PCA is a statistical method used to reduce high-dimensional data (such as scRNA-Seq data) into lower dimensions, while retaining most of the original data information (21). PCA is an orthogonal linear transformation of the data points of the original dataset (22), creating new variables known as PCs that are unrelated amongst themselves and each PC captures decreasing proportions of the total variance of the original dataset (23). There are several approaches to detect the number of PCs that need to be kept in order to retain most of the variability of the original dataset, while excluding variability that is caused by noise. One of the most commonly used methods is keeping the top PCs that explain an arbitrarily selected percentage of variability, although that may include a large number of PCs that explain variability that is attributed to noise. On the other hand, the PCs and the variability of the dataset they explain can be plotted and the top ones can be selected using the ‘elbow’ method (24); however, in many cases, the ‘elbow’ may not be easily defined. In both cases, the remainder of the PCs are discarded, thus efficiently reducing the dataset dimensions (25).

When cells in scRNA-Seq data are treated as data points, PCs are linear combinations of genes, known as latent genes (26). As scRNA-Seq data provide no prior information about the identity of each cell, PCA, as an unsupervised method, may capture the linear associations present in the scRNA-Seq gene expressions, producing a low-dimension dataset, having an equal amount of cells as originally studied, and a smaller number of latent genes than in the original dataset, while retaining most of its variance (20). The produced low-dimensional gene expression matrix is commonly used as input to visualisation algorithms or for additional analyses.

To visualise high-dimensional data in a comprehensible form, data first need to undergo dimensionality reduction and then, to be mapped into two dimensions if a plot is drawn (20). Alternatively, if 3D-visualisation software is used, data need to be mapped into three dimensions. For scRNA-Seq data, there are two major methods for dimensionality reduction into two or three dimensions, and subsequent visualisation: t-distributed stochastic neighbour embedding (t-SNE) and uniform manifold approximation and projection (UMAP). t-SNE (14) was created as an improvement to the SNE method (27), which uses a Gaussian distribution to determine the similarity of the low-dimensional points and determines the low-dimensional representation through a loss function. t-SNE uses a Student-t distribution and an improved loss function, ultimately offering better spread of the data points and faster run time, respectively. UMAP (28) constructs a k-neighbour weighted graph and subsequently computes a lower-dimension layout of it. UMAP is more recent and was developed as an alternative to t-SNE, having an even lower execution time, while claiming to preserve the global structure of the data; i.e., the overall arrangement of the clusters, better.

t-SNE and UMAP, as non-linear methods, are commonly used in scRNA-Seq analysis pipelines to perform visualisation of the cells, being able to capture the non-linear relationships of the data. Cells (as data points) with similar expression patterns are grouped closer to each other in the three-dimensional space. Subsequently, by colour-coding each cell using given annotations, e.g., cell-type, tissue, etc., it is possible to define novel cell sub-populations with distinct expression patterns, through visual exploration (29). In a similar manner, genes may also be visualised. In this case, the users are able to discover groups of co-expressed genes with similar expression patterns (30), although thorough gene annotations are necessary to define the biologically-connected gene clusters.

Both t-SNE and UMAP are able to preserve the global, as well as the local structure of data, using proper data initialisation, PCA being one of the options for this step (31), while also having similar execution times with parameter tuning. Thus, it is recommended to perform a different dimensionality reduction approach as a pre-processing step prior to trying out both methods, when visualising scRNA-Seq data, and determining which plot better depicts the organisation of the cell clusters.

PCA, t-SNE and UMAP are already established techniques and integral parts in the pre-processing and visualisation of scRNA-Seq data (29) and are also included in major processing pipelines and software, such as SEURAT (32) and Cell Ranger (10). Thus, these methods are used in the majority of scientific studies that include scRNA-Seq data analysis. Nevertheless, the increasing diversity and dimensionality of scRNA-Seq data necessitated the usage of more advanced techniques for their efficient analysis.

The advancement of neural networks using multiple hidden layers, coupled with increased computing power, has led to the evolution of machine learning to deep learning (33). The ability of deep learning-based methods to be trained and learn the distribution of the input data was proven valuable for the construction of tools that deal with the high-dimensionality and sparsity of scRNA-Seq data. One such tool is scvis (34), an autoencoder-based method for the dimensionality reduction and subsequent visualisation of scRNA-Seq data. Autoencoders are an archetypal deep-learning technique consisting of two neural networks with hidden layers: One encoder network and one decoder network. Autoencoders are trained to learn compressed representations of input data (35). At first glance, scvis is similar in functionality to t-SNE and UMAP, as it is mainly used for the visualisation of cells and detection of new cell subtypes. However, scvis can detect both linear and non-linear associations in the data and has been shown to possess improved performance, achieving similar or better grouping of data points, while also scaling better with larger datasets (34). Nevertheless, data initialisation is equally necessary in the case of scvis, to preserve both global and local alignment of the original data.

