable population identification. For example, use PhenoGraph to identify rare populations and FlowSOM to confirm major lineages. Compare cluster boundaries and assess whether populations identified by one algorithm are split or merged by another.

### Step 5: Validate Clusters with Biological Markers

Clustering results should be validated against known biological markers. For CyTOF data, check whether clusters express expected combinations of surface or intracellular proteins. For single-cell mass spectrometry data, verify that clusters show coherent protein expression profiles consistent with known cell types. The HematoMap study demonstrated the value of mapping cells onto a curated reference hierarchy to validate clustering results and identify lineage aberrations. This approach can be adapted to other tissue types when reference atlases are available.

### Step 6: Evaluate Stability and Robustness

Assess whether clustering results are stable across parameter choices and subsampling. Run the algorithm with different random seeds, different numbers of nearest neighbors for PhenoGraph, or different meta-cluster counts for FlowSOM. The benchmark study evaluated robustness using simulated datasets and found that FlowSOM offered excellent robustness. Analysts should document parameter sensitivity and report whether conclusions depend on specific parameter choices.

### Step 7: Document and Report Parameters

Record all preprocessing steps, algorithm parameters, and software versions. Reproducibility requires complete documentation of the analysis pipeline. The [nf-core documentation](https://nf-co.re/docs) provides standards for reproducible workflow configuration that can be applied to single-cell proteomics analysis. The [Galaxy Training Network](https://training.galaxyproject.org/) offers tutorials on creating reproducible analysis workflows that can be shared with collaborators.

## Records and Measurements for Clustering Analysis

Maintaining detailed records of clustering analysis is essential for reproducibility and for troubleshooting when results are unexpected. The following measurements should be recorded for each clustering run.

### Data Preprocessing Records

Document the raw data source, including accession numbers for public datasets or instrument files for experimental data. Record the transformation applied, including the transformation type and parameters. Note any feature filtering steps, including the criteria used to remove proteins or cells. Record the final dimensions of the data matrix used for clustering.

### Algorithm Parameters

For k-Means, record the number of clusters k, the initialization method, and the number of random starts. For FlowSOM, record the grid dimensions, the number of meta-clusters, and the consensus clustering parameters. For PhenoGraph, record the number of nearest neighbors k, the distance metric, and the community detection algorithm. The [Bioconductor project](https://bioconductor.org/) provides documentation for each algorithm that specifies available parameters and their defaults.

### Performance Metrics

Record the running time and peak memory usage for each clustering run. The benchmark study evaluated these metrics across 28 algorithms and found substantial variation. Time-efficient methods such as TSCAN, SHARP, and MarkovHC were recommended for users prioritizing speed, while memory-efficient methods such as scDCC and scDeepCluster were recommended for users with limited computational resources. These metrics help analysts plan computational requirements for large datasets.

### Cluster Quality Metrics

Record internal validation metrics such as silhouette width, Davies-Bouldin index, or Calinski-Harabasz index. These metrics provide quantitative measures of cluster separation and compactness. When reference labels are available, record external validation metrics such as adjusted Rand index or normalized mutual information. The benchmark study used multiple metrics to evaluate clustering performance, recognizing that no single metric captures all aspects of cluster quality.

### Population Composition Records

For each cluster, record the number of cells, the median expression of key marker proteins, and the proportion of cells from each sample or condition. These records support downstream differential abundance analysis and help identify batch effects or technical artifacts that may influence clustering.

## Common Failure Patterns in Single-Cell Proteomics Clustering

Several recurring problems appear when clustering single-cell proteomics data. Recognizing these failure patterns helps analysts diagnose issues and adjust their approach.

### Overclustering and Underclustering

Overclustering occurs when a single biological population is split into multiple clusters. This often happens when k-Means is used with too many clusters or when FlowSOM meta-cluster counts are set too high. Underclustering occurs when distinct populations are merged, which can happen when PhenoGraph uses too few nearest neighbors or when FlowSOM meta-cluster counts are too low. The benchmark study noted that cell type granularity affects clustering performance, and analysts should compare results across a range of parameter values to identify stable population structure.

