The PIUMA package - Phenotypes Identification Using Mapper from topological data Analysis
4 January 2026
Package
PIUMA 1.7.2
1 Introduction
This guide provides an overview of the PIUMA1 PIUMA is the Italian word for feather package, a comprehensive R package for performing Topological Data Analysis on high-dimensional datasets, such as -omics data. As of version 1.6 of PIUMA, we provided two tutorials for TDA in R using PIUMA, one as a basic end-to-end pipeline to do community mining, and the other one to showcase the application of TDA using Seurat objects, making a specific case for single-cell data processing.
1.1 Motivation
Phenotyping is a process of characterizing and classifying individuals based on observable traits or phenotypic characteristics. In the context of medicine and biology, phenotyping involves the systematic analysis and measurement of various physical, physiological, and behavioral features of individuals, such as height, weight, blood pressure, biochemical markers, imaging data, and more. Phenotyping plays a crucial role in precision medicine as it provides essential knowledge for understanding individual health characteristics and disease manifestations, by combining data from different sources to gain comprehensive insights into an individual’s health status and disease risk. This integrated approach allows for more accurate disease diagnosis, prognosis, and treatment selection. The same considerations could be also be extended in omics research, in which the expression values of thousands of genes and proteins, or the incidence of somatic and germline polymorphic variants are usually assessed to link molecular activities with the onset or the progression of diseases. In this field, phenotyping is needed to identify patterns and associations between phenotypic traits and a huge amount of available features. These analyses can uncover novel disease subtypes, identify predictive markers, and facilitate the development of personalized treatment strategies. In this context, the application of unsupervised learning methodologies could help the identification of specific phenotypes in huge heterogeneous cohorts, such as clinical or -omics data. Among them, the Topological Data Analysis (TDA) is a rapidly growing field that combines concepts from algebraic topology and computational geometry to analyze and extract meaningful information from complex and high-dimensional data sets (Carlsson 2009). Moreover, TDA is a robust and effective methodology that preserves the intrinsic characteristics of data and the mutual relationships among observations, by presenting complex data in a graph-based representation. Indeed, building topological models as networks, TDA allows complex diseases to be inspected in a continuous space, where subjects can ‘fluctuate’ over the graph, sharing, at the same time, more than one adjacent node of the network (Dagliati et al. 2020). Overall, TDA offers a powerful set of tools to capture the underlying topological features of data, revealing essential patterns and relationships that might be hidden from traditional statistical techniques (Casaclang-Verzosa et al. 2019).
2 News in Version PIUMA 1.6
PIUMA 1.6 is a major release that brings true end-to-end TDA workflows to R. The headline feature is embedded, TDA-guided, geometry-informed community mining: new functions operate directly on the TDAobj class so you can run Mapper-based community detection entirely in R, with special emphasis on TDA-driven clustering for scRNA-seq atlases.
You can check out the integrative vignette for seamless use with Seurat.
3 Installation
PIUMA can be installed by:
if (!require("BiocManager", quietly = TRUE)) {
install.packages("BiocManager")
}
BiocManager::install("PIUMA")4 Scope of this Vignette
This vignette is intended to offer to the user the basic pipeline and usage of PIUMA, using a scRNAseq dataset as an example. Mapper() output will be taken using reasonable but arbitrary hyperparameters.