Another autoencoder-based technique is deep count autoencoder (DCA) (36). As opposed to scvis, DCA is used for the denoising of scRNA-Seq data, which refers to the efficient imputation of data, while also aiming to improve the expression estimation of all gene counts (37). DCA exhibits better performance compared to commonly used imputation techniques, such as SAVER (38) and scImpute (39), showcasing the application of autoencoders for performing simultaneous dimensionality reduction and imputation. The rapid advancement of deep learning has enabled further improvements in neural networks, in the form of variational autoencoders (VAEs) and generative adversarial networks (GANs), which have skyrocketed in popularity.

VAEs (40) represent a paradigm shift in the field of deep learning, particularly in their application to complex, high-dimensional datasets. At their core, VAEs are an advancement of traditional autoencoders (35), although VAEs diverge significantly by incorporating a probabilistic framework. This framework involves the encoder network mapping input data not to a deterministic point, but to a probability distribution within a latent space. Consequently, the decoder network reconstructs the input data by sampling from this latent distribution. This probabilistic approach is underpinned by the principles of variational inference, enabling the approximation of complex data distributions. The incorporation of stochasticity in the encoding process allows VAEs to generate new data samples by sampling from the learned latent space distribution.

VAEs have been proven as an effective tool for reducing scRNA-Seq data dimensionality, while retaining the biological properties of the original dataset (41). VAEs not only compress gene expression data into a more manageable latent space, considering that such datasets can contain data of >100,000 cells, but they also capture the biological variance across cells, while mitigating the impact of the inherent noise and sparsity of scRNA-Seq data (42). The sampling of the probabilistic latent space in VAEs yields different datasets each time, yet properly trained models tend to produce results that exhibit minimal variance among them (40). Furthermore, utilising non-linear transformations for producing a low-dimensional latent space through the training on non-linear mappings of high-dimensional data could improve data clustering (43). Thus, the low-dimensional gene expression generated by trained VAEs, can facilitate downstream analyses (44), such as cell clustering, gene co-expression or regulatory network inference or protein-protein association network construction. Such applications of VAEs have been developed, including DiffVAE (45) for modelling cell differentiation, BEENE (46) for improved batch correction, β-TCVAE (47), which was used for data integration in single-cell GTEx (48) and FAVA (49) for the inference of high-quality protein-protein association networks. The newest version of STRING, used FAVA for the computation of the co-expression scores, as the results of this method outperformed their previous ones, since they were able to capture both linear and non-linear associations of the scRNA-Seq data (50).

GANs (51) are a class of deep learning algorithms that have garnered significant attention for their ability to generate high-quality, synthetic data samples. A GAN consists of two neural networks, the generator and the discriminator, engaged in a continuous adversarial process. The generator attempts to produce data samples indistinguishable from real data, while the discriminator strives to differentiate between the generator's synthetic data and actual data. This adversarial training encourages the generator to produce increasingly realistic samples, adjusting its parameters to produce data that better model the complex distribution of the input data.

In the context of the analysis of scRNA-Seq data, GANs are particularly valuable as they can learn to capture and reproduce the intricate structures and patterns inherent in such data. Instead of performing dimensionality reduction in a direct way, i.e., by performing feature extraction on the genes or samples, GANs generate new datasets of a desired number of dimensions, thus indirectly reducing the dimensionality of the original dataset. GANs can be employed to learn the complex distribution of scRNA-Seq data, and once trained, GANs may generate synthetic, yet biologically plausible, single-cell gene expression profiles (52). These ‘fabricated’ datasets can be used to augment the original dataset as input to other algorithms, in the cases where data scarcity prevents the easy procurement of training datasets and be utilised in place of a high-dimensional dataset, while providing a similar amount of biological information or by imitating data derived from specific biological conditions (53). GANs outperform the usual methods for synthetic scRNA-Seq dataset generation, when their output is used to construct gene regulatory networks, as GANs can more efficiently generate realistic datasets and thus allowing downstream network creation algorithms that perform well on synthetic datasets to generalise well on real data (54). Applications of GANs in scRNA-Seq data include cscGAN (55) and LSH-GAN (56), used for dataset generation. Certain methods, such as AGImpute (57), combine both autoencoders and GANs in their approach, in this case, to perform cell-type aware imputation of scRNA-Seq data.