
==== Front
Bioinformatics
Bioinformatics
bioinformatics
Bioinformatics
1367-4803
1367-4811
Oxford University Press

10.1093/bioinformatics/btae382
btae382
Digital Health
AcademicSubjects/SCI01060
Federated unsupervised random forest for privacy-preserving patient stratification
https://orcid.org/0000-0001-7035-9535
Pfeifer Bastian Institute for Medical Informatics, Statistics and Documentation, Medical University Graz, Graz, 8010, Austria

https://orcid.org/0000-0002-5011-3068
Sirocchi Christel Department of Pure and Applied Sciences, University of Urbino, Urbino, 61029, Italy

https://orcid.org/0000-0002-2468-4086
Bloice Marcus D Institute for Medical Informatics, Statistics and Documentation, Medical University Graz, Graz, 8010, Austria

https://orcid.org/0000-0001-9824-9004
Kreuzthaler Markus Institute for Medical Informatics, Statistics and Documentation, Medical University Graz, Graz, 8010, Austria

https://orcid.org/0000-0001-5792-3971
Urschler Martin Institute for Medical Informatics, Statistics and Documentation, Medical University Graz, Graz, 8010, Austria

Corresponding author. Institute for Medical Informatics, Statistics and Documentation, Medical University of Graz, Auenbruggerplatz 2/V, 8010 Graz, Austria. E-mail: bastian.pfeifer@medunigraz.at (B.P.)
9 2024
04 9 2024
04 9 2024
40 Suppl 2 Proceedings of ECCB2024 ii198ii207
© The Author(s) 2024. Published by Oxford University Press.
2024
https://creativecommons.org/licenses/by/4.0/ This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Motivation

In the realm of precision medicine, effective patient stratification and disease subtyping demand innovative methodologies tailored for multi-omics data. Clustering techniques applied to multi-omics data have become instrumental in identifying distinct subgroups of patients, enabling a finer-grained understanding of disease variability. Meanwhile, clinical datasets are often small and must be aggregated from multiple hospitals. Online data sharing, however, is seen as a significant challenge due to privacy concerns, potentially impeding big data’s role in medical advancements using machine learning. This work establishes a powerful framework for advancing precision medicine through unsupervised random forest-based clustering in combination with federated computing.

Results

We introduce a novel multi-omics clustering approach utilizing unsupervised random forests. The unsupervised nature of the random forest enables the determination of cluster-specific feature importance, unraveling key molecular contributors to distinct patient groups. Our methodology is designed for federated execution, a crucial aspect in the medical domain where privacy concerns are paramount. We have validated our approach on machine learning benchmark datasets as well as on cancer data from The Cancer Genome Atlas. Our method is competitive with the state-of-the-art in terms of disease subtyping, but at the same time substantially improves the cluster interpretability. Experiments indicate that local clustering performance can be improved through federated computing.

Availability and implementation

The proposed methods are available as an R-package (https://github.com/pievos101/uRF)

ECCB2024
==== Body
pmc1 Introduction

Federated machine learning is crucial in preserving data privacy and security while enabling collaborative model training across decentralized devices or organizations (Brauneck et al. 2023). It empowers various stakeholders to jointly improve machine learning models without sharing sensitive data, making it ideal for applications in healthcare, where data confidentiality is paramount (Dayan et al. 2021). Disease subtyping has emerged as a pivotal strategy in precision medicine (Leng et al. 2022), aiming to unravel the inherent heterogeneity within complex disorders. Multi-omics data, encompassing genomics, transcriptomics, proteomics, and more, provides a holistic view of biological systems, offering unprecedented insights into the molecular underpinnings of diseases (Lipkova et al. 2022). Clustering techniques applied to multi-omics data have become instrumental in identifying distinct subgroups of patients, enabling a finer-grained understanding of disease variability (Rappoport and Shamir 2018). These approaches hold immense promise for tailoring treatments and interventions to the specific molecular signatures associated with each disease subtype, thereby advancing the era of personalized and targeted therapeutics.

This article introduces a multi-omics federated clustering approach utilizing unsupervised random forest to address some of the aforementioned challenges. The proposed random forest incorporates a novel unsupervised splitting rule for disease subtype discovery. At the same time, it allows the determination of cluster-specific feature importance, unraveling key molecular contributors to distinct patient groups. Moreover, our methodology is designed for federated execution, a crucial aspect in the medical domain where data privacy is an ethical necessity.