4.1 The testing dataset
We tested PIUMA on a subset of the single-cell RNA Sequencing dataset (GSE:GSE193346 generated and published by Feng et al. (2022) to demonstrate that distinct transcriptional profiles are present in specific cell types of each heart chambers, which were attributed to have roles in cardiac development (Feng et al. 2022). In this tutorial, our aim will be to exploit PIUMA for identifying sub-population of vascular endothelial cells, which can be associated with specific heart developmental stages. The original dataset consisted of three layers of heterogeneity: cell type, stage and zone (i.e., heart chamber). Our test dataset was obtained by subsetting vascular endothelial cells (cell type) by Seurat object, extracting raw counts and metadata. Thus, we filtered low expressed genes and normalized data by DaMiRseq :
#############################################
############# NOT TO EXECUTE ################
########## please skip this chunk ###########
#############################################
dataset_seu <- readRDS("./GSE193346_CD1_seurat_object.rds")
# subset vascular endothelial cells
vascularEC_seuobj <- subset(x = dataset_seu,
subset = markFinal == "vascular_ec")
df_data_counts <- vascularEC_seuobj@assays$RNA@counts
df_cl <- as.data.frame(df_data_counts)
meta_cl <- vascularEC_seuobj@meta.data[, c(10,13,14,15)]
meta_cl[sapply(meta_cl, is.character)] <- lapply(meta_cl[sapply(meta_cl,
is.character)],
as.factor)
## Filtering and normalization
colnames(meta_cl)[4] <- "class"
SE <- DaMiR.makeSE(df_cl, meta_cl)
data_norm <- DaMiR.normalization(SE,
type = "vst",
minCounts = 3,
fSample = 0.4,
hyper = "no")
vascEC_norm <- round(t(assay(data_norm)), 2)
vascEC_meta <- meta_cl[, c(3,4), drop=FALSE]
df_TDA <- cbind(vascEC_meta, vascEC_norm)
At the end, the dataset was composed of 1180 cells (observations) and 838 expressed genes (features). Moreover, 2 additional features are present in the metadata: ‘stage’ and ‘zone’. The first one describes the stage of heart development, while the second one refers to the heart chamber.
Users can directly import the testing dataset by:
library(PIUMA)
library(ggplot2)
data(vascEC_norm)
data(vascEC_meta)
df_TDA <- cbind(vascEC_meta, vascEC_norm)
dim(df_TDA)
#> [1] 1180 840
head(df_TDA[1:5, 1:7])
#> stage zone Rpl7 Dst Cox5b Eif5b Rpl31
#> AACCAACGTGGTACAG-a5k1 E15.5 RV 5.08 2.95 2.51 2.20 3.42
#> AACCATGAGGAAGTCC-a5k1 P3 LV 4.84 2.40 3.40 1.68 3.40
#> AACGAAAAGACCATAA-a5k1 P0 RV 4.42 2.43 2.61 2.33 2.61
#> AAGCGAGGTAGGAGGG-a5k1 P0 LV 3.74 2.52 2.52 2.01 2.52
#> AAGCGTTGTCTCGGAC-a5k1 E16.5 LV 4.99 3.31 2.33 2.33 3.624.2 The TDA object
The PIUMA package comes with a dedicated data structure to easily store the
information gathered from all the steps performed by a Topological Data
Analysis. As in the version 1.6 of PIUMA, this object, called TDAobj, is an S4
class containing 11 slots:
orig_data:data.framewith the original data (without outcomes)scaled_data:data.framewith re-scaled data (without outcomes)outcomeFact:data.framewith the original outcomesoutcome:data.framewith original outcomes converted as numericcomp:data.framecontaining the components of projected datadist_mat:data.framecontaining the computed distance matrixdfMapper:data.framecontaining the nodes, with their elements,jacc:matrixof Jaccard indexes between each pair ofdfMappernodesnode_data_mat:data.framewith the node size and the average valuegraph:listcontaining the Jaccard matrix transformed in igraph objectclustering:listcontaining two essential data.frames with topological clustering information per nodes and per observation
The makeTDAobj function allows users to 1) generate the TDAobj from a
data.frame, 2) select one or more variables to be considered as outcome, and
3) perform the 0-1 scaling on the remaining dataset:
TDA_obj <- makeTDAobj(df_TDA, c("stage","zone"))
For genomic data, such as RNA-Seq or scRNA-Seq, we have also developed a custom function to import a SummarizedExperiment object into PIUMA:
data("vascEC_meta")
data("vascEC_norm")
library(SummarizedExperiment)
dataSE <- SummarizedExperiment(assays=as.matrix(t(vascEC_norm)),
colData=as.data.frame(vascEC_meta))
TDA_obj <- makeTDAobjFromSE(dataSE, c("stage","zone"))
4.3 Preparing data for Mapper
To perform TDA, some preliminary preprocessing steps have to be carried out;
specifically, the scaled data stored in TDA_obj@scaled_data, called
point-cloud in TDA jargon, has to be projected in a low dimensional space and
transformed in distance matrix, exploiting the dfToProjection and
dfToDistance functions, respectively. In this example, we will use the
umap as projection strategy, to obtain the first 2 reduced dimensions
(nComp = 2) and the Euclidean distance (distMethod = "euclidean") as
distance metrics. PIUMA allows setting 6 different projection strategies with
their specific arguments: UMAP, TSNE, PCA, MDS, KPCA, and ISOMAP and
3 types of well-known distance metrics are available: Euclidean, Pearson’s
correlation and the Gower’s distance (to be preferred in case of categorical
features are present). Users can also use standard external functions both to
implement the low-dimensional reduction (e.g., the built-in princomp
function) and to calculate distances (e.g., the built-in dist function).