### Batch Effects Mistaken for Biological Variation

Technical variation between acquisition runs or sample batches can create artificial clusters that do not correspond to biological populations. This is a particular risk in CyTOF data, where signal drift and reagent lot changes can introduce systematic variation. The DEMOC study addressed this challenge by integrating transcriptomic and proteomic data to leverage complementary information and improve clustering stability. Analysts should examine whether clusters correspond to batches instead of biological conditions and apply batch correction methods when necessary.

### Rare Population Loss

Rare cell populations are often missed by clustering algorithms that optimize global criteria. k-Means is particularly prone to this failure because it assigns cells to the nearest centroid, and rare populations may not generate their own centroid. PhenoGraph is more sensitive to rare populations because community detection can identify small, dense groups. The benchmark study found that community detection-based methods offer specific strengths, and analysts studying rare cells should prioritize these methods.

### Sensitivity to Distance Metric Choice

The choice of distance metric substantially affects clustering results, particularly for PhenoGraph and k-Means. Euclidean distance is common but may not be appropriate for high-dimensional proteomics data where different proteins have different variances. Correlation-based distances can capture expression pattern similarity but may be sensitive to noise. The HematoMap study used cosine distance to assess similarities between leukemic cells and normal hematopoietic cells, demonstrating that distance metric choice should be tailored to the biological question.

### Computational Resource Exhaustion

Large single-cell proteomics datasets can exhaust available memory or require excessive computation time. PhenoGraph graph construction becomes computationally expensive for datasets with millions of cells. k-Means scales well but may require many iterations for convergence. FlowSOM is generally efficient because the self-organizing map reduces the data before clustering. The benchmark study provided guidance on memory-efficient and time-efficient methods, and analysts should consider these tradeoffs when planning analyses.

## Limitations of Clustering-Based Population Identification

Clustering algorithms partition cells based on measured protein expression, but the resulting clusters do not always correspond to biologically meaningful cell types. Several limitations should be considered when interpreting clustering results.

### Clusters Are Data-Derived, Not Biologically Defined

Clustering identifies groups of cells with similar protein expression profiles, but these groups may not correspond to established cell types. Cells in different functional states may have similar expression profiles, and cells of the same type may be split across clusters due to continuous variation. The HematoMap study addressed this limitation by mapping cells onto a curated reference hierarchy of normal hematopoiesis, providing biological context for clustering results. Analysts should validate clusters against known markers and consider whether cluster boundaries align with biological distinctions.

### Protein Panel Coverage Limits Resolution

The number of proteins measured determines the resolution of population identification. CyTOF panels with 30 to 50 markers can distinguish major immune lineages but may not resolve fine subtypes that differ in proteins not included in the panel. Single-cell mass spectrometry can measure more proteins but often with lower sensitivity and higher missingness. The scMNMF study noted that high-dimensional and sparse characteristics of single-cell multi-omics data limit clustering performance. Analysts should recognize that clustering results are constrained by the measured protein features.

### Continuous Biological Variation Is Discretized

Clustering imposes discrete boundaries on what may be continuous biological variation. Cell differentiation and activation states often form continua instead of discrete populations. Clustering forces cells into distinct groups, which can obscure gradual transitions. Trajectory inference methods may be more appropriate for studying continuous processes, but clustering is often a necessary first step for identifying the major states before trajectory analysis.

### Algorithm Choice Influences Results

Different algorithms can produce substantially different cluster assignments for the same dataset. The benchmark study found modality-specific strengths and limitations across 28 algorithms, highlighting the complementary nature of existing methods. Analysts should not treat clustering results as ground truth but rather as hypotheses about population structure that require validation. Running multiple algorithms and comparing results provides a more robust basis for biological interpretation.

## Quality Controls and Validation Approaches

Implementing quality controls throughout the clustering workflow reduces the risk of spurious findings and improves the reliability of population identification.

### Pre-Clustering Quality Controls

Filter cells based on quality metrics before clustering. For CyTOF data, remove cells with low total signal, high background, or abnormal event length. For single-cell mass spectrometry data, filter cells with low protein detection rates or excessive missing values. The [Galaxy Training Network](https://training.galaxyproject.org/) provides tutorials on quality control for single-cell data that can be adapted to proteomics workflows.

