Computational Systems Biology Methods and Protocols.7z

smooth measure of the effective number of neighbors. The perfor-

mance of t-SNE is fairly robust to changes in the perplexity and

typical values are between 5 and 50. The second parameter is the

low dimension s, which is arbitrarily set to two for convenient

visualization. However, no research has been conducted to investi-

gate how much the low dimension parameter should be set to.

We proposed that the low dimension parameter can be set as

the intrinsic dimensionality of the sparse gene expression matrix.

For the first time, we estimated the intrinsic dimensionality of

scRNA-seq data using six methods (Table 3). They were

eigenvalue-based estimation (EigValue) [17], maximum likelihood

estimation (MLE) [22], correlation dimension (CorrDim) [23],

nearest neighbor evaluation (NearNb) [24], geodesic minimum

spanning tree (GMST) [25], and packing numbers (PackingNum-

bers) [26]. These methods were implemented using the MATLAB

toolbox for dimensionality reduction (available at http://

lvdmaaten.github.io/drtoolbox/). Although preliminary results

were obtained using only a colon cancer scRNA-seq dataset (Sub-

heading2), it still suggested that the intrinsic dimensionality could

be six estimated by EigValue. Since five other methods are

parameter-dependent except EigValue, further estimation needs

to be performed using adjusted parameters based on grid search,

avoiding the arbitrary settings. The final intrinsic dimensionality

must be determined by combined use of six or more methods.

Until this chapter was written, the most popular application of

cluster analysis using scRNA-seq data was to identify cells in terms

of known or novel types and then perform downstream analyses

(e.g., differential expression or regulatory network analysis) based

Table 3
Estimating intrinsic dimensionality of scRNA-seq data

Method Raw Raw Gaussian ERCC ERCC Gaussian DESeq DESeq Gaussian

EigValue 7 6 5 6 7 6

MLE 19.00 19.92 15.27 19.92 22.28 19.92

CorrDim 0.47 2.89 0.56 2.89 0.51 2.89

NearNb 0.05 0 0.03 0 0.01 0

GMST 5.21 28.01 4.71 29.78 6.25 17.36

PackingNumbers 0 0 0 0 0 0

EigValue represents eigenvalue-based estimation. MLE represents maximum likelihood estimation. CorrDim represents
correlation dimension. NearNb represents nearest neighbor evaluation. GMST represents geodesic minimum spanning
tree. PackingNumbers represents packing numbers. Raw represents gene expression data using read counts of nuclear
RNA (Table2). Raw Gaussian represents raw data processed by the standard Gaussianization. ERCC represents normal-
ized data using the ERCC method. ERCC Gaussian represents ERCC-normalized data processed by the standard
Gaussianization. DESeq represents normalized data using DESeq. DESeq Gaussian represents DESeq-normalized data
processed by the standard Gaussianization. The standard Gaussianization was performed on each row of the gene
expression matrix (Fig.2a) by the difference of mean and divided by the standard deviation

322 Shan Gao