set.seed(1)
# calculate the distance matrix
TDA_obj <- dfToDistance(TDA_obj, distMethod = "euclidean")
# calculate the projections (lenses)
TDA_obj <- dfToProjection(TDA_obj,
"UMAP",
nComp = 2,
umapNNeigh = 25,
umapMinDist = 0.3,
showPlot = FALSE)
# plot point-cloud based on stage and zone
df_plot <- as.data.frame(cbind(getOutcomeFact(TDA_obj),
getComp(TDA_obj)),
stringAsFactor = TRUE)
ggplot(data= df_plot, aes(x=comp1, y=comp2, color=stage))+
geom_point(size=3)+
facet_wrap(~zone)
Figure 1: Scatterplot from UMAP
Four scatter plots are drawn, using the first 2 components identified by UMAP. Each panel represents cells belonging to a specific heart chamber, while colors refer to the development stage.
As shown in Figure 1, the most of vascular endothelial cells are located in ventricles where, in turn, it is possible to more easily appreciate cell groups based on developmental stages.
4.4 TDA Mapper
One of the core algorithms in TDA is the TDA Mapper, which is designed to provide a simplified representation of the data’s topological structure, making it easier to interpret and analyze. The fundamental idea behind TDA Mapper is to divide the data into overlapping subsets called ‘clusters’ and, then, build a simplicial complex that captures the relationships between these clusters. This simplicial complex can be thought of as a network of points, edges, triangles, and higher-dimensional shapes that approximate the underlying topology of the data. The TDA Mapper algorithm proceeds through several consecutive steps:
- Data Partitioning: the data is partitioned into overlapping subsets, called ‘bins’, where each bin corresponds to a neighborhood of points;
- Lensing: a filter function, called ‘lens’, is chosen to assign a value to each data point;
- Clustering: the overlapping bins are clustered based on the values assigned by the filter function. Clusters are formed by grouping together data points with similar filter function values;
- Simplicial Complex: a simplicial complex is constructed to represent the relationships between the clusters. Each cluster corresponds to a vertex in the complex, and edges are created to connect overlapping clusters;
- Visualization: the resulting simplicial complex can be visualized, and the topological features of interest can be easily identified and studied.
TDA Mapper has been successfully applied to various domains, including biology, neuroscience, materials science, and more. Its ability to capture the underlying topological structure of data while being robust to noise and dimensionality makes it a valuable tool for gaining insights from complex datasets. PIUMA is thought to implement a 2-dimensional lens function and then apply one of the 4 well-known clustering algorithm: ‘k-means’, ‘hierarchical clustering’, DBSCAN or OPTICS.
TDA_obj <- mapperCore(TDA_obj,
nBins = 15,
overlap = 0.3,
clustMeth = "kmeans")
# number of clusters (nodes)
dim(getDfMapper(TDA_obj))
#> [1] 367 1
# content of two overlapping clusters
getDfMapper(TDA_obj)["node_102_cl_1", 1]
#> [1] "GCGGAAACAGAGTTGG-a5k1 GTGCAGCAGCTGGAGT-a25k TCAGTGACAGCTTTGA-a25k TGTTCTATCAAGCCGC-a25k"
getDfMapper(TDA_obj)["node_117_cl_1", 1]
#> [1] "CCACCATGTTGAGTCT-a5k1 GCCCAGAGTTGCTCAA-a5k1 GCGGAAACAGAGTTGG-a5k1 TCCAGAAGTGTTCCTC-a5k1 GTCCTCATCGGCTGAC-a25k TGCTCGTAGCCTGTGC-a25k"Here, we decided to generated 15 bins (for each dimension), each one
overlapping by 30% with the adjacent ones. The k-means algorithm is,
then, applied on the sample belonging to each ‘squared’ bin. In this example,
the Mapper aggregated samples in 369 partially overlapping clusters. Indeed, as
shown in the previous code chunk, the nodes node_102_cl_1 and node_117_cl_1
shared 2 out of 4 cells.