### Post-Clustering Validation

Validate clusters using independent biological information. Check whether clusters express expected marker combinations. Compare cluster proportions across experimental conditions to identify biologically plausible differences. The HematoMap study demonstrated the use of a reference hierarchy to validate clustering results and identify lineage aberrations in leukemia samples. Similar approaches can be applied when reference atlases are available for the tissue or cell type under study.

### Parameter Sensitivity Analysis

Test whether clustering results are robust to parameter changes. Run the algorithm with different parameter values and assess whether major populations remain stable. The benchmark study evaluated robustness using simulated datasets and found that some methods are more robust than others. FlowSOM showed excellent robustness in the benchmark, making it a reliable choice when parameter optimization is difficult.

### Cross-Method Consistency

Compare clustering results across multiple algorithms to identify populations that are consistently detected. Populations identified by multiple methods are more likely to represent true biological structure. The DEMOC study demonstrated that integrating transcriptomic and proteomic data improves clustering stability, and similar benefits can be achieved by integrating results from multiple clustering algorithms.

## Safety and Regulatory Context for Clustering Analysis

While clustering algorithms themselves do not pose safety risks, their application in clinical or diagnostic contexts requires attention to regulatory and ethical considerations.

### Clinical Translation Considerations

Clustering results from research datasets may inform clinical decisions if validated appropriately. The HematoMap study aimed to enhance leukemia risk stratification and personalized treatments, demonstrating the translational potential of clustering-based approaches. However, any clinical application requires rigorous validation, regulatory approval, and adherence to diagnostic standards. Analysts working with clinical samples should consult institutional review boards and regulatory authorities before using clustering results for patient management.

### Data Privacy and Security

Single-cell proteomics data from human subjects contain sensitive biological information. Researchers must comply with data protection regulations and institutional policies governing human subjects research. The [NCBI Data Resources](https://www.ncbi.nlm.nih.gov/) provide controlled access to human datasets, and researchers should follow established data sharing and security protocols. The [Carpentries Lessons](https://carpentries.org/lessons) offer foundational training on responsible data management practices.

### Reproducibility Standards

Regulatory and funding agencies increasingly require reproducible analysis pipelines. The [nf-core documentation](https://nf-co.re/docs) provides standards for community pipeline development that emphasize reproducibility and configuration management. The [Galaxy Training Network](https://training.galaxyproject.org/) offers accessible training on creating reproducible workflows. Adopting these standards ensures that clustering analyses can be independently verified and replicated.

## Professional Escalation Criteria

Analysts should escalate clustering analysis issues to supervisors, collaborators, or specialized bioinformatics support when certain conditions are met.

### Escalate When Clustering Results Are Biologically Implausible

If clustering produces populations that contradict established biological knowledge, escalate the issue. This may indicate technical problems with the data, inappropriate preprocessing, or algorithm misconfiguration. The benchmark study found that different methods have modality-specific strengths and limitations, and an experienced bioinformatician can help diagnose whether results reflect biological reality or technical artifacts.

### Escalate When Computational Resources Are Insufficient

If clustering analysis exceeds available computational resources, escalate to institutional high-performance computing support. The benchmark study provided guidance on memory-efficient and time-efficient methods, and a computational specialist can help optimize the analysis pipeline. The [nf-core documentation](https://nf-co.re/docs) offers configuration guidance for running workflows on different computing infrastructures.

### Escalate When Clinical Decisions Depend on Results

If clustering results will inform clinical decisions, escalate to appropriate clinical and regulatory experts. The HematoMap study demonstrated the potential for clustering-based tools to enhance leukemia risk stratification, but clinical application requires careful validation and regulatory oversight. Analysts should not make clinical recommendations based on clustering results without appropriate expertise and oversight.

### Escalate When Reproducibility Is Questioned

If collaborators or reviewers question the reproducibility of clustering results, escalate to bioinformatics support to ensure the analysis pipeline is fully documented and version-controlled. The [Carpentries Lessons](https://carpentries.org/lessons) provide foundational training on version control and reproducible computing practices that support this process.