To the best of our knowledge, there is currently no existing approach designed for federated multi-omics clustering within the context of disease subtype discovery.

2 Related work

The recent years have seen a wide range of advanced methods for multi-omics clustering (Subramanian et al. 2020). Most prominent is similar network fusion (SNF) (Wang et al. 2014). For each data (omics) type, it models the similarity between patients as a network and then fuses these networks via an interchanging diffusion process. Spectral clustering is applied to the fused network to infer the final cluster assignments. A method which builds upon SNF is called NEMO and was recently introduced in Rappoport and Shamir (2019). They provide solutions to partial data involving missing values and implement a novel “eigen-gap” method (Von Luxburg 2007) to infer the optimal number of clusters. Yang et al. (2021) proposed a deep adversarial learning method for disease subtyping called subtype-GAN. Utilizing latent variables obtained from the neural network, subtype-GAN employs consensus clustering and a Gaussian mixture model to discern the molecular subtypes of tumor samples. A conceptually related method to fuse omics data was introduced by Pfeifer and Schimek (2021). The underlying late-fusion algorithm expects a set of binary matrices, reflecting the clustering solution of each omics type, of dimension n×n, where a matrix entry of one means that two samples are in the same cluster, and where n is the number of samples. Based on these matrices, the algorithm executes a standard hierarchical bottom-up procedure for building a dendrogram. At each fusion step, the algorithm can use the distances from the available binary views to fuse the samples. The final affinity of two samples is reflected by the number of iterations appearing within the same cluster while building the dendrogram. The aforementioned method was later utilized for ensemble-based multi-omics clustering (Pfeifer et al. 2023).

However, to the best of our knowledge, no approach has been developed for federated multi-omics clustering in the context of disease subtype discovery. Federated computing for random forest-based clustering is fairly straightforward and more interpretable compared to other approaches like SNF (Wang et al. 2014) and NEMO (Rappoport and Shamir 2019). The nature of random forests, which build an ensemble of decision trees independently, aligns well with the decentralized structure of federated learning.

Here, we propose federated unsupervised random forest for multi-omics clustering. We introduce a novel unsupervised splitting rule, and we showcase the ability of our method to provide cluster-specific feature importance.

3 Materials and methods

3.1 Random forest classifier

Random forests (Breiman 2001) consist of an ensemble of classification or regression trees. Each individual tree, denoted as T, represents a mapping from the feature space to the response variable. The trees are constructed independently of each other using a bootstrapped or subsampled dataset. In a tree T, any given node t corresponds to a subset, typically a hyper-rectangle, in the feature space. A split of node t divides the hyper-rectangle Rt into two separate hyper-rectangles which correspond to the left child tleft and right child tright of node t, respectively. For a specific node t in tree T, the notation N(t) denotes the number of samples that fall into the hyper-rectangle Rt and (1) E^t{y}:=1N(t)∑i:xi∈Rtyi

denotes their average response. Each tree T is grown using a recursive procedure which proceeds in two steps for each node t. First, a subset M⊂[p] of features is chosen uniformly at random. Then the optimal split variable x(t)∈M and split value z(t)∈R are determined by maximizing: (2) ΔI(t,x(t),z(t)):=I(t)−N(tleft)I(tleft)−N(tright)I(tright)N(t)

for some impurity measure I(t), typically chosen as MSE, Gini index, or entropy, where in supervised trees y serves as the response. We typically refer to ΔI(t,x(t),z(t)) as the “decrease in impurity” for node t due to x(t) and z(t).

3.2 A novel unsupervised splitting rule for random forests

In a random forest, employing an unsupervised splitting rule the response vector y is not required to build a tree. Here, we propose an unsupervised splitting rule defined as (3) ΔF(t,x(t),z(t)):=(D□(tleft)+D□(tright))/2D∇(t)

where (4) D□(t):=∑i,j(xi(t)−xj(t))2N(t)(N(t)−1), for i≠j

and (5) D∇(t):=∑i,j(xi(tleft)−xj(tright))2N(tleft)N(tright),

where x is a given candidate feature and xi, xj refers to the specific value in sample i and sample j. The above specified unsupervised splitting rule is inspired by the Fixation Index; often utilized in the field of population genomics to infer population structure (Wright 1949, Holsinger and Weir 2009). Essentially, it computes the average pairwise distances between the samples within two groups formed by a node split, divided by the average pairwise distances of the samples between the groups. Once the unsupervised random forest is built, we count the number of times two samples appear in the same leaf node. From these counts, an affinity matrix is derived which serves as an input for a hierarchical clustering algorithm.

