dataesr/scientific-paragraphs-categorization huggingface dataset:
In particular, the total number of RBH relations among the components, average clustering coefficient and modularity of the RBH graph, and the number and typical sizes of the identified graph communities have been assessed. The conclusion was that the stabilized version of ICA, where the non-Gaussianity of metagenes (and not metasamples) was maximized, is superior to other matrix factorization methods with respect to these measurements. Three major matrix factorization approaches were systematically discussed in a recent review for their ability to discover functional subsystems or tissue-type specific signals  [45]. The main conclusion was that it might be advantageous to use several matrix factorizations simultaneously. The same authors further suggested using the BioBombe approach  [46] , where three matrix factorization methods (PCA, ICA, and NMF) and two autoencoder-based dimension reduction techniques were systematically compared based on the pancancer TCGA datasets comprising 11,069 tumoral samples.
In the first case, the effective global dimensionality of the data can be determined through the standard Kaiser rule, use of broken stick distribution, Horn's parallel analysis or estimating the conditional number of the covariance matrix  [47]. One can also use more advanced methods for determining the effective data dimensionality such as the ones using concentration of measure phenomena  [48]  or data point cloud linear separability statistics  [49]. However, the second case appears to be more consistent in applications, even being computationally more challenging. Thus, in Reference  [24] , Bayesian information criterion (BIC) was exploited to determine the optimal number of independent components in the analysis of a metabolome dataset comprising 1764 samples and 218 measured metabolites.
In other words, their s k distributions are characterized by the presence of one or few weights with exceptionally large values, separated by a significant gap from the other values. Secondly, it was shown that a certain level of over-decomposition of transcriptomic datasets, i. e. , choosing the number of independent components several times larger than MSTD, does not drastically change the definition of most of the components within the MSTD range. At the same time, it was observed that increasing the number of independent components over the MSTD value sometimes leads to biologically meaningful splitting of the components. For example, a component within the MSTD range which was associated with the total level of immune infiltrate in tumoral microenvironment splits into three components in higher-order decompositions which can be associated with the presence of T-cells, B-cells, and macrophages  [34, 42].
Functional enrichment analysis results of ICA metagenes can be visualized using maps representing functional redundancy between reference gene sets, such as InfoSigMap or enrichment maps  [53]. There exist integrated solutions allowing the computation of ICA components for omics datasets and containing a built-in set of tools for their interpretation. For example, in the BIODICA package (Available online: https://github. com/LabBandSB/BIODICA), a set of tools is provided for performing hypergeometric tests of the metagenes, automated feeding of Gene Set Enrichment Analysis with ICA metagenes, projecting metagenes onto biological network maps, correlating computed metagenes with a reference database of previously annotated metagenes, associating components with categorical and numerical sample annotations, and tools for meta-analysis of ICA decompositions.
Frequently, each one-dimensional sk distribution is analyzed for determining a set of the most contributing genes (e. g. , characterized by the most extreme absolute values in sk). The simplest idea is to select the variables (e. g. , genes) bypassing the threshold in p standard deviations, with some choice for p (typically, p ≥ 3). A combined set of the most contributing to different ICs genes can be used to define a subset of data for further analysis. Interestingly, ICA decomposition can be used to identify and disregard technical biases among omics datasets produced by different platforms. For example, in the study of 198 bladder cancers in.
Frequently, each one-dimensional s k distribution is analyzed for determining a set of the most contributing genes (e. g. , characterized by the most extreme absolute values in s k ). The simplest idea is to select the variables (e. g. , genes) bypassing the threshold in p standard deviations, with some choice for p (typically, p ≥ 3). A combined set of the most contributing to different ICs genes can be used to define a subset of data for further analysis. Interestingly, ICA decomposition can be used to identify and disregard technical biases among omics datasets produced by different platforms. For example, in the study of 198 bladder cancers in Reference  [33] , one of the most stable components was found to be associated with a complex time-dependent batch effect. The nature of this batch was not known in advance and was only discovered by correlating the corresponding a k vector to the dates of sample preparation.
Another component frequently identified in the analysis of transcriptomic data is related to GC-content, which might reflect the influence of GC-content on the RNA amplification step common for both microarray-based and sequencing-based methodologies. In Reference  [39] , a small dataset of three primary melanoma tumors and two matched controls, characterized at the level of transcriptome and miRNA, were merged together with a large reference melanoma dataset from the Cancer Genome Atlas. The ICA decomposition was performed for the merged transcriptomic and miRNA data separately. For both molecular data types, it was possible to identify those independent components capturing technical differences among platforms while focusing the analysis on biologically meaningful factors whose quantification was comparable among platforms.