4.5 Nodes Similarity and Enrichment
Once chosen the hyperparameters, the output of mapper is a data.frame,
stored in the dfMapper slot, in which each row represents a group of samples
(here, a group of cells), called ’node’ in network theory jargon.
PIUMA allows the users to also generate a matrix that specifies the similarity
between nodes ‘edge’ allowing to represent the data as a network.
Since the similarity, in this context, consists of the number of samples,
shared by nodes, PIUMA implements a function (jaccardMatrix) to calculate the
Jaccard’s index between each pairs of nodes.
# Jaccard Matrix
TDA_obj <- jaccardMatrix(TDA_obj)
head(round(getJacc(TDA_obj)[1:5,1:5],3))
#> node_3_cl_1 node_4_cl_1 node_4_cl_2 node_5_cl_1 node_5_cl_2
#> node_3_cl_1 NA NA 0.167 NA NA
#> node_4_cl_1 NA NA NA NA NA
#> node_4_cl_2 0.167 NA NA NA 0.308
#> node_5_cl_1 NA NA NA NA NA
#> node_5_cl_2 NA NA 0.308 NA NA
round(getJacc(TDA_obj)["node_102_cl_1","node_117_cl_1"],3)
#> [1] 0.111Regarding the similarity matrix, we obtained a Jaccard matrix where each
clusters’ pair was compared; looking, for example, at the Jaccard Index for
nodes node_102_cl_1 and node_117_cl_1, we correctly got 0.5 (2/4 cells).
Moreover, the tdaDfEnrichment function allows inferring the features values
for the generated nodes, by returning the averaged variables values of samples
belonging to specific nodes. Generally, this step is called ‘Node Enrichment’.
In addition the size of each node is also appended to the output data.frame
(the last column name is ‘size’).
TDA_obj <- tdaDfEnrichment(TDA_obj,
cbind(getScaledData(TDA_obj),
getOutcome(TDA_obj)))
head(getNodeDataMat(TDA_obj)[1:5, tail(names(getNodeDataMat(TDA_obj)), 5)])
#> mt.Nd5 mt.Cytb stage zone size
#> node_3_cl_1 0.195 0.536 11.000 3.000 1
#> node_4_cl_1 0.240 0.720 13.000 1.000 1
#> node_4_cl_2 0.257 0.634 14.167 1.667 6
#> node_5_cl_1 0.988 0.999 13.000 1.000 1
#> node_5_cl_2 0.279 0.654 15.273 1.545 11Printing the last 5 columns of the data.frame returned by tdaDfEnrichment
(node_data_mat slot), we can show the averaged expression values of each nodes
for 4 mitochondrial genes as well as the number of samples belonging to the
nodes.
4.6 Network Assessment
The geometry of the resulting TDA output graph may reveal hints on data organisation. Inferring the geometry of a graph from a TDA output and applying an appropriate clustering method, which is the main core and objective of PIUMA, might revel interesting communities. In particular, not all geometries are the same: biological datasets sometimes harbor scale-free hubs, so PIUMA also provides complementary strategies to reassess your network from a scale-free perspective. In particular, PIUMA implements two different strategies:
supervised approach, usually called ‘anchoring’, in which the entropy of the network generated by TDA is calculated averaging the entropies of each node using one single outcome as class (i.e., ‘anchor’). The lower the entropy, the better the network.unsupervised approachthat exploits a topological measurement to force the network to be scale-free. Scale-free networks are characterized by few highly connected nodes (hub nodes) and many poorly connected nodes (leaf nodes). Scale-free networks follows a power-law degree distribution in which the probability that a node has k links follows \[P(k) \sim k^{-\gamma}\], where \(k\) is a node degree (i.e., the number of its connections), \(\gamma\) is a degree exponent, and \(P(k)\) is the frequency of nodes with a specific degree. Degree exponents between \(2 < \gamma < 3\) have been observed in most biological and social networks. Forcing our network to be scale-free ensures to unveil communities in our data. The higher the correlation between P(k) and k, in log-log scale, the better the network. We also introduced a measure of connectivity of the Mapper() output as well as a ‘Product Score’ defined as (|corlogklogpk| × Connectivity) that simultaneously rewards scale-free behavior and overall graph cohesion. We introduced this correction since very sparse networks with many isolated nodes may appear scale-free but are not useful for data representation.