## A Practical Decision Framework for Matching Algorithm Choice to Dataset Characteristics

Selecting between PhenoGraph, FlowSOM, and k-Means requires a structured decision process that goes beyond general recommendations. The benchmark study of 28 clustering algorithms on 10 paired transcriptomic and proteomic datasets found that no single method performs best across all scenarios, and that modality-specific strengths and limitations require analysts to match algorithm choice to specific data characteristics. This section provides a decision framework based on measurable dataset properties, analysis goals, and validation requirements.

### Primary Decision Criteria

The first decision point concerns the number of cell populations expected in the dataset. If prior experiments or biological knowledge establish a clear population count, k-Means becomes a viable option because the analyst can specify k directly. If the analysis is exploratory and the population structure is unknown, PhenoGraph or FlowSOM should be used because they do not require advance specification of cluster numbers. The benchmark study found that cell type granularity affects clustering performance, meaning the expected level of detail in population structure should inform algorithm choice.

The second decision point concerns dataset size and computational resources. k-Means scales efficiently to millions of cells and requires minimal memory. FlowSOM also handles large datasets efficiently because the self-organizing map reduces the effective number of data points before clustering. PhenoGraph graph construction becomes computationally intensive for datasets exceeding approximately 500,000 cells, though approximate nearest-neighbor methods can reduce this burden. The benchmark study evaluated peak memory and running time across 28 algorithms and found substantial variation, with some methods recommended for time efficiency and others for memory efficiency. Analysts should estimate dataset size and available computational resources before selecting an algorithm.

The third decision point concerns the expected population structure. If the dataset contains rare cell populations that are biologically important, PhenoGraph is the preferred choice because community detection on a nearest-neighbor graph can isolate small, dense groups. If the dataset contains overlapping populations with gradual transitions, FlowSOM may perform better because the self-organizing map preserves topological relationships. If populations are expected to be well separated and roughly spherical, k-Means can produce acceptable results with less computational overhead.

### Decision Matrix for Common Scenarios

The following decision matrix translates dataset characteristics into algorithm recommendations. This matrix is based on the operational principles of each algorithm and the findings of the benchmark study.

| Dataset Scenario | Recommended Algorithm | Primary Rationale |
|-----------------|----------------------|-------------------|
| Known population count, well-separated groups, large dataset | k-Means | Efficient scaling, direct specification of k |
| Unknown population structure, rare cells important | PhenoGraph | Community detection identifies dense local groups |
| High-throughput CyTOF, large cell numbers, robust performance needed | FlowSOM | Top benchmark performer with excellent robustness |
| Sparse single-cell mass spectrometry data | PhenoGraph with adapted distance metric | Can accommodate missingness through distance calculations |
| Mixed populations with overlapping boundaries | FlowSOM | Self-organizing map preserves topological relationships |
| Limited computational resources | k-Means or FlowSOM | Lower memory footprint than graph-based methods |
| Discovery-oriented analysis with unknown granularity | PhenoGraph or FlowSOM | No advance cluster number specification required |

### Parameter Selection and Sensitivity Testing

Each algorithm requires parameter choices that substantially affect clustering results. The decision framework should include a parameter sensitivity testing protocol to ensure that conclusions do not depend on arbitrary parameter values.

For k-Means, the number of clusters k is the primary parameter. The elbow method on the within-cluster sum of squares, the silhouette method, or the gap statistic can provide estimates, but these methods give approximations instead of definitive answers. Analysts should run k-Means across a range of k values and examine whether population assignments remain stable across adjacent values. If small changes in k produce dramatically different cluster assignments, the data may not have well-defined cluster structure, and a graph-based or self-organizing map approach may be more appropriate.

For FlowSOM, the grid dimensions and the number of meta-clusters are the primary parameters. The self-organizing map grid size determines the resolution of the topological representation, with larger grids capturing finer structure at higher computational cost. The number of meta-clusters can be estimated using the elbow method on the consensus clustering results. The benchmark study found that FlowSOM offered excellent robustness, suggesting that results are relatively stable across parameter choices, but analysts should still document the parameter values used and test sensitivity.

