Biological researchers often face challenges in analyzing clinical samples due to the limited amount of samples they can collect. This issue hinders the use of traditional statistical methods; instead, they often rely on their domain knowledge to guide the exploration of the data. To ease the task, we aim to develop a system to support the researchers by integrating data from biological knowledge graphs (KGs), such as Reactome and UniProt, which can drive data exploration through recommendation system techniques. In this article, we present the ifrst step towards such a system by studying whether the data from biological KGs can be represented through embeddings so that proteins of interest are organized and categorized according to their shared functionalities. We propose Cluster-GAE, a graph autoencoder method inspired by Cluster-GCN. Cluster-GAE combines graph sampling techniques with Graph Neural Networks (GNNs) to learn embedding representations from large-scale biological networks. Our experiments suggest that Cluster-GAE produces embeddings with properties similar to the embeddings of traditional KG embedding methods without the need to process the whole graph at once. Moreover, the experiments show that the embeddings produced by Cluster-GAE are of a higher quality than the embeddings produced by a KG obtained through traditional sampling techniques, in particular Random Walk and Forest Fire. Finally, through t-SNE visualization and functional enrichment analysis, we showcase the ability of Cluster-GAE to identify protein clusters that are related to diferent biological processes, molecular functions, and cellular components.
Biological researchers collect clinical samples to study living organisms, quantifying the amounts of
thousands of proteins of interest and looking for relations among them. However, collecting samples is
expensive and time-consuming. Therefore, trials often include only a limited number of samples [
Biological databases, such as Reactome [
In this context, this work presents an exploratory analysis of diferent graph encoder capabilities
to capture relevant information on the node embeddings. Specifically, we analyze the efectiveness
of GAE and graph sampling techniques to leverage biological knowledge graphs, such as Reactome
and UniProt, to create embeddings. Such embeddings can later be used to discover protein-protein
associations in the context of analysis of limited numbers of clinical samples. We propose Cluster-GAE,
a method that combines GAE and Cluster-GCN [
In the following, we first introduce the background and related work in Section 2. Next, we illustrate the overall solution we envision in Section 3, and we describe the part we implemented so far, which is later experimentally analysed in Section 4. We conclude with some remarks and the next steps in Section 5.
Let be a set of proteins of interest and a phenomenon, e.g. being sick. Let be a clinical sample data set. Each clinical sample can be represented as a vector of size | | + 1, which contains the amount of proteins of interest and the presence or absence of the phenomenon. Therefore, can be represented as a matrix of size | | + 1 × , where is the number of clinical samples.
Biologist researchers are interested in discovering relations between groups of proteins (i.e. subsets of
) and the phenomenon through the analysis of . The main challenge for the analysis is the number of
proteins | |, which is much larger than the number of clinical samples . This is because the collection
of clinical samples is costly and time-consuming, so trials often involve a number of subjects [
This combination of few data instances and numerous features presents substantial challenges
for conventional statistical analysis [
A natural way to cope with the problem is to adopt feature selection techniques like Stabl [
Alternatively, one can consider exploiting pre-existing knowledge about the proteins , coming from
literature, to drive the analysis of . Such knowledge is, for example, stored in biological knowledge
graphs (KGs) such as UniProt [
While the traditional manner of exploiting these knowledge graphs is to manually query the proteins
and navigate through the relations [
Pershad et al. [
However, biological researchers are rarely equally interested in all proteins. They have a number of proteins they are interested in, and they aim to discover what are the connected proteins, and how they vary w.r.t. each other. Therefore, we argue that this can be modeled as an item-item recommendation task, where given one or more proteins, the goal is to retrieve a list of related proteins which can be later analyzed by the researchers.
Instead of working on the whole graph, we filter a subgraph with the proteins of interest. To do it, we query Reactome to extract the part of the graph that contains the protein/features present in the clinical samples to analyze. Specifically, for each protein in , we extract the nodes of the features and nodes up to two hops of distance.
This is implemented as Cypher queries, which are evaluated over Reactome using Neo4J. Listing 1 shows an example query, which is parametrized. At Line 1, the query reads the list of protein names (Line 1). At Lines 2 and 3, the query retrieves the Reacome nodes associated with the input proteins. The block at Lines 4–7 retrieves the neighbor nodes (at a maximum distance of two) of the input protein nodes. The block at Lines 10-11 adds constraints on the nodes to be retrieved, such as being related to mice (mus musculus), a possible type of organism studied by the clinical samples. Finally, the operation at Line 12 returns the edges.
After the construction of the out graph, we verified its connectivity, to avoid having isolated proteins which could not be processed in the next steps.
Listing 1: The query executed by the sample-based selector
Despite the graph induced by the clinical samples is smaller than the original biological knowledge graph, its size is still large. Therefore, the learning algorithm that extracts the embeddings needs to exploit an adequate strategy to cope with the graph volume. We considered two alternatives: the GAE extractor and the Cluster-GAE extractor. The former uses graph sampling to reduce the size of the knowledge graph and generates the embeddings using a GAE. The latter does not perform the graph sampling. Instead, it uses the approach initially proposed by Cluster-GCN based on a divide-and-conquer strategy.