# Anchoring (supervised)
entropy <- checkNetEntropy(getNodeDataMat(TDA_obj)[, "zone"])
entropy
#> [1] 1.316
# Scale free network (unsupervised)
netModel <- checkScaleFreeModel(TDA_obj, showPlot = TRUE)
#> Scale for x is already present.
#> Adding another scale for x, which will replace the existing scale.
#> `geom_smooth()` using formula = 'y ~ x'
#> `geom_smooth()` using formula = 'y ~ x'
Figure 2: Power-law degree distribution
The correlation between P(k) (y-axis) and k (x-axis) is represented in linear scale (on the left) and in log-log scale (on the right). The regression line (orange line) is also provided.
netModel
#> $Connectivity
#> [1] 0.893733
#>
#> $gamma
#> [1] 1.804252
#>
#> $corkpk
#> [1] -0.7102301
#>
#> $pValkpk
#> [1] 0.009647595
#>
#> $corlogklogpk
#> [1] -0.5955781
#>
#> $pVallogklogpk
#> [1] 0.04101903
#>
#> $ProductScore
#> [1] 0.5322878Although the anchoring metric can be valuable when you already know class
labels, the unsupervised power-law fit is often preferable because it requires
no prior knowledge In our example, we obtained a
global entropy of 1.3, Pearson correlations of –0.75 (linear) and –0.58
(log–log), and an estimated \(\gamma\) of 2.09, confirming scale-free structure
(a typical scale-free network has (\(2 < \gamma < 3\))).
By comparing entropy, correlation or exponent,by using checkNetEntropy and
checkScaleFreeModel, across different parameters you can select the
configuration that most faithfully uncovers community structure in your data.
Moreover, the connectivity of the network is 0.89, while the ProductScore is
0.53. A connectivity below 1.0 tells us that the graph is not fully unified but
comprises more than one substantial subgraph, hinting that it is only partially
fragmented. At the same time, a moderate ‘Product Score’ suggests a meaningful
power-law signature among those connected nodes.
Taken together, these metrics point to a scale-free topology, marked by
prominent hub nodes. To assign a predicted geometry quickly, with sensible
thresholds and fallbacks for non-SF cases, we implemented the
predict_mapper_class() function:
# quick inference of geometry, metrics-based
TDA_obj <- jaccardMatrix(TDA_obj)
TDA_obj <- setGraph(TDA_obj)
TDA_obj <- predict_mapper_class(TDA_obj, verbose = TRUE)
#> predict_mapper_class: SFThis function simply uses heuristics to propose the most likely network topology
4.7 Cluster assignment
Once the structure of network has been assessed, the last key point is to properly identify a clusters in the network, and, thus, to assign cluster categories to each network node and each observation. PIUMA implements its own algorithm to detect clusters (Paragraph 4.7.1), while offers an easy way to perform clustering outside the package, for example using Cytoscape, a well-known tools for handling graphs (Paragraph 4.7.2)
4.7.1 Geometry-guided Community Mining of TDA Mapper() Graph
Once the Mapper pipeline has produced a fully populated TDA_obj, complete with
its graph structure, Jaccard similarity matrix, and igraph representation, you
can invoke our geometry-aware clustering routine with a single call to
autoClusterMapper. This function selects the most appropriate
community-finding algorithm based on the predicted graph geometry,
while still allowing you to override its choice if you prefer a different method.
Under the hood, we map each canonical geometry to the algorithm best
suited to its topological signature:
- Scale-free or configuration models (
SF/CM) are handled by fast-greedy modularity optimization, which excels at revealing hub-centric structures. - Small-world graphs (
WS) leverage the walktrap algorithm’s ability to follow short random walks and uncover locally dense regions. - Random geometric graphs (
RGG) employ edge-betweenness community detection to separate spatial clusters by cutting the highest-traffic links. - Stochastic block models (
SBM) use optimal modularity to isolate block-structured communities. - Erdős–Rényi graphs (
ER) fall back on label-propagation, which naturally diffuses labels across a uniformly random network.