For PhenoGraph, the number of nearest neighbors k and the distance metric are the primary parameters. Smaller k values produce more local neighborhoods and can identify finer populations, while larger k values produce smoother neighborhoods and may merge rare populations. The choice of distance metric, whether Euclidean, cosine, or correlation-based, affects which cells are considered similar. The HematoMap study used cosine distance to assess similarities between leukemic cells and normal hematopoietic cells, demonstrating that distance metric choice should be tailored to the biological question. Analysts should test PhenoGraph across a range of k values and distance metrics to identify stable population structure.

### Integration with Multi-Omics Data

The decision framework becomes more complex when single-cell proteomics data are analyzed alongside transcriptomic or other omics data. The benchmark study explored the benefits of integrating omics information for clustering tasks and found that integration can improve clustering performance. The DEMOC study demonstrated that a deep embedded multi-omics clustering approach that considers both transcriptomic and proteomic data outperformed single-omic clustering methods on CITE-seq data. The scMNMF study presented a matrix factorization approach for joint dimensionality reduction and clustering of single-cell multi-omics data.

When multi-omics data are available, analysts should consider whether to cluster each modality separately and compare results, or to integrate modalities before clustering. The benchmark study found that existing single-omics clustering schemes can be applied to integrated features, but performance depends on the integration method used. The decision framework should include an assessment of whether multi-omics integration is expected to improve population identification for the specific biological question. If the proteomic data alone provide sufficient resolution for the populations of interest, single-modality clustering may be simpler and more interpretable. If complementary information from transcriptomic data is expected to resolve populations that proteomic data alone cannot distinguish, integration should be considered.

### Implementation Steps for the Decision Framework

The following steps provide a practical implementation protocol for the decision framework.

First, characterize the dataset by recording the number of cells, the number of protein features, the proportion of missing values, and the expected population structure based on prior knowledge. This characterization directly informs algorithm selection.

Second, estimate computational requirements by considering dataset size and available resources. The benchmark study provided guidance on memory-efficient methods such as scDCC and scDeepCluster and time-efficient methods such as TSCAN, SHARP, and MarkovHC. While these specific methods are not the focus of this comparison, the principle of matching algorithm choice to computational constraints applies equally to PhenoGraph, FlowSOM, and k-Means.

Third, select a primary algorithm based on the decision matrix and run it with default or recommended parameters. Document all parameter values and preprocessing steps.

Fourth, run at least one additional algorithm from a different family to provide a cross-method comparison. For example, if FlowSOM is the primary algorithm, run PhenoGraph as a comparison. The benchmark study emphasized that existing methods have complementary strengths and limitations, and that integrating results from multiple approaches provides more reliable population identification.

Fifth, compare cluster assignments across algorithms and identify populations that are consistently detected. Populations identified by multiple methods are more likely to represent true biological structure. Investigate discrepancies between algorithms to determine whether they reflect parameter sensitivity, algorithm assumptions, or genuine biological complexity.

Sixth, validate the final clustering results using known biological markers and, when available, reference atlases. The HematoMap study demonstrated the value of mapping cells onto a curated reference hierarchy to validate clustering results and identify lineage aberrations. Similar approaches can be applied when reference atlases are available for the tissue or cell type under study.

### Recording Framework Decisions

The decision framework should be documented as part of the analysis record. Record the dataset characteristics that informed algorithm selection, including cell count, feature count, missing value proportion, and expected population structure. Record the algorithm chosen, the parameters used, and the rationale for the choice. Record the results of parameter sensitivity testing, including the range of parameter values tested and whether population assignments remained stable. Record the results of cross-method comparisons, including which populations were consistently detected across algorithms and which differed.

This documentation supports reproducibility and provides a basis for troubleshooting when results are unexpected. The [nf-core documentation](https://nf-co.re/docs) provides standards for reproducible workflow configuration that can be applied to single-cell proteomics analysis. The [Galaxy Training Network](https://training.galaxyproject.org/) offers tutorials on creating reproducible analysis workflows that can be shared with collaborators. The [Bioconductor project](https://bioconductor.org/) provides documentation for each algorithm that specifies available parameters and their defaults.