Interestingly, ICA-based analysis sometimes can lead to identification of the factors whose origin is intermediate between technical and biological. For example, in Reference  [33]  one of the factors reproducible in several bladder cancer datasets was strongly associated with the surgery type (transurethral resection of the bladder tumor versus cystectomy) and at the same time was enriched with early response genes. This suggests that different ways of tissue processing might leave characteristic patterns in the transcriptome which can be discovered using ICA. Some components identified through ICA could describe various cell populations present in the sample in addition to cells of direct interest. Typically, this was the case for the stroma-related signals in the ICA-based analysis of tumor bulk samples (see Figure  2 ).
ICA can efficiently deconvolute the contribution from the cells of different types to the bulk transcriptome, which allows studying the properties of tumor cells more directly. In the aforementioned study of bladder cancer, decomposition of bulk tumors into 20 components allowed for the clear distinction of the signals reflecting the presence of immune cells (with the main signal coming from the multiple types of lymphocytes, adipocytes, fibroblasts  [33]. Another frequently employed idea is to use the results of ICA decomposition in order to define a set of variables for further application of various machine learning methods. Zhang et al. [55]  were among the first who applied ICA as a data-preprocessing step for classification of cancer patients. They used ICA independently on normal and cancer datasets and identified top gene markers able to discriminate between these conditions.
Their approach was quite indirect but showed the ability of ICA to prioritize genes. In a study by Huang et al. [56] , ICA was followed by a penalized discriminant method, and the authors showed high accuracy of ICA-based approach on several datasets. In both mentioned papers, the authors segregated cancer and normal tissues, which is now considered a trivial task, taking into account the large effect of cancer on cell transcriptome. Later, Zheng et al. [57]  proposed a consensus ICA, robust to initial estimations. They showed the applicability of the approach on three datasets, in two of which they classified subtypes of tumors. Support vector machine (SVM) was used to predict classes based on the metasamples, and the authors needed to perform preliminary feature selection to improve their classification accuracy.
Selecting a couple of independent components with clearly identified biological meaning can lead to a biologically meaningful 2D data display. For example, in Reference  [62] , visualizing a single cell dataset in the plane of two independent components associated with proliferative genes clearly revealed the 2D dynamics of tumor cell progression through the cell cycle. The difference with PCA-based data visualization is that, in the case of ICA, there exists no principal pair of components (such as PC1 and PC2) which can be considered as the most representative for visualizing the multi-dimensional distances. This remark should be taken with care since, frequently, the first PCs are affected by technical artifacts and are to be neglected in further analysis. In the case of ICA, any pair of ICs in no particular order can be used for data visualization taking into account their tentative interpretation.
ICA for Unraveling Functional Subsystems of a Living Cell or a Cell Ecosystem One of the strongest motivations behind applications of ICA to omics data is in that it can help identifying functional subsystems (or functional modules and complex biological processes) which are the building blocks determining response to perturbation of a tumoral cell or a whole cellular ecosystem such as tumor microenvironment (TME) composed of different cell types. The underlying principle is that genes or proteins do not react to an external stimulus individually but always integrate into a (sub-)system with more or less defined limits. Importantly, it is biologically feasible to assume the phenomenon of plurifunctionality, i. e. , potential participation of an elementary entity (such as gene or protein) into several functional subsystems.
A typical example of this kind is the identification of the functional subsystem of proliferation in single-cell RNA-Seq data, where the corresponding metasamples frequently have two modes, corresponding to proliferative and non-proliferative cell states. Functional subsystems have been systematically identified using ICA from a large cohort of transcriptomic profiles in Reference  [43] , where 298 Gene Expression Omnibus (GEO) datasets profiling 9395 human samples (from various conditions including cancer samples) were used to identify 423 "fundamental components of human biology". As an example of their use, the authors characterized the molecular mechanisms of parthenolide anti-cancer drug action. Recently, similar large-scale analysis has been applied to a larger dataset, containing 2753 datasets and 97,049 samples  [22].
Compared to the earlier study, the authors improved the methodology in order to avoid redundant and correlated transcriptional component definitions, applying Horn's parallel analysis in order to select the optimal number of components and systematically evaluating the components' reproducibility after resampling. This analysis resulted in defining 139 reproducible and informative transcriptional modules whose value for the downstream analysis was explicitly demonstrated. Identification of the functional subsystems and distinguishing them from potentially technology driven factors can be strongly improved by the application of ICA analysis to multiple similar datasets independently (without merging them). In this scenario, the ICA results from several datasets were compared with each other in terms of the correlation or other suitable similarity measure among metagenes (Figure  4 ).