This principled pairing of geometry and algorithm not only speeds up community discovery but also ensures that the resulting clusters respect the intrinsic shape of the data, yielding biologically meaningful modules that might be overlooked by generic clustering approaches.
In practice, if the automatic geometry mapping underperforms, walktrap is a solid fallback that works well across many Mapper graphs.
TDA_obj <- autoClusterMapper(TDA_obj,method = 'automatic')We then merge the resulting cluster assignments with our UMAP coordinates and plot each heart chamber in a faceted scatterplot, labeling only the non-singleton clusters:
library(ggrepel)
library(dplyr)
#>
#> Attaching package: 'dplyr'
#> The following objects are masked from 'package:stats':
#>
#> filter, lag
#> The following objects are masked from 'package:base':
#>
#> intersect, setdiff, setequal, union
# plot point-cloud based on stage and zone
df_plot <- as.data.frame(cbind(getOutcomeFact(TDA_obj),
getComp(TDA_obj)),
stringAsFactor = TRUE)
df_plot$cell_id <- rownames(df_plot)
df_plot <- merge(df_plot, TDA_obj@clustering$obs_cluster,
by.x = "cell_id", by.y = "obs", all.x = TRUE)
centroids <- df_plot %>%
group_by(zone, cluster) %>%
summarize(
n_cells = dplyr::n(),
comp1 = mean(comp1, na.rm = TRUE),
comp2 = mean(comp2, na.rm = TRUE),
.groups = 'drop'
) %>%
filter(!grepl("^Singleton", as.character(cluster))) # Exclude singleton clusters
ggplot(df_plot, aes(x = comp1, y = comp2, color = factor(cluster))) +
geom_point(size = 3, alpha = 0.7) +
geom_label_repel(
data = centroids,
aes(label = cluster, fill = factor(cluster)),
color = "white",
fontface = "bold",
box.padding = 0.5,
segment.color = NA,
min.segment.length = 0
) +
facet_wrap(~ zone) +
labs(color = "Cluster",
title = "Geometry-Guided Community Detection",
subtitle = "Cluster centroids labeled (singletons excluded)",
caption = "Singleton clusters shown without labels") +
theme_minimal() +
scale_color_viridis_d(option = "D") +
scale_fill_viridis_d(option = "D", guide = "none")
Figure 3: Geometry-guided Clustering on Mapper()’s Graph
Four scatter plots are drawn, using the first 2 components identified by UMAP, faceting for each specific heart chamber. Cells are colored for the topological clusters identified with PIUMA. Topological clusters are also labelled on the graph, while Singletons are excluded.
#for more inspection: obs X clusters
head(TDA_obj@clustering$obs_cluster)
#> obs cluster
#> 1 AAACGAACATCGGTTA-E18P1 2
#> 2 AAACGCTTCATAGACC-E18P1 1
#> 3 AAAGGGCAGTCTGTAC-a10k 1
#> 4 AAAGGGCCATGACTTG-a25k 1
#> 5 AAATGGACAGCAAGAC-P9CD1 9
#> 6 AAATGGAGTCGAAACG-P9CD1 1
# nodes X obs X clusters
head(TDA_obj@clustering$nodes_cluster)
#> node obs cluster
#> 1 node_3_cl_1 ACTCTCGAGATCCAAA-P9CD1 9
#> 2 node_4_cl_1 TCGCTCATCTCGTCAC-P9CD1 Singleton_19
#> 3 node_4_cl_2 ACTCTCGAGATCCAAA-P9CD1 9
#> 4 node_4_cl_2 CTCCCTCGTATGCGGA-P9CD1 9
#> 5 node_4_cl_2 GTCTTTACAAGAAATC-P9CD1 9
#> 6 node_4_cl_2 TCGACGGTCTGCTAGA-P9CD1 9We can see that clusters appear distinctly in defined zones of the UMAP in this faceted view per anatomical region. Our geometry-guided approach prioritizes communities formed by connected graph components, excluding disconnected singletons that lack structural relevance to the underlying geometry. We observe well-defined cluster boundaries in the embedding space, indicating that identified communities represent biologically meaningful cellular groupings rather than scattered artifacts.