### Troubleshooting the Decision Framework

When clustering results do not match biological expectations, the decision framework itself should be examined. The following troubleshooting steps address common issues.

If the selected algorithm produces biologically implausible populations, first check whether the data preprocessing steps were appropriate. Transformation choices, feature filtering, and scaling decisions all affect clustering results. The benchmark study emphasized that differences in data distribution between modalities require careful method selection, and preprocessing choices should be revisited before changing algorithms.

If parameter sensitivity testing reveals unstable population assignments, the data may not have well-defined cluster structure. In this case, consider whether the measured protein features provide sufficient resolution for the populations of interest. The scMNMF study noted that high-dimensional and sparse characteristics of single-cell multi-omics data lead to generally poor clustering performance, and analysts should recognize that clustering results are constrained by the measured protein features.

If cross-method comparisons reveal substantial disagreement between algorithms, investigate the source of the disagreement. Different algorithms make different assumptions about cluster shape and density, and populations that are detected by some methods but not others may represent borderline cases that require biological validation. The benchmark study found modality-specific strengths and limitations across 28 algorithms, and no single method should be treated as ground truth.

If computational resources are insufficient for the selected algorithm, consider whether a more efficient algorithm can address the same biological question. The benchmark study provided guidance on memory-efficient and time-efficient methods, and analysts should consider these tradeoffs when planning analyses. For very large datasets, FlowSOM may be preferable to PhenoGraph because the self-organizing map reduces the data before clustering.

### Escalation Criteria for Framework Decisions

Analysts should escalate decision framework issues to supervisors, collaborators, or specialized bioinformatics support under specific conditions. If clustering results are biologically implausible and troubleshooting does not resolve the issue, escalate to an experienced bioinformatician who can diagnose whether results reflect biological reality or technical artifacts. If computational resources are insufficient for the selected algorithm and alternative algorithms do not address the biological question, escalate to institutional high-performance computing support. If clinical decisions depend on clustering results, escalate to appropriate clinical and regulatory experts before proceeding. The HematoMap study demonstrated the potential for clustering-based tools to enhance leukemia risk stratification, but clinical application requires careful validation and regulatory oversight.

## Frequently Asked Questions

### What is the main difference between PhenoGraph, FlowSOM, and k-Means for single-cell proteomics?

PhenoGraph builds a nearest-neighbor graph and applies community detection to find densely connected groups of cells. FlowSOM trains a self-organizing map and then clusters the map nodes to identify populations. k-Means partitions cells into a specified number of clusters by minimizing within-cluster variance. The main practical difference is that PhenoGraph and FlowSOM do not require the analyst to specify the number of clusters in advance, while k-Means does. The benchmark study found that FlowSOM performed well across both transcriptomic and proteomic datasets with excellent robustness, while community detection methods such as PhenoGraph offered specific strengths.

### Which clustering algorithm should I use for CyTOF data with 40 protein markers?

FlowSOM is a strong default choice for CyTOF data because it was designed for high-throughput cytometry and performed well in the benchmark study. PhenoGraph is a good alternative when you need to identify rare populations or when you do not want to specify the number of clusters. k-Means is less suitable for CyTOF data because it requires the number of clusters in advance and tends to perform worse than graph-based or self-organizing map approaches on proteomics data.

### How do I choose the number of clusters for k-Means clustering?

The number of clusters for k-Means can be estimated using the elbow method on the within-cluster sum of squares, the silhouette method, or gap statistic. However, these methods provide estimates instead of definitive answers, and the optimal number depends on the biological question. For exploratory analysis, PhenoGraph or FlowSOM may be more appropriate because they do not require specifying the number of clusters in advance.

### Can I use these clustering algorithms on single-cell mass spectrometry data with missing values?

k-Means and FlowSOM require a complete data matrix, so missing values must be imputed or features with excessive missingness must be filtered before clustering. PhenoGraph can be adapted to handle missing values through appropriate distance calculations, but the choice of distance metric becomes critical. The scMNMF study noted that high-dimensional and sparse characteristics of single-cell multi-omics data lead to generally poor clustering performance, so careful preprocessing is essential.