In mathematical terms, for each tree Ti, let Ci be an n × n binary matrix, with n the number of samples. The value of Ci[j,k] is set to 1, when two samples j and k end up in the same leaf node of Ti. After training T trees, the total (non-federated) count matrix Clocal can be defined as the sum of the binary count matrices from all trees: (6) Clocal=∑i=1TCi

We normalize the total count matrix Clocal by dividing it by its maximal entry: (7) A^local=Clocalmax(Clocal)

The affinity matrix A^total can be clustered by any distance-based clustering method. Here, we employ Ward’s linkage method (Ward 1963, Murtagh and Legendre 2014) throughout the manuscript.

In case of multi-omics data, the aforementioned procedure is executed for each omics type and we calculate the element-wise sum of the derived count matrices. The resulting count matrix is again normalized by its maximum value.

3.3 Federated ensemble learning

The herein proposed ensemble classifier can be efficiently learned in a federated manner. Same as for federated supervised random forests (Hauschild et al. 2022), each participant trains a local “clusterer” comprising multiple decision trees. The trained decision trees, including their split rules, are then shared by the participants. The federated global model is a concatenation of all local trees.

Let X(k) represent the local client-specific data for client k, and Mglobal be the global federated model obtained by concatenating trees from all clients. (8) Mglobal=[T1(1),T2(1),…,TN1(1),T1(2),T2(2),…,TN2(2),…,T1(Kmax),T2(Kmax),…,TNmax(Kmax)]

Here, Nk represents the total number of trees on a specific client, and Kmax is the total number of clients. The client-specific data X(k) is propagated through Mglobal to derive a federated global affinity matrix. For each tree Ti(k) in Mglobal, the local data X(k) traverses the tree to identify the leaf nodes. The binary matrix Ci(k) is then updated based on the occurrences of pairs of samples in the same leaf node. The global federated count matrix Cglobal is the sum of binary count matrices across all trees in Mglobal: (9) Cglobal=∑k=1Kmax∑i=1NkCi(k)

The federated affinity matrix A^global is again obtained by normalizing the count matrix Cglobal by its maximum value. (10) A^gobal=Cglobalmax(Cglobal)

The federated affinity matrix A^global can be clustered by any distance-based clustering method.

3.4 Cluster-specific feature importance

Once an unsupervised random forest is trained and a cluster solution is determined, the unsupervised random forest can be used as a predictive model and the full capacity to quantify feature importance can be exploited. To this end, it is possible to derive cluster-specific feature importance in a one versus all manner given the cluster solution as the outcome class. Note, training in this case is still unsupervised, because an unsupervised splitting rule is exploited. The outcome classes are solely used to assess feature importance by labeling the samples within the nodes.

4 Evaluation strategy

4.1 Evaluation on synthetic data

The unsupervised random forest featuring a novel splitting rule, here denoted as “uRF”, was assessed for its ability to generate an affinity matrix suitable for clustering, and it was compared to Euclidean distance, a widely used, intuitive, and computationally effective method for generating affinity matrices. Euclidean distance is effective in discerning isolated compact globular structures by assuming that sample points are distributed around the mean but presents notable drawbacks, including sensitivity to scale and vulnerability to outliers. Synthetic datasets were generated to evaluate the clustering performance of the Ward linkage method on affinity matrices derived from the proposed unsupervised random forest method, Euclidean distance on non-normalized data, and Euclidean distance on standard normalized data. This evaluation encompasses scenarios where Euclidean distance is expected to perform well and those where it might face challenges. Four sets of experiments were conducted to assess clustering performance in diverse scenarios: globular clusters of equal size, globular clusters with outliers, globular clusters of varying sizes, and non-globular clusters shaped as concentric circles. Thirty synthetic datasets of two features were generated for each scenario and parameter configuration. The unsupervised random forests were trained with 500 trees, leaf node size set to 5, and one feature uniformly sampled from the feature space at each node. The performance of Ward clustering on affinity matrices obtained using the three methods was quantified using the Adjusted Rand Index (ARI).

