Author: Neo Christopher Chung <nchchung@gmail.com>, Wei Hao <whao@princeton.edu>, John D. Storey <jstorey@princeton.edu>

Title: Statistical Inference for Unsupervised Learning
Description: Test for association between the observed data
and their systematic patterns of variations, that are often extracted by unsupervised learning.
Systematic patterns may be captured by latent variables using principal component analysis (PCA), factor analysis (FA), and related methods. This allows one to, for example, obtain principal components (PCs) and conduct rigorous statistical testing for association between observed variables and PCs. Similarly, unsupervised clustering, such as K-means clustering, partition around medoids (PAM), and other algorithms, finds subpopulations among the observed variables. The jackstraw test can estimate statistical significance of cluster membership, so that one can evaluate the strength of membership assignments. This package also includes several related methods to support statistical inference and probabilistic feature selection for unsupervised learning.
Imports: corpcor, cluster, ClusterR, qvalue, methods, lfa, stats

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.
Imports: corpcor, cluster, methods, ClusterR, qvalue, lfa, stats,

<jstorey@princeton.edu>, Wei Hao <whao@princeton.edu>, Alejandro Ochoa <alejandro.ochoa@duke.edu>
Description: Test for association between the observed data and their estimated latent variables. The jackstraw package provides a resampling strategy and testing scheme to estimate statistical significance of association between the observed data and their latent variables. Depending on the data type and the analysis aim, the latent variables may be estimated by principal component analysis (PCA), factor analysis (FA), K-means clustering, and related algorithms. The jackstraw methods learn over-fitting characteristics inherent in this circular analysis, where the observed data are used to estimate the latent variables and used again to test against that estimated latent variables. When latent variables are estimated by PCA, the jackstraw enables statistical testing for association between observed variables and latent variables, as estimated by low-dimensional principal components (PCs). This essentially leads to identifying variables that are significantly associated with PCs. Similarly, unsupervised clustering, such as K-means clustering, partition around medoids (PAM), and others, finds coherent groups in high-dimensional data. The jackstraw estimates statistical significance of cluster membership, by testing association between data and cluster centers. Clustering membership can be improved by using the resulting jackstraw p-values and posterior inclusion probabilities (PIPs), with an application to unsupervised evaluation of cell identities in single cell RNA-seq.
Imports: methods, stats, qvalue, corpcor, irlba, rsvd, ClusterR,