ELF: Extract Landmark Features By Optimizing Topology Maintenance, Redundancy, and Specificity

Feature selection is the process of selecting a subset of landmark features for model construction when there are many features and a comparatively few samples. The far-reaching development technologies such as biological sequencing at single cell level make feature selection a more challenging work. The difficulty lies in four facts: those features measured are in high dimension and with noise; dropouts make the data much sparse; many features are either redundant or irrelevant; and samples are not well-labeled in the experiments. Here, we propose a new model called ELF (Extract Landmark Features) to address the above challenges. ELF aims to simultaneously maximize topology maintenance to keep the pairwise relationships among samples, minimize feature redundancy to diversify the features, and maximize feature specificity to make every selected feature more representative. This makes ELF a nonlinear combinatorial optimization. To solve this difficult problem, we propose a heuristic algorithm based on greedy strategy. We show ELF's outstanding performance on two single cell RNA-seq datasets. One is the direct reprogramming from mouse embryonic fibroblasts to induced neuron and the other is hepatoblast differentiation. ELF is able to choose only hundreds of landmark genes to maintain the cells’ correlativity. Topology maintenance, redundancy removal, and specificity each plays its important role in selecting landmark features and revealing cells’ biological functions. In addition, ELF can be generally applied in other scenarios. We demonstrate that ELF can reveal pivotal pixel in writing region and human face in two public image datasets. We believe that ELF is a useful tool to obtain more interpretable results by revealing key features while clustering the samples well.