The biological knowledge discovery by PCCF measure and PCA-F projection

Analyzing the similarity of samples and genes by MG-PCC algorithm, t-SNE-SS and t-SNE-SG maps

BACKGROUND

For analyzing these gene expression data sets under different samples, clustering and visualizing samples and genes are important methods. However, it is difficult to integrate clustering and visualizing techniques when the similarities of samples and genes are defined by PCC(Person correlation coefficient) measure.

RESULTS

Here, for rare samples of gene expression data sets, we use MG-PCC (mini-groups that are defined by PCC) algorithm to divide them into mini-groups, and use t-SNE-SSP maps to display these mini-groups, where the idea of MG-PCC algorithm is that the nearest neighbors should be in the same mini-groups, t-SNE-SSP map is selected from a series of t-SNE(t-statistic Stochastic Neighbor Embedding) maps of standardized samples, and these t-SNE maps have different perplexity parameter. Moreover, for PCC clusters of mass genes, they are displayed by t-SNE-SGI map, where t-SNE-SGI map is selected from a series of t-SNE maps of standardized genes, and these t-SNE maps have different initialization dimensions. Here, t-SNE-SSP and t-SNE-SGI maps are selected by A-value, where A-value is modeled from areas of clustering projections, and t-SNE-SSP and t-SNE-SGI maps are such t-SNE map that has the smallest A-value.

CONCLUSIONS

From the analysis of cancer gene expression data sets, we demonstrate that MG-PCC algorithm is able to put tumor and normal samples into their respective mini-groups, and t-SNE-SSP(or t-SNE-SGI) maps are able to display the relationships between mini-groups(or PCC clusters) clearly. Furthermore, t-SNE-SS(m)(or t-SNE-SG(n)) maps are able to construct independent tree diagrams of the nearest sample(or gene) neighbors, where each tree diagram is corresponding to a mini-group of samples(or genes).

Multiple-cumulative probabilities used to cluster and visualize transcriptomes

Analysis of gene expression data by clustering and visualizing played a central role in obtaining biological knowledge. Here, we used Pearson's correlation coefficient of multiple-cumulative probabilities (PCC-MCP) of genes to define the similarity of gene expression behaviors. To answer the challenge of the high-dimensional MCPs, we used icc-cluster, a clustering algorithm that obtained solutions by iterating clustering centers, with PCC-MCP to group genes. We then used t-statistic stochastic neighbor embedding (t-SNE) of KC-data to generate optimal maps for clusters of MCP (t-SNE-MCP-O maps). From the analysis of several transcriptome data sets, we demonstrated clear advantages for using icc-cluster with PCC-MCP over commonly used clustering methods. t-SNE-MCP-O was also shown to give clearly projecting boundaries for clusters of PCC-MCP, which made the relationships between clusters easy to visualize and understand.