Covariate-Assisted Community Detection on Sparse Networks

Community detection is an important problem when processing network data. Traditionally, this is done by exploiting the connections between nodes, but connections can be too sparse to detect communities in many real datasets. Node covariates can be used to assist community detection; see Binkiewicz et al. (2017); Weng and Feng (2022); Yan and Sarkar (2021); Yang et al. (2013). However, how to combine covariates with network connections is challenging, because covariates may be high-dimensional and inconsistent with community labels. To study the relationship between covariates and communities, we propose the degree corrected stochastic block model with node covariates (DCSBM-NC). It allows degree heterogeneity among communities and inconsistent labels between communities and covariates. Based on DCSBM-NC, we design the adjusted neighbor-covariate (ANC) data matrix, which leverages covariate information to assist community detection. We then propose the covariate-assisted spectral clustering on ratios of singular vectors (CA-SCORE) method on the ANC matrix. We prove that CA-SCORE successfully recovers community labels when 1) the network is relatively dense; 2) the covariate class labels match the community labels; 3) the data is a mixture of 1) and 2). CA-SCORE has good performance on synthetic and real datasets. The algorithm is implemented in the R(R Core Team (2021)) package CASCORE

PCA matrix denoising is uniform

Principal component analysis (PCA) is a simple and popular tool for processing high-dimensional data. We investigate its effectiveness for matrix denoising. We assume i.i.d. high dimensional Gaussian noises with standard deviation $\sigma$ are added to clean data generated from a low dimensional subspace. We show that the distance between each pair of PCA-denoised data point and the clean data point is uniformly bounded by \Otilde(\sigma), assuming a low-rank data matrix with mild singular value assumptions. We show such a condition could arise even if the data lies on curves. We then provide a general lower bound for the error of the denoised data matrix, which indicates PCA denoising gives a uniform error bound that is rate-optimal. Furthermore, we examine how the error bound impacts downstream applications such as empirical risk minimization, clustering, and manifold learning. Numerical results validate our theoretical findings and reveal the importance of the uniform error.Comment: 26 pages, 2 figure

Analysis of High Frequency Noise of Inverter Rotary Compressor

The inverter compressor driven by the inverter will cause high frequency noise, which will have adverse influence on total noise value and sound quality. In order to improve this problem, an existing compact rotary inverter compressor is studied in this paper. The influence law of inverter carrier wave of space vector pulse width modulation(SVPWM) technique on motor vibration and noise of compressor is analyzed and summarized. Combining order analysis and motor modal analysis, the results show that the high harmonic current induced by inverter carrier wave will produce high frequency electromagnetic force which excites the stator resonance, and finally results in high frequency noise of the compressor. Through optimization of the motor structure, the high frequency noise is reduced by more than 5dB(A), the sound quality is improved as well

Graph matching beyond perfectly-overlapping Erdős–Rényi random graphs

Graph matching is a fruitful area in terms of both algorithms and theories. Given two graphs G1=(V1,E1) and G2=(V2,E2), where V1 and V2 are the same or largely overlapped upon an unknown permutation π∗, graph matching is to seek the correct mapping π∗. In this paper, we exploit the degree information, which was previously used only in noiseless graphs and perfectly-overlapping Erdős–Rényi random graphs matching. We are concerned with graph matching of partially-overlapping graphs and stochastic block models, which are more useful in tackling real-life problems. We propose the edge exploited degree profile graph matching method and two refined variations. We conduct a thorough analysis of our proposed methods’ performances in a range of challenging scenarios, including coauthorship data set and a zebrafish neuron activity data set. Our methods are proved to be numerically superior than the state-of-the-art methods. The algorithms are implemented in the R (A language and environment for statistical computing, R Foundation for Statistical Computing, Vienna, 2020) package GMPro (GMPro: graph matching with degree profiles, 2020)