In the first set of experiments, synthetic datasets were generated with three globular clusters of varying distances to evaluate the method with respect to the degree of separation among clusters. Each cluster comprises 100 data points distributed normally around centers located at coordinates (1, 0), (0, 1), and (1, 1). The degree of separation is controlled by a standard deviation ranging from 0.1 to 0.5 at intervals of 0.1, resulting in improved separation as the standard deviation decreases. Then, synthetic datasets with globular clusters were generated with a varying percentage of outliers ranging from 2% to 10% at intervals of 2%. Here, cluster data are positioned around the same cluster centers as in the previous case with a constant standard deviation of 0.25, while outliers are generated with centers in (3, 0), (0, 3), and (3, 3) and standard deviation of 1. Next, synthetic datasets with three globular clusters of different sizes and varying distances among clusters were generated with centers at coordinates (0, 0), (1, 1), and (−2, 2) and standard deviations equal to 0.1, 0.1 + m0.1, and 0.1 + m0.2, with m ranging from 1 to 5, so that as m decreases, the clusters become better separated while maintaining different sizes. For example, for m equal to 3, clusters have standard deviations equal to 0.1, 0.4, and 0.7, with a difference in standard deviation between each cluster and the next in size of 0.3. The final set of experiments examined the performance of the clustering methods on non-globular clusters, specifically two concentric rings centered at coordinates (0, 0). The data for the first ring was simulated with a minimum and maximum radius of 1 and 2, respectively, resulting in a width of 1. The second ring, also with a width of 1, was generated at a distance from the first ring ranging from 1 to 3 at intervals of 0.5.

4.2 Sanity checks on machine learning benchmark datasets

To further evaluate the herein proposed unsupervised splitting rule, we conducted experiments on six machine learning benchmark datasets (Table 1), which all are annotated with classification labels. We generated an affinity matrix utilizing the proposed unsupervised random forest which we used for clustering. We conducted a comparison with results obtained by calculating the affinity matrix using the Euclidean distance, once based on nonnormalized data and another time with standard normalized data. For the random forest, the default leaf node size was set to 5, the number of features sampled from the feature space was set to 2, and the number of trees was 100. We varied the number of features for building a decision tree as well as the minimum leaf size. However, the fact that only two features are sampled from the feature space results in an increased randomization in the tree-building process. Recent work on unsupervised random forests highlight the beneficial behavior of this setting when the goal is to derive an affinity matrix for unsupervised clustering (Bicego and Escolano 2021). As a performance metric accounting for cluster quality, we used ARI.

Table 1. Benchmark datasets.

				#Samples per	
Datasets	#Samples	#Features	#Cluster	Cluster	
Breast cancer	106	9	6	21, 15, 18, 16, 14, 22	
Glass	214	9	4	70, 76, 17, 51	
Ionosphere	351	34	2	225, 126	
Iris	150	4	3	50, 50, 50	
Parkinson	195	22	2	48, 147	
Wine	178	13	3	59, 71, 48	

4.3 Federated patient stratification based on multi-omics data

Before we evaluated the proposed methodology in a federated setting, we investigated the general capacity of our method to detect disease subtypes. For this purpose, we retrieved cancer data from The Cancer Genome Atlas. Specifically, we retrieved data from four different cancer types, namely glioblastoma multiforme, kidney renal clear cell (KIRC) carcinoma, sarcoma (SARC), and acute myeloid leukemia (AML). The data were preprocessed as follows: patients and features with more than 20% missing values were removed and the remaining missing values were imputed with k-nearest neighbor imputation. In the methylation data, we selected those 5000 features with maximal variance in each dataset. All features were then normalized to have a mean 0 and a standard deviation of 1. We randomly sampled 100 patients 30 times from the data pool and performed the Cox log-rank test, which is an inferential procedure for the comparison of event time distributions among independent (i.e. clustered) patient groups. We compared the results with SNF (Wang et al. 2014), NEMO (Rappoport and Shamir 2019), HCfused (Pfeifer and Schimek 2021), PINSplus (Nguyen et al. 2019), and Parea (Pfeifer et al. 2023).

In the federated case, we also randomly sampled 100 patients but distributed the subsampled data across three clients. Each client derived an affinity matrix on its local data and applied hierarchical clustering to obtain the clusters. After training, the local models were shared and the ensembles were concatenated to a global federated model. The local data were client-wise propagated through the global model to obtain an affinity matrix which also served as an input for our clustering method. We compared the clustering solution and quality from the local model with the global model. The aforementioned procedure was repeated 50 times. In an additional experiment, we randomly sampled 100 patients, based on which a clustering solution was determined and then defined as the ground truth. Subsequently, we distributed the data across three clients and we reported on the performance of the local model compared to the performance of the global model. The procedure was repeated 50 times and we utilized ARI as a performance measure.