In the case of cancer, one of the first applications of this approach was done in Reference  [27]  for 800 breast cancer samples from four independently profiled cohorts with a conclusion that independent components matched well the underlying cancer mechanisms. This type of meta-analysis was further upscaled in Reference  [33] , where 22 non-redundant cancer transcriptomic datasets were analyzed. Some of the datasets were related to the same cancer type, i. e. , eight of them were collecting samples of bladder cancer and six were from breast cancer. Because the datasets used in this study were produced using different technological platforms, this analysis identified the technical biases captured by individual components in specific datasets and not reproduced among others. It also distinguished cancer type-specific functional subsystems (such as differentiation program of urothelial tissue) and generic and potential pancancer-wise important functional subsystems (such as the transcriptional program of proliferation or oxphos).
Interestingly, one of the bladder cancer-specific components associated with differentiation of urothelial tissue was also associated with amplification of a genomic region, containing a particular transcription factor (PPARG). This led to a conclusion about the role of PPARG in differentiated bladder tumors which was validated experimentally. In Reference  [38] , 14 non-redundant colon cancer transcriptomic datasets were analyzed by ICA, and the resulting s k vectors were matched with each other through correlation in order to reveal the functional modules implicated in colon cancer tumor cells' and the variability of tumoral microenvironment. In the case of a very good match between ICA-based metagene definitions from several independent datasets, one can define a consensus metagene definition from the meta-analysis (a meta-metagene).
An exemplary set of such reference metagenes was built in Reference  [33]  and used in other studies to facilitate the interpretation of the ICA results. This set included (a) ICA-derived and universal for many cancer types of proliferation-, oxphos-, immune infiltration-, interferon signaling-associated metagenes; (b) consensus metagenes associated with the presence of non-tumor cells of several types in TME; and (c) bladder cancer-specific transcriptional modules (such as differentiation program of urothelial tissue). A comprehensive catalogue of ICs identified in the pancancer TCGA dataset containing 32 cancer types was produced in Reference  [34]. It appears to be a useful effort to extend the collection of reference consensus metagenes, since they seem to be highly generalizable (reproducible in independent datasets)  [22, 38].
Applications to Unsupervised Cell Type Deconvolution In cancer biology, bulk omics data (especially transcriptome and methylome) represent heterogeneous samples such as peripheral blood mononuclear cell (PBMC) and tumor biopsies, in which the expression profiles of distinct cell types are mixed in each sample at a priori unknown proportions. The tumor microenvironment is composed of many different cells including a plethora of immune cells, stromal cells, and blood and lymphatic vessels  [66]. The quantities and the nature of the TME compartments change with the cancer type and cancer stage. Recent works showed that In the case of a very good match between ICA-based metagene definitions from several independent datasets, one can define a consensus metagene definition from the meta-analysis (a meta-metagene).
An exemplary set of such reference metagenes was built in Reference  [33]  and used in other studies to facilitate the interpretation of the ICA results. This set included (a) ICA-derived and universal for many cancer types of proliferation-, oxphos-, immune infiltration-, interferon signaling-associated metagenes; (b) consensus metagenes associated with the presence of non-tumor cells of several types in TME; and (c) bladder cancer-specific transcriptional modules (such as differentiation program of urothelial tissue). A comprehensive catalogue of ICs identified in the pan-cancer TCGA dataset containing 32 cancer types was produced in Reference  [34]. It appears to be a useful effort to extend the collection of reference consensus metagenes, since they seem to be highly generalizable (reproducible in independent datasets)  [22, 38].
Applications to Unsupervised Cell Type Deconvolution In cancer biology, bulk omics data (especially transcriptome and methylome) represent heterogeneous samples such as peripheral blood mononuclear cell (PBMC) and tumor biopsies, in which the expression profiles of distinct cell types are mixed in each sample at a priori unknown proportions. The tumor microenvironment is composed of many different cells including a plethora of immune cells, stromal cells, and blood and lymphatic vessels  [66]. The quantities and the nature of the TME compartments change with the cancer type and cancer stage. Recent works showed that immune cells could influence tumor cells in different ways and that the immune therapies take advantage of the protective function of the immune system and aim to activate patients' immune defense.
They were proven to correctly estimate the cell-type abundance in silico simulated datasets, in vitro cell mixtures, and blood or PBMC transcriptomes coupled with fluorescence-activated cell sorting (FACS) estimations. However, it remains unclear how many cell types or cell states can be quantified from bulk transcriptomes as each tool comes with own definition of cell-types (e. g. , T-cell) and subtypes (e. g. , CD4-activated T-cell) or cell states (e. g. , cytotoxic T-cell). In response to this problem, reference-free (also called unsupervised) approaches propose a more data-driven way of performing the deconvolution. This group of approaches is able to discover the cell types and their markers as well as approximate profiles of those cell types (perform "complete deconvolution"). Different types of matrix factorization are suitable for solving this problem.
