A sparse negative binomial mixture model for clustering RNA-seq count data

Clustering with variable selection is a challenging yet critical task for modern small-n-large-p data. Existing methods based on sparse Gaussian mixture models or sparse $K$-means provide solutions to continuous data. With the prevalence of RNA-seq technology and lack of count data modeling for clustering, the current practice is to normalize count expression data into continuous measures and apply existing models with a Gaussian assumption. In this article, we develop a negative binomial mixture model with lasso or fused lasso gene regularization to cluster samples (small $n$) with high-dimensional gene features (large $p$). A modified EM algorithm and Bayesian information criterion are used for inference and determining tuning parameters. The method is compared with existing methods using extensive simulations and two real transcriptomic applications in rat brain and breast cancer studies. The result shows the superior performance of the proposed count data model in clustering accuracy, feature selection, and biological interpretation in pathways.

Kinematic cluster analysis of the crouch gait pattern in children with spastic diplegic cerebral palsy using sparse K-means method

BACKGROUND

Crouch gait pattern is a common gait pattern in children with diplegic cerebral palsy with excessive knee flexion throughout stance phase. Few studies have grouped this pattern of gait and usually have examined only the features of gait in the sagittal plane and mostly lower extremities without considering pelvis and trunk behavior. Studies usually categorize the gait pattern according to important variables from the researcher's point of view. Sparse K-means is high dimensional clustering methods that perform clustering and variable selection simultaneously even with low sample size and large number of variables. Our aim was to define existing clusters of crouch gait pattern in children with spastic diplegic cerebral palsy.

METHODS

Cluster analysis was applied on the lower extremity, pelvis and trunk gait kinematics data of 64 limbs of children with crouch gait pattern and 64 limbs of typically developing children. Eighty-nine kinematic variables were used as input variables for clustering.

FINDINGS

Four clusters of crouch gait pattern were defined. Sparse K-means identified influential variables and identified the knee and hip flexion as a major factor in clustering. Kinematic of the trunk, pelvis and ankle was determined in each cluster. Trunk and pelvis kinematic features were strongly correlated with the knee and hip joint flexion severity.

INTERPRETATION

Obtained clusters were confirmed observationally. With increasing knee flexion, the kinematic of the trunk and pelvis were further away from the patterns of typically developing individuals. The clusters ranking appear to be reasonable based on the crouch severity.