Manifold denoising by Nonlinear Robust Principal Component Analysis

Authors: He Lyu, Ningyu Sha, Shuyang Qin, Ming Yan, Yuying Xie, Rongrong Wang

NeurIPS 2019 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental The efficacy of our method is demonstrated on both synthetic and real datasets. 7 Numerical experiment Simulated Swiss roll: We demonstrate the superior performance of NRPCA on a synthetic dataset following the mixed noise model (1). The MNIST datasest: We observed some interesting dimension reduction result of MNIST with the help of NRPCA. Biological data: We illustrate the potential usefulness of NRPCA algorithm on an embryoid body (EB) differentiation dataset over a 27-day time course
Researcher Affiliation Academia He Lyu, Ningyu Sha, Shuyang Qin, Ming Yan, Yuying Xie, Rongrong Wang Department of Computational Mathematics, Science and Engineering Michigan State University {lyuhe,shaningy,qinshuya,myan,xyy,wangron6}@msu.edu
Pseudocode Yes Algorithm 1: Estimate the mean curvature Γ(p) at some point p Algorithm 2: Estimate the overall curvature Γ(Ω) for some region Ω Algorithm 3: Nonlinear Robust PCA
Open Source Code No The paper does not provide any explicit statements or links for open-source code availability.
Open Datasets Yes Simulated Swiss roll: We sampled 2000 noiseless data Xi uniformly from a 3D Swiss roll... The MNIST datasest: ... Biological data: We illustrate the potential usefulness of NRPCA algorithm on an embryoid body (EB) differentiation dataset over a 27-day time course, which consists of gene expressions for 31,000 cells measured with single-cell RNA-sequencing technology (sc RNAseq) [13, 16].
Dataset Splits No The paper does not provide explicit training/validation/test dataset splits for reproducibility.
Hardware Specification No The paper does not specify any particular hardware (e.g., GPU/CPU models, memory) used for running the experiments.
Software Dependencies No The paper mentions various algorithms and methods (e.g., FISTA, Singular Value Hard Thresholding, Dijkstra's algorithm, Isomap, Laplacian Eigenmaps, LLE) but does not provide specific version numbers for any software dependencies.
Experiment Setup Yes We applied NRPCA to the simulated data with patch size k = 15. after the NRPCA denoising (with k = 11). We first normalized the sc RNAseq data following the procedure described in [16] and randomly selected 1000 cells using the stratified sampling framework to maintain the ratios among different developmental stages. We applied our NRPCA method to the normalized subset of EB data and then applied Locally Linear Embedding (LLE) to the denoised results.