The GAE extractor exploits graph sampling to reduce the size of the graph. The goal is to improve computation performance while retaining the essential structural properties of the original graph. As sampling algorithms, we consider Random Walk (RW) with Restart [14] and Forest Fire (FF) [14]. We set as a constraint the necessity of having a connected graph as an output of the process.
After that, a GAE model learns low-dimensional, yet informative representations of the graph’s
nodes. The GAE model comprises an encoder and a decoder, with the encoder being a GCN that embeds
nodes into a latent space. The decoder then attempts to reconstruct the graph’s adjacency matrix from
these embeddings. This process is facilitated by a reconstruction loss function that guides the model to
capture the essential topological similarities based on features between nodes [
The Cluster-GAE extractor divides the data into partitions and then samples from these partitions
during the GAE training phase. This extractor omits the sampling step described above. Instead, it
adapts the Cluster-GCN algorithm [
This modification allows us to generate meaningful embeddings and understand the underlying structure of the graph. Basically, this method divides the data into partitions and then samples from these partitions during the training phase.
The last step consists of using the embeddings to group features using clustering or detecting similar proteins/features using embedding distance, recommending how to group the features to analyze to the researcher.
This section presents our preliminary analysis of the system, specifically on the embedding extractor component. We analyze the behavior of the GAE and Cluster-GAE extractors by analyzing the quality of the generated embeddings through cluster analysis. The code for the experiments is available at https://github.com/dkw-aau/clinical-sample-enrichment.
We use a dataset consisting of clinical samples from mice characterized by 3 825 proteins, one boolean variable associated with the presence of the phenomenon of study, and 48 data instances.
Using the features of the dataset, we query Ractome with a query similar to the one in Listing 1. The query builds a graph with 50, 164 nodes and 1, 667, 138 edges. Compared to Reactome, which includes 2, 427, 555 nodes and 10, 102, 445 edges, we observe that the generated graph is denser, as it preserves 2.06% of the nodes and 16.5% of the edges.
To evaluate the extractors, we consider two metrics.
Firstly, we use the Earth Mover’s Distance (EMD). EMD evaluates the dissimilarity between two probability distributions, ofering a quantitative assessment of the diferences in protein embedding matrices across diferent sampling methods [15].
Secondly, we use clustering metrics. These metrics evaluate the quality of clustering results by assessing how well the identified clusters adhere to desirable properties like compactness, separation, and connectedness. The clustering metrics we consider are: • Silhouette Score: Measures how similar an object is to its own cluster compared to other clusters.
A higher silhouette score indicates better-defined clusters [16]. • Calinski-Harabasz Index: Measures the ratio of the between-cluster dispersion to the withincluster dispersion. A higher Calinski-Harabasz index indicates denser and more well-separated clusters [17]. • Davies-Bouldin Index: Measures the average similarity between each cluster and its most similar cluster. A lower Davies-Bouldin index indicates better cluster separation [18].
We study how the sampling method afects the generated embeddings. We create graph embeddings using the sampling pipeline but omit the sampling step. As a direct comparison of the embeddings is not feasible due to the randomness in the learning process, we compare the distances between embeddings of various proteins in the dataset. We calculated the cosine distance for all protein embeddings derived from diferent extractions: the GAE extractor with RW and, FF and the Cluster-GAE extractor. Subsequently, we compute the EMD between the extractors and a baseline, named No sampling. This baseline consists of a GAE extractor without any sampling procedure.
Table 2 presents the EMD values for embeddings of dimensions 64 and 128. We observe that the behaviour of the Cluster-GAE embeddings is the most similar to the one of the baseline. This is evidence that preserving the input graph allows the exploitation of more information in the learning process.
Looking into the performance of the two GAE extractors, we observe that the one using FF as a sampling method produces closer embeddings to the baseline. When the embedding dimension is 128, the EMD value of the GAE extractor with FF is closer to the one of the Cluster-GAE extractor than the GAE extractor with RW. The results suggest that FF is efective in preserving the input graph structure.
While the previous analysis ofers some insights into the efect of sampling, it does not provide useful information about the quality of the embeddings. Therefore, we perform a cluster analysis to obtain 0 1 2 −60 −40 −20 0 20 40 qualitative and quantitative insights on the learned space.
As the clustering algorithm, we use K-means, as this algorithm is well-recognized for its efectiveness with embeddings across various domains [19, 20]. Specifically, we consider K-means with = 2 and = 3.
Table 1 displays the cluster metrics for the embeddings produced by the various extractors. In general, Cluster-GAE produces embeddings that are distinctly clustered and well-separated. This observation holds true regardless of the vector dimensions.
To visually investigate the space created by the Cluster-GAE extractor, we used t-SNE. Figure 3 shows the embeddings with dimensions created by Cluster-GAE and clustered through K-means when = 3. The figure shows that there are two prominent clusters and a third, smaller yet more distinct cluster.