### How do I validate that my clustering results represent real cell populations?

Validate clusters using known biological markers. Check whether clusters express expected combinations of proteins for the cell types you expect to find. Compare cluster proportions across experimental conditions to identify biologically plausible differences. The HematoMap study demonstrated the value of mapping cells onto a curated reference hierarchy to validate clustering results and identify lineage aberrations.

### What should I do if different clustering algorithms produce different results?

Different algorithms make different assumptions about cluster shape and density, so divergent results are expected. Run multiple algorithms and compare results to identify populations that are consistently detected across methods. The benchmark study found that existing methods have complementary strengths and limitations, and integrating results from multiple approaches provides more reliable population identification.

### How large a dataset can each algorithm handle?

k-Means scales efficiently to millions of cells. FlowSOM is also efficient because the self-organizing map reduces the data before clustering. PhenoGraph graph construction can become computationally intensive for very large datasets, though approximate nearest-neighbor methods can reduce the burden. The benchmark study evaluated running time and peak memory across 28 algorithms and found substantial variation, with some methods recommended for time efficiency and others for memory efficiency.

### Do I need to normalize or transform my data before clustering?

Yes, data transformation is essential before clustering. For CyTOF data, arcsinh transformation with a cofactor of 5 is standard. For single-cell mass spectrometry data, log transformation or other approaches that handle the dynamic range of protein measurements are appropriate. Scaling features to comparable ranges is important for distance-based algorithms such as k-Means. The [EMBL-EBI Training](https://www.ebi.ac.uk/training) program offers practical guidance on data preprocessing for single-cell analysis.

## Related Bioinformatics Guides

- [Single-Cell Isolation Techniques: A Practical Comparison](/knowledge/bioinformatics/single-cell-isolation-techniques-a-practical-comparison)
- [Spatial Proteomics vs. Single-Cell Proteomics: Choosing the Right Approach](/knowledge/bioinformatics/spatial-proteomics-vs-single-cell-proteomics-choosing-the-right-approach)
- [Spatial Proteomics Method of the Year: What It Means for Your Research](/knowledge/bioinformatics/spatial-proteomics-method-of-the-year-what-it-means-for-your-research)
- [Single-Cell Genomics: From Concept to Application](/knowledge/bioinformatics/single-cell-genomics-from-concept-to-application)
- [Single-Cell Annotation: A Workflow for Cell Type Identification](/knowledge/bioinformatics/single-cell-annotation-a-workflow-for-cell-type-identification)

## References and Further Reading

- [NCBI Data Resources](https://www.ncbi.nlm.nih.gov/). National Center for Biotechnology Information.
- [EMBL-EBI Training](https://www.ebi.ac.uk/training). European Bioinformatics Institute.
- [Bioconductor](https://bioconductor.org/). Bioconductor Project.
- [Galaxy Training Network](https://training.galaxyproject.org/). Galaxy Project.
- [nf-core Documentation](https://nf-co.re/docs). nf-core.
- [The Carpentries Lessons](https://carpentries.org/lessons). The Carpentries.
- [Comparative benchmarking of single-cell clustering algorithms for transcriptomic and proteomic data.](https://pubmed.ncbi.nlm.nih.gov/40903792). Genome biology, 2025.
- [UNC93B1 promotes pancreatic cancer progression through modulation of cGAS-STING signaling.](https://pubmed.ncbi.nlm.nih.gov/41716413). Frontiers in immunology, 2026.
- [scMNMF: a novel method for single-cell multi-omics clustering based on matrix factorization.](https://pubmed.ncbi.nlm.nih.gov/38754408). Briefings in bioinformatics, 2024.
- [DEMOC: a deep embedded multi-omics learning approach for clustering single-cell CITE-seq data.](https://pubmed.ncbi.nlm.nih.gov/36047285). Briefings in bioinformatics, 2022.
- [Resolving Leukemia Heterogeneity and Lineage Aberrations with HematoMap.](https://pubmed.ncbi.nlm.nih.gov/39945785). Genomics, proteomics & bioinformatics, 2025.

> This article is educational and does not replace validated analysis plans, institutional policy, clinical interpretation, or specialist review.