5 Results and discussion

The evaluation of the proposed approach using synthetic datasets across diverse scenarios revealed that the unsupervised random forest with the novel splitting rule can generate affinity matrices that accurately reflect sample distances, leading to improved clustering when processed by a clustering algorithm. Notably, the proposed method demonstrated comparable performance to Euclidean-based methods in scenarios where Euclidean distance is most effective, while it outperformed it significantly in other scenarios.

In the case of globular clusters of the same size, a scenario where Euclidean distance is expected to perform well, all three methods experience an expected decrease in ARI as cluster overlap increases. However, their performance remains consistently comparable across all experiments, as illustrated in Fig. 1a. Further experiments conducted on well-separated globular clusters with different densities, obtained by assigning different numbers of samples to each cluster, revealed that all three methods are also robust to varying density and consistently deliver comparable results. In the presence of outliers, all methods experience a decline in accuracy as the percentage of outliers increases, as shown in Fig. 1b. Remarkably, “uRF” maintains stable performance above 0.7, whereas Euclidean-based methods drop below 0.5 for outlier percentages exceeding 4%. In the case of clusters of different sizes, shown in Fig. 1c, “uRF” maintains a good performance with an ARI consistently above 0.85, while other methods can effectively distinguish clusters only when well-separated, with performance dropping to 0.5 as clusters overlap. The ability to distinguish clusters of varying sizes is particularly relevant in the context of sub-clusters. Additional experiments, where synthetic data was generated to include one main cluster and two sub-clusters, yielded similar outcomes: Euclidean-based methods are only effective when clusters are sufficiently separated while “uRF” consistently demonstrates good performance in all cases. While Euclidean-based methods enable effective clustering for globular data provided that there is sufficient separation among clusters, this does not extend to nonglobular clusters, as the method cannot detect non-convex structures. The results in Fig. 1d show that regardless of the distance between the two rings, these methods struggle to accurately identify the clusters, yielding an ARI below 0.1. In contrast, “uRF” can effectively discriminate the clusters when they are sufficiently separated, achieving an ARI of 1 for distances above 1.5. Additional experiments with other nonconvex cluster shapes, such as half moons, confirmed these observations. These results underscore the limitations of Euclidean distance in various clustering scenarios, highlighting the proposed approach’s flexibility and robust performance in the presence of outliers, varying cluster sizes, and nonconvex shapes, commonly encountered in omics data analysis.

Figure 1. Clustering performance in terms of Adjusted Rand Index (ARI) of the Ward clustering algorithm on affinity matrices derived from the proposed unsupervised Random Forest with novel split rule uRF, Euclidean distance (HC), and Euclidean distance on standardized data (HCscaled), evaluated in four scenarios: (a) globular clusters of equal size, (b) globular clusters with outliers, (c) globular clusters of varying sizes, and (d) non-globular clusters shaped as concentric circles.

The evaluation on the six machine learning benchmark datasets (Table 1) indicate that the random forest-derived affinity matrix using our novel splitting rule was beneficial across almost all benchmark datasets (see Fig. 2). In five out of six cases, we obtained superior results compared to the Euclidean distance-derived affinity matrix. The number of features available for splitting a node has a considerable effect on the outcome (Fig. 2). The square root of the total number of available features is often specified as a default. However, from Fig. 2, we can see that for the Breast cancer dataset, as well as for the Wine dataset, this might not be the best possible choice. In case of the Wine dataset, for instance, an increasing number of available candidate features has a negative effect on the accuracy. Furthermore, we could observe that the minimum leaf size is a crucial parameter (see Supplementary Fig. S1). In the case of Iris, for instance, a minimum leaf node size of 50 drastically decreases the clustering performance. The breast cancer dataset was also sensitive to this specific parameter. Overall, given the results in Figs 1 and 2, and Supplementary Fig. S1, we claim that the proposed unsupervised splitting rule serves our clustering purposes.

Figure 2. Varying the number of sampled features for splitting a tree node. The resulting dendrograms are cut such that the number of clusters align with the ground truth.