In Reference  [42]  icasso-stabilized fastICA was applied to a set of six large breast cancer patient cohorts profiled for gene expression. It was demonstrated that the immune-related factors, especially the signal of T-cell, B-cell, and macrophages were highly reproducible in independent datasets (Figure  5b ). In Reference  [75] , the DeconICA R package (Available online: https://github. com/UrszulaCzerwinska/ DeconICA) was developed with the objective to apply ICA to the task of cell type deconvolution. It was shown that ICA is able to efficiently estimate the cell type proportions with better accuracy than leading supervised algorithms even though it can identify less cell sub-types than most of the published solutions. It suggests that ICA-based deconvolution is less prone to overfitting and enables discovery and quantification of strong and stable signals (not necessary the most abundant but rather the most specific).
DeconICA was applied to a big corpus of data containing more than 100 transcriptomic datasets composed of over 28,000 samples of 40 tumor types generated by different technologies and processed independently. In addition, the ICA-derived metagenes were used as context-specific signatures in order to study the characteristics of immune cells in different tumor types. The analysis revealed a large diversity and plasticity of immune cells dependent and independent on tumor type. Some conclusions of the study can be helpful in the identification of new drug targets or biomarkers for immunotherapy of cancer. [76]  containing measurements of two references transcriptomic profiles of cell lines and their mixtures at known proportions. The first two ICs identify the types and the effect of the platform.
(b) Correlation graph among selected components from ICA applied to six non-redundant breast cancer transcriptomic datasets. Three cliques formed in the graph correspond to major immune cell types. The thickness of the edges reflects the absolute correlation value. "Immune" meta-metagene was defined in Reference  [33]  as the one associated with the presence of immune infiltrate in a tumor. This figure was reproduced with permission from Reference  [42]. Cell-type composition can be also computed from DNA methylation data. In the EWAS (Epigenome Wide Association Studies), the variation origination from cell types is considered as an important confounding factor that should be removed before comparing cases and controls and defining Differentially Methylated Positions (DMPs). For example, in Reference  [77]  ten tools for epigenome deconvolution were reviewed.
ICA Applications to Single-Cell Omics Data Analysis Statistical properties of ICA seem to be very attractive to justify its application to the emerging wealth of single-cell omics data profiles. ICA can serve here to improve the data analysis regarding dimensionality reduction, removing technical biases, integrating datasets. ICA also looks promising and represents an alternative to the standard dimensionality reduction followed by clustering methodology for identifying cell types or states, suggesting a more continuous way of considering them, with a possibility of existence of intermediate or mixed cell populations. Similar to bulk RNA-seq, technical biases and batch effects are limiting factors for single-cell RNA-Seq and should be either removed or taken into account. One example of ICA application to normalize batch effect was recently reported by Dirkse et al.
[79]. The authors observed a strong difference between the original patient-derived cell line and its two subpopulations measured in the second batch (all cells undergo the same protocol of cell growth and sorting, so biological differences   [76]  containing measurements of two references transcriptomic profiles of cell lines and their mixtures at known proportions. The first two ICs identify the types and the effect of the platform. (b) Correlation graph among selected components from ICA applied to six non-redundant breast cancer transcriptomic datasets. Three cliques formed in the graph correspond to major immune cell types. The thickness of the edges reflects the absolute correlation value. "Immune" meta-metagene was defined in Reference  [33]  as the one associated with the presence of immune infiltrate in a tumor.
ICA was used to define the continuous spectrum of differentiation in hematopoietic cells from scRNA-Seq data in Reference  [87] ; several latent factors were associated to the underlying biological mechanisms of differentiation. In Reference  [80]  three independent components computed for a scRNA-Seq dataset were matched with transcriptional programs specific to B-cells, macrophages, and monocytes and used to provide an interpreTable 3D data visualization. Interestingly, in order to establish the biological origin of these components, they were correlated to the ICA decomposition of the transcriptomic atlas of murine cell types from which 120 independent components were extracted. ICA served as a principal machine learning method for discovering functional subsystems involved in the response of Ewing sarcoma cells to the induction of the chimeric oncogenic transcription factor EWSR-FLI1  [62].
In Reference  [85] , ICA was applied in order to define subtypes of the immune-related cells present in the TME of melanoma (with original data from Reference  [86] ) and relate them to the mechanisms of innate immune response. ICA was used to define the continuous spectrum of differentiation in hematopoietic cells from scRNA-Seq data in Reference  [87] ; several latent factors were associated to the underlying biological mechanisms of differentiation. In Reference  [80]  three independent components computed for a scRNA-Seq dataset were matched with transcriptional programs specific to B-cells, macrophages, and monocytes and used to provide an interpreTable 3D data visualization. Interestingly, in order to establish the biological origin of these components, they were correlated to the ICA decomposition of the transcriptomic atlas of murine cell types from which 120 independent components were extracted.