Statistical Inference for Unsupervised Learning

Test for association between the observed data and their systematic patterns of variations. The jackstraw enables statistical testing for association between observed variables and latent variables, as captured by principal component analysis (PCA), factor analysis (FA), or other estimates. Similarly, unsupervised clustering, such as K-means clustering, partition around medoids (PAM), and others, finds subpopulations among the observed variables. The jackstraw estimates statistical significance of cluster membership, including unsupervised evaluation of cell identities in single cell RNA-seq. P-values and posterior probabilities allows one to rigorously evaluate the strength of cluster membership assignments. See the GitHub repository for the latest developments and further helps.

This R package performs association tests between the observed data and their systematic patterns of variation. Systematic variation can be modeled by latent variables, that are likely arising from biological processes, experimental conditions, and environmental factors. We are often interested in estimating these patterns using principal component analysis (PCA), factor analysis (FA), K-means clustering, partition around medoids (PAM), and related methods. The jackstraw methods learn over-fitting characteristics inherent in unsupervised learning, where the observed data are used to estimate the systematic patterns and to be tested again.

Using a variety of unsupervised learning techniques, the jackstraw provides a resampling strategy and testing scheme to estimate statistical significance of association between the observed data and their systematic patterns of variation. For example, the cell cycle in microarray data may be estimated by principal components (PCs); then, we can use the jackstraw for PCA to identify genes that are significantly associated with these PCs. On the other hand, cell identities in single cell RNA-seq data are identified by K-means clustering; then, the jackstraw for clustering can evaluate reliability of computationally determined cell identities.

The jackstraw tests enable us to identify the variables (or observations) that are driving systematic variation, in an unsupervised manner. Using jackstraw_pca, we can find statistically significant variables with regard to the top r principal components. Alternatively, jackstraw_kmeans can identify the variables that are statistically significant members of clusters. There are many functions to support statistical inference for unsupervised learning, such as finding a number of PCs or clusters and estimating posterior probabilities from jackstraw p-values. Furthermore, this package includes more general and experimental algorithms such as jackstraw_subspace for the dimension reduction techniques and jackstraw_cluster for the clustering algorithms.

Chung, N.C. (2018) Statistical significance of cluster membership for determination of cell identities in single cell genomics. Biorxiv, 10.1101/248633

Chung, N.C. and Storey, J.D. (2015) Statistical significance of variables driving systematic variation in high-dimensional data. Bioinformatics, 31(4): 545-554


To use a stable version from CRAN:


To use a development version from GitHub:



Some of dependencies may fail to automatically install, particularlay lfa and qvalue from Bioconductor. This would result in a warning similar to:

Error: package or namespace load failed for ‘jackstraw’ in loadNamespace(j <- i[[1L]], c(lib.loc, .libPaths()), versionCheck = vI[[j]]):
 there is no package called ‘lfa’

Then, please install these two packages manually using the following command:

biocLite(c('lfa', 'qvalue'))

Thanks to idc9 for raising this issue.


Reference manual

It appears you don't have a PDF plugin for this browser. You can click here to download the reference manual.


1.3.1 by Neo Christopher Chung, 8 months ago

Report a bug at

Browse source code at

Authors: Neo Christopher Chung <[email protected]> , John D. Storey <[email protected]> , Wei Hao <[email protected]>

Documentation:   PDF Manual  

GPL-2 license

Imports corpcor, cluster, methods, ClusterR, qvalue, lfa, stats, irlba, rsvd

Suggests parallel, knitr, rmarkdown

See at CRAN