Moreover, we investigated a model-internal approach to determine the optimal number of clusters (see Supplementary Fig. S2). The underlying assumption was that the best k value is the most stable solution when the number of trees is decreased. We first derived an affinity matrix using the herein-proposed unsupervised random forest. Afterward, we created a dendrogram using Ward’s hierarchical clustering. We cut the tree at a level where it resulted in a specified number of clusters k. From this clustering solution, we created a multiclass response vector. These labels served as an input for the unsupervised random forest classifier to label the samples. With this approach, we have created a predictive machine-learning model. We checked the predictive performance of this model using the ARI index. Overall, we could learn that the classifier does reflect Ward’s clustering solution very well, as indicated by the high ARI values (see Supplementary Fig. S2). We subsequently reduced the number of trees for a given k and we tracked the ARI performance accordingly. A visual inspection of the plots in Supplementary Fig. S2 gives us a hint of what the optimal k might be. In the case of Iris, for instance, a decrease in the number of trees has almost no effect at the k = 2 level, thus we can assume that at least two clusters are present within the data. When k = 3 is applied, the median ARI value is still at its maximum with ARI  = 1. Starting with k = 4, there is a visible drop in performance when the number of trees is decreased. This observation suggests k = 3 clusters within the data, which aligns perfectly with the ground truth.

In the application of cancer data, we do not have the ground-truth classification labels. While our model-internal approach to infer the best number of clusters is promising, it still cannot be executed in an automatic way, and therefore it is more suitable to perform a detailed visual inspection. Thus, we decided to utilize the Silhouette coefficient to infer the optimal number of clusters. The Silhouette coefficient has been shown to work well for disease subtyping purposes (Pfeifer and Schimek 2021, Pfeifer et al. 2023). From Fig. 3, we can see that our approach, here denoted as “uRF”, is competitive with the state-of-the-art. Our “uRF” method clearly outperforms PINSplus and SNF and is competitive with NEMO and HCfused. For Sarcoma and AML the median is below the α=0.05 significance level. Given these results, we could claim that the derived affinity matrix using our unsupervised random forest is suitable for omics-based patient stratification. We further illustrate the versatility of our method on the kidney cancer (KIRC) dataset. In Fig. 4, we show the survival curves based on a clustering on the whole dataset, without any subsampling (as it is done in Fig. 3). Our algorithm inferred four clusters. Cluster 2 and cluster 4 are high risk clusters, where a high mortality can be observed. We also show the cluster-specific feature importance and the Pearson correlation of these importance values between the detected clusters. The correlation plots suggest that cluster 2 and cluster 4 differ substantially in the Methylation data. Cluster 1 and cluster 3 have a high correlation of r = 0.73, whereas all other cluster combinations are almost uncorrelated. A detailed inspection of the displayed data points would allow us to detect the genes or markers with the greatest signal differences. Finally, in the federated experiment, we could show that the aggregated global ensemble model performs well, and often better than the local model. In all cases, the clustering quality verified by the Cox log-rank P-value was higher for at least two clients (see Fig. 5) and not far behind for the remaining cases. The results from the second experiment, where we first calculate the ground truth on the whole dataset and afterward distribute the data, show almost identical results (see Fig. 6) to what we report in Fig. 5. From this experiment, we can learn that a federated random forest subsequently trained on multiple subsets of the data is competitive with a model which was trained on the whole dataset. It should be noted, however, that in the case of AML, the local model from client 3 performed substantially better than the global model (see Fig. 6).

Figure 3. Non-federated disease subtype discovery based on multi-omics data in comparison with alternative approaches. Bars represent the method-specific P-values of the Cox log-rank test from 30 iterations. The vertical line refers to the α=0.05 significance level. In the case of “uRF” the Silhouette coefficient was used to determine the optimal number of clusters.

Figure 4. Kidney (KIRC) cancer dataset. Survival curves of the four detected clusters are displayed. The other panels show the cluster-specific feature importance values and their inter-cluster correlation.

Figure 5. Federated disease subtype discovery based on multi-omics data. Shown is the number of times the global model outperformed the local model and vice-versa, on four different cancer types. The results are based on 50 iterations where we randomly distributed the data across three clients. The results are compared using the P-values of the Cox log-rank test.

Figure 6. Federated multi-omics clustering. Shown is the number of times the global model outperformed the local model and vice-versa, on four different cancer types. The results are based on 50 iterations where we randomly distributed the data across three clients. The results are compared using the ARI index.

Overall, these findings emphasize the potential of federated learning in achieving comparable results to centralized approaches while preserving data privacy and distribution across multiple clients.

