Robust Principal Component Analysis Integrating Sparse and Low-Rank Priors

Principal Component Analysis (PCA) is a widely used technique for data analysis and dimensionality reduction, but its sensitivity to feature scale and outliers limits its applicability. Robust Principal Component Analysis (RPCA) addresses these limitations by decomposing data into a low-rank matrix capturing the underlying structure and a sparse matrix identifying outliers, enhancing robustness against noise and outliers. This paper introduces a novel RPCA variant, Robust PCA Integrating Sparse and Low-rank Priors (RPCA-SL). Each prior targets a specific aspect of the data’s underlying structure and their combination allows for a more nuanced and accurate separation of the main data components from outliers and noise. Then RPCA-SL is solved by employing a proximal gradient algorithm for improved anomaly detection and data decomposition. Experimental results on simulation and real data demonstrate significant advancements.

Robust Principal Component Analysis via Truncated Nuclear Norm Minimization

Robust principal component analysis(PCA) is widely used in many applications, such as image processing, data mining and bioinformatics. The existing methods for solving the robust PCA are mostly based on nuclear norm minimization. Those methods simultaneously minimize all the singular values, and thus the rank cannot be well approximated in practice. We extend the idea of truncated nuclear norm regularization(TNNR) to the robust PCA and consider truncated nuclear norm minimization(TNNM) instead of nuclear norm minimization(NNM). This method only minimizes the smallest N-r singular values to preserve the low-rank components, where N is the number of singular values and r is the matrix rank. Moreover, we propose an effective way to determine r via the shrinkage operator. Then we develop an effective iterative algorithm based on the alternating direction method to solve this optimization problem. Experimental results demonstrate the efficiency and accuracy of the TNNM method. Moreover, this method is much more robust in terms of the rank of the reconstructed matrix and the sparsity of the error.

Local singularity and S–A methods for analyzing ore-producing anomalies in the Jianbiannongchang area of Heilongjiang,China

The Heilongjiang Jianbiannongchang area is located at the confluence of the Great and Lesser Xing’an Ranges.This area has a complex magmatic and tectonic evolutionary history that has resulted in a complex and diverse geological background for mineralization.In this study,isometric logarithmic ratio(ILR)transformations of Au,Cu,Pb,Zn,and Sb contents were performed in the1:50,000 soil geochemical data of the Jianbiannongchang area.Robust principal component analysis(RPCA)was conducted based on ILR transformation.The local singularity and spectrum-area(S-A)methods were used to extract information on mineralogic anomalies.The results showed that:(1)the transformed data eliminated the influence of the original data closure effect,and the PC1and PC2 information obtained by applying RPCA reflected ore-producing element anomalies dominated by Au and Cu.(2)The local singularity method can enhance the information of the local strong and weak slow anomalies.After performing local singularity analysis on PC1 and PC2,the obtained local anomalies reflected the local singularity spatial anomaly patterns related to Cu and Au mineralization in this area,which is an effective method for trapping ore-producing anomalies.(3)Furthermore,the composite anomaly decomposition of PC1 and PC2 was performed using the S-A method,and the screened anomalous and background fields reflect the ore-producing anomalies related to Cu and Au mineralization.This information is in agreement with known Cu and Au mineralization.(4)The geochemical anomalies with mineralization potential were obtained outside the known mineralization sites by integrating the information of oreproducing anomalies extracted by the local singularity and S-A methods,providing the theoretical basis and exploration direction for future exploration in the study area.

Mainlobe jamming suppression via improved BSS method for rotated array radar

This study deals with the problem of mainlobe jamming suppression for rotated array radar.The interference becomes spatially nonstationary while the radar array rotates,which causes the mismatch between the weight and the snapshots and thus the loss of target signal to noise ratio(SNR)of pulse compression.In this paper,we explore the spatial divergence of interference sources and consider the rotated array radar anti-mainlobe jamming problem as a generalized rotated array mixed signal(RAMS)model firstly.Then the corresponding algorithm improved blind source separation(BSS)using the frequency domain of robust principal component analysis(FDRPCA-BSS)is proposed based on the established rotating model.It can eliminate the influence of the rotating parts and address the problem of loss of SNR.Finally,the measured peakto-average power ratio(PAPR)of each separated channel is performed to identify the target echo channel among the separated channels.Simulation results show that the proposed method is practically feasible and can suppress the mainlobe jamming with lower loss of SNR.

Identifying porphyry-Cu geochemical footprints using local neighborhood statistics in Baft area, Iran

Identifying geochemical anomalies related to ore deposition processes facilitates the practice of vectoring toward undiscovered mineral deposit sites.In districtscale exploration studies,analysis of dispersion patterns of ore-forming elements results in more-reliable targets.Therefore,deriving significant geochemical footprints and mapping the ensuing geochemical anomalies are of important issues that lead exploration geologists toward anomaly sources,e.g.,mineralization.This paper aims to examine the effectiveness of local relative enrichment index and singularity mapping technique,as two methods of local neighborhood statistics,in the delineation of anomalous areas for further exploration.A data set of element contents obtained from stream sediment samples in Baft area,Iran,therefore was applied to illustrate the procedure proposed.The close relationship between anomalous patterns recognized and known Cu-occurrences demonstrated that the procedures proposed can efficiently model complex dispersion patterns of geochemical anomalies in the study area.The results showed that singularity mapping method is a better technique,compared to local relative enrichment index,to delineate targets for follow-up exploration in the area.We made this comparison because,as pointed out by exploration geochemists,dispersion patterns of geochemical indicators in stream sediments vary in different areas even for the same deposit type.The variety in the dispersion patterns is due to the operation of post-mineralization subsystems,which are affected by local factors such as landscape of the areas under study.Therefore,the effectiveness of the methods should be evaluated in every area for every targeted deposit.