Two key outputs let you explore the results in detail:
-obs_cluster: A table mapping each observation (cell) to its assigned cluster,
using a k-nearest-neighbor-enhanced discriminator to resolve ambiguous node
memberships.
-nodes_clusters: A node-centric mapping that preserves the full relationship
between the original graph topology and the clusters.
Both they are available in:
str(TDA_obj@clustering)
#> List of 2
#> $ nodes_cluster:'data.frame': 2366 obs. of 3 variables:
#> ..$ node : chr [1:2366] "node_3_cl_1" "node_4_cl_1" "node_4_cl_2" "node_4_cl_2" ...
#> ..$ obs : chr [1:2366] "ACTCTCGAGATCCAAA-P9CD1" "TCGCTCATCTCGTCAC-P9CD1" "ACTCTCGAGATCCAAA-P9CD1" "CTCCCTCGTATGCGGA-P9CD1" ...
#> ..$ cluster: chr [1:2366] "9" "Singleton_19" "9" "9" ...
#> $ obs_cluster :'data.frame': 1178 obs. of 2 variables:
#> ..$ obs : chr [1:1178] "AAACGAACATCGGTTA-E18P1" "AAACGCTTCATAGACC-E18P1" "AAAGGGCAGTCTGTAC-a10k" "AAAGGGCCATGACTTG-a25k" ...
#> ..$ cluster: chr [1:1178] "2" "1" "1" "1" ...4.7.2 Export data for Cytoscape
Cytoscape is a well-known tool to handle, process and analyze networks
(Shannon et al. 2003). Two files are needed to generate and enrich network in
Cytoscape: the jaccard Matrix (TDA_obj@jacc), to generate the structure of the
network (nodes and edges) and a data.frame with additional nodes information
to enrich the network (TDA_obj@node_data_mat):
write.table(x = round(getJacc(TDA_obj),3),
file = "./jaccard.matrix.txt",
sep = "\t",
quote = FALSE,
na = "",
col.names = NA)
write.table(x = getNodeDataMat(TDA_obj),
file = "./nodeEnrichment.txt",
sep = "\t",
quote = FALSE,
col.names = NA)
To explore the network resulted following the PIUMA framework, we imported
jaccard.matrix.txt in Cytoscape by the aMatReader plugin
(Settle et al. 2018) (PlugIn -> aMatReader -> Import Matrix file) while
nodeEnrichment.txt by File -> Import -> Table from File. Then, we
identified network communities by the GLay cluster function from the
‘clustermaker2’ plugin (Utriainen and Morris 2023).
As shown in Figure 3, using the transcriptome of vascular endothelial cells, it is possible to identify 11 communities of cells (top-right). Interestingly, some of them are in the same developmental stage (top-left). Moreover, there are clusters showing similar expression for some genes but different expression for other genes, suggesting that the sub-population could have a different biological function.For example, orange and yellow clusters have a similar average expression of Igfpb7 (bottom-right) but different expression level of Aprt (bottom-left).
Session Info
sessionInfo()
#> R Under development (unstable) (2025-12-22 r89219)
#> Platform: x86_64-pc-linux-gnu
#> Running under: Ubuntu 24.04.3 LTS
#>
#> Matrix products: default
#> BLAS: /home/biocbuild/bbs-3.23-bioc/R/lib/libRblas.so
#> LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.12.0 LAPACK version 3.12.0
#>
#> locale:
#> [1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C
#> [3] LC_TIME=en_GB LC_COLLATE=C
#> [5] LC_MONETARY=en_US.UTF-8 LC_MESSAGES=en_US.UTF-8
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#> time zone: America/New_York
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#> attached base packages:
#> [1] stats graphics grDevices utils datasets methods base
#>
#> other attached packages:
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#> [5] BiocStyle_2.39.0
#>
#> loaded via a namespace (and not attached):
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#> [15] Hmisc_5.2-4 sass_0.4.10
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#> [95] pkgconfig_2.0.3References
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