6 Conclusion

In conclusion, our study introduces a novel approach to federated patient stratification, leveraging an unsupervised splitting rule to derive an affinity matrix. The subsequent application of hierarchical clustering on this matrix has demonstrated promising results on synthetic data, machine learning benchmark datasets, and real-world cancer data. Our approach not only showcases robust performance in accurately categorizing patients into meaningful subgroups but also addresses some of the challenges of privacy and data security using federated machine learning. Moreover, it enables the identification of feature importance specific to clusters, revealing the driving molecular factors influencing distinct patient groups.

Future work may include the implementation of additional privacy-preserving techniques like differential privacy or homomorphic encryption of the shared models to mitigate potential data leakage. These techniques would add an additional layer of security, making it more challenging for potential adversaries to extract meaningful information from the shared models.

Supplementary Material

btae382_Supplementary_Data

Supplementary data

Supplementary data are available at Bioinformatics online.

Conflict of interest

None declared.

Funding

This paper was published as part of a supplement financially supported by ECCB2024.

Data availability

The processed raw data of the TCGA Multi Omics Cancer benchmark are available at https://acgt.cs.tau.ac.il/multi_omic_benchmark/download.html. All further data underlying the results of this publication are available on request.
==== Refs
References

Bicego M , EscolanoF. On learning random forests for random forest-clustering. In: 2020 25th International Conference on Pattern Recognition (ICPR). pp. 3451–3458. IEEE, 2021.
Brauneck A , SchmalhorstL, Kazemi MajdabadiMM  et al  Federated machine learning in data-protection-compliant research. Nat Mach Intell  2023;5 :2–4.
Breiman L.  Random forests. Mach Learn  2001;45 :5–32.
Dayan I , RothHR, ZhongA  et al  Federated learning for predicting clinical outcomes in patients with COVID-19. Nat Med  2021;27 :1735–43.34526699
Hauschild A-C , LemanczykM, MatschinskeJ  et al  Federated random forests can improve local performance of predictive models for various healthcare applications. Bioinformatics  2022;38 :2278–86.35139148
Holsinger KE , WeirBS.  Genetics in geographically structured populations: defining, estimating and interpreting FST. Nat Rev Genet  2009;10 :639–50.19687804
Leng D , ZhengL, WenY  et al  A benchmark study of deep learning-based multi-omics data fusion methods for cancer. Genome Biol  2022;23 :1–32.34980209
Lipkova J , ChenRJ, ChenB  et al  Artificial intelligence for multimodal data integration in oncology. Cancer Cell  2022;40 :1095–110.36220072
Murtagh F , LegendreP.  Ward’s hierarchical agglomerative clustering method: which algorithms implement Ward’s criterion?  J Classif  2014;31 :274–95.
Nguyen H , ShresthaS, DraghiciS  et al  PINSPlus: a tool for tumor subtype discovery in integrated genomic data. Bioinformatics  2019;35 :2843–6.30590381
Pfeifer B , SchimekMG.  A hierarchical clustering and data fusion approach for disease subtype discovery. J Biomed Inform  2021;113 :103636.33271342
Pfeifer B , BloiceMD, SchimekMG.  Parea: multi-view ensemble clustering for cancer subtype discovery. J Biomed Inform  2023;143 :104406.37257630
Rappoport N , ShamirR.  Multi-omic and multi-view clustering algorithms: review and cancer benchmark. Nucleic Acids Res  2018;46 :10546–62.30295871
Rappoport N , ShamirR.  NEMO: cancer subtyping by integration of partial multi-omic data. Bioinformatics  2019;35 :3348–56.30698637
Subramanian I , VermaS, KumarS  et al  Multi-omics data integration, interpretation, and its application. Bioinform Biol Insights  2020;14 :117793221989905–24.
Von Luxburg U.  A tutorial on spectral clustering. Stat Comput  2007;17 :395–416.
Wang B , MezliniAM, DemirF  et al  Similarity network fusion for aggregating data types on a genomic scale. Nat Methods  2014;11 :333–7.24464287
Ward JH Jr . Hierarchical grouping to optimize an objective function. J Am Statist Assoc  1963;58 :236–44.
Wright S.  The genetical structure of populations. Ann Eugen  1949;15 :323–54.
Yang H , ChenR, LiD  et al  Subtype-GAN: a deep learning approach for integrative cancer subtyping of multi-omics data. Bioinformatics  2021;37 :2231–7.33599254