We further investigate the quality of the embedding generated by Cluster-GAE through a functional enrichment analysis [21].
We use g:Profiler 1 to run such an analysis. This tool takes a set of proteins and a target organism as inputs and identifies overrepresented biological processes, molecular functions, and cellular components to which those proteins might be related. To analyze the properties of the clusters, we run the g:profile analysis using the proteins of clusters. We expect each cluster to be related to diferent results in a large way. This means that the quality of the clustering is reflected in the degree to which these functions are distinct between clusters.
We divided the analysis by the three top-level categories of the Gene Ontology, namely “Biological Process” (BP), “Molecular Function” (MF), and “Cellular Components” (CC). We consider < 0.05 when performing the functional enrichment analysis. Figure 2 presents the top-5 results for each category divided into clusters. This Top-5 is based on − 10 (), i.e., these are the results with the lowest . We expect that an efective clustering algorithm would identify proteins that are related to specific BPs, MFs, and CCs in the same group. In other words, if diferent clusters share few functional results, the clustering is efective in capturing the distinct BPs, MFs, and CCs; therefore providing evidence of the biological relevance of the clusters.
The results show that for BPs, there is a clear separation of the top-5 retrieved processes for each cluster. However, there is an overlap between Clusters 0 and 1 for “organonitrogen compound metabolic” and between proteins in Clusters 1 and 2 for the “small molecule metabolic.” All in all, there is a clear diference. If we consider all the results, Cluster 0 might be involved in 682, and 67.01% of them are unique to this cluster, Cluster 1 might contribute to 462 processes, where 47.15% of them are only related to this Cluster. Cluster 2 contributes to 72 processes and uniquely contributes to 25.0% of them. Moreover, 43.06% of Cluster 2 processes are shared with both Cluster 0 and 1. In this sense, Cluster 2 mainly comprises proteins that can participate in the BPs of both Clusters.
When considering MFs, there is a more extensive overlap between Clusters 0 and 1 on the potential MFs. However, there are some unique identifiable MFs associated with each cluster. Regarding all MFs retrieved for each Cluster, Clusters 0, 1, and 2 might be associated with 122, 93, and 23 MFs, respectively. 59.02% of Cluster 1 MFs are unique to that cluster, 44.09% of the MFs of Cluster 2 are not shared, and 43.48% of the MFs of Cluster 2 did not appear in other Clusters. Therefore, for molecular MFs, we can see that clustering separates the molecules according to their functions.
Something similar happens with MFs when we consider CCs. In the top 5, we observe mostly shared results for Clusters 0 and 1, with some unique components. When analyzing the full results of the functional enrichment, we observed that Clusters 0, 1, and 2 are related to 220, 151, and 20 CCs, respectively, and 64.09% are unique to Cluster 0, 45.03% are unique to Cluster 1, and 15.0% are unique to Cluster 2. Like in the case of molecular function, Cluster 2 encompasses proteins that are related to common CCs, as 65.0% of the 20 CCs are shared by both Clusters 0 and 1.
In summary, the results suggest that the embeddings convey information about the protein’s role in BPs, MFs, and CCs. Therefore, applying k-means using these embeddings results in clusters with a large number of unique roles in the type of results of functional enrichment analysis.
This article presented our ongoing research in building support tools for biological researchers. The solution we envision exploits biological KGs to suggest new proteins for researchers to study in the context of clinical sample analysis.
We presented some possible strategies to learn embeddings from a biological KG. The experimental analysis suggested that Cluster-GAE is efective in processing biological KGs and creating embedding spaces, when compared to embedding techniques that exploit sampling to reduce the size of the graph.
Moreover, the embeddings of the proteins learned through Cluster-GAE can efectively be clustered according to the biological processes they contribute to. The functional enrichment analysis using g:Profiler highlights that proteins grouped within the same cluster tend to be associated with similar biological pathways and processes.
One of the current limitations we face is that we used one dataset. It is necessary to repeat the analysis on diferent datasets, ideally associated to various organisms and with diverse biological conditions, to ensure that our findings generalize.
The next natural step is to build the recommendations on top of the learned embeddings. The ifrst approach is to rely exclusively on the embeddings and compute recommendations from them (e.g., through nearest neighbor techniques). However, the recommendation process should also take advantage of the information coming from clinical samples. Despite limited in the size of the samples, the contained values are a valuable source of information that should contribute to the recommendation process.
The natural focus to build a recommender system is on non-personalized recommender systems. However, the presence of various researchers analyzing the same samples opens opportunities for collaborative filtering approaches. Furthermore, incorporating user-interaction data, such as previous protein selections or research interests, could further enhance the personalization and relevance of recommendations.
Currently, the major issue for creating a recommender system for protein selection in biological
research is the lack of datasets to evaluate its performance. State-of-the-art methods in protein selection
in a dataset, such as Stabl [
With time, our goal is to create a real-life dataset by providing researchers with recommendations and storing their feedback. After collecting a dataset, we plan to extend the recommender system to consider not only the biological knowledge graph as input but also details of the research being carried out to provide personalized recommendations.
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