Principal component analysis for second-order stationary vector time series

We extend the principal component analysis (PCA) to second-order stationary vector time series in the sense that we seek for a contemporaneous linear transformation for a $p$-variate time series such that the transformed series is segmented into several lower-dimensional subseries, and those subseries are uncorrelated with each other both contemporaneously and serially. Therefore those lower-dimensional series can be analysed separately as far as the linear dynamic structure is concerned. Technically it boils down to an eigenanalysis for a positive definite matrix. When $p$ is large, an additional step is required to perform a permutation in terms of either maximum cross-correlations or FDR based on multiple tests. The asymptotic theory is established for both fixed $p$ and diverging $p$ when the sample size $n$ tends to infinity. Numerical experiments with both simulated and real data sets indicate that the proposed method is an effective initial step in analysing multiple time series data, which leads to substantial dimension reduction in modelling and forecasting high-dimensional linear dynamical structures. Unlike PCA for independent data, there is no guarantee that the required linear transformation exists. When it does not, the proposed method provides an approximate segmentation which leads to the advantages in, for example, forecasting for future values. The method can also be adapted to segment multiple volatility processes.Comment: The original title dated back to October 2014 is "Segmenting Multiple Time Series by Contemporaneous Linear Transformation: PCA for Time Series

High dimensional stochastic regression with latent factors, endogeneity and nonlinearity

We consider a multivariate time series model which represents a high dimensional vector process as a sum of three terms: a linear regression of some observed regressors, a linear combination of some latent and serially correlated factors, and a vector white noise. We investigate the inference without imposing stationary conditions on the target multivariate time series, the regressors and the underlying factors. Furthermore we deal with the endogeneity that there exist correlations between the observed regressors and the unobserved factors. We also consider the model with nonlinear regression term which can be approximated by a linear regression function with a large number of regressors. The convergence rates for the estimators of regression coefficients, the number of factors, factor loading space and factors are established under the settings when the dimension of time series and the number of regressors may both tend to infinity together with the sample size. The proposed method is illustrated with both simulated and real data examples

Distributional Domain-Invariant Preference Matching for Cross-Domain Recommendation

Learning accurate cross-domain preference mappings in the absence of overlapped users/items has presented a persistent challenge in Non-overlapping Cross-domain Recommendation (NOCDR). Despite the efforts made in previous studies to address NOCDR, several limitations still exist. Specifically, 1) while some approaches substitute overlapping users/items with overlapping behaviors, they cannot handle NOCDR scenarios where such auxiliary information is unavailable; 2) often, cross-domain preference mapping is modeled by learning deterministic explicit representation matchings between sampled users in two domains. However, this can be biased due to individual preferences and thus fails to incorporate preference continuity and universality of the general population. In light of this, we assume that despite the scattered nature of user behaviors, there exists a consistent latent preference distribution shared among common people. Modeling such distributions further allows us to capture the continuity in user behaviors within each domain and discover preference invariance across domains. To this end, we propose a Distributional domain-invariant Preference Matching method for non-overlapping Cross-Domain Recommendation (DPMCDR). For each domain, we hierarchically approximate a posterior of domain-level preference distribution with empirical evidence derived from user-item interactions. Next, we aim to build distributional implicit matchings between the domain-level preferences of two domains. This process involves mapping them to a shared latent space and seeking a consensus on domain-invariant preference by minimizing the distance between their distributional representations therein. In this way, we can identify the alignment of two non-overlapping domains if they exhibit similar patterns of domain-invariant preference.Comment: 9 pages, 5 figures, full research paper accepted by ICDM 202

Adaptive and Robust Methods of Reconstruction (ARMOR) for Thermoacoustic Tomography

In this paper, we present new adaptive and robust methods of reconstruction (ARMOR) for thermoacoustic tomography (TAT), and study their performances for breast cancer detection. TAT is an emerging medical imaging technique that combines the merits of high contrast due to electromagnetic or laser stimulation and high resolution offered by thermal acoustic imaging. The current image reconstruction methods used for TAT, such as the delay-and-sum (DAS) approach, are data-independent and suffer from low-resolution, high sidelobe levels, and poor interference rejection capabilities. The data-adaptive ARMOR can have much better resolution and much better interference rejection capabilities than their data-independent counterparts. By allowing certain uncertainties, ARMOR can be used to mitigate the amplitude and phase distortion problems encountered in TAT. The excellent performance of ARMOR is demonstrated using both simulated and experimentally measured data

Dynamical modulation of solar flare electron acceleration due to plasmoid-shock interactions in the looptop region

A fast-mode shock can form in the front of reconnection outflows and has been suggested as a promising site for particle acceleration in solar flares. Recent development of magnetic reconnection has shown that numerous plasmoids can be produced in a large-scale current layer. Here we investigate the dynamical modulation of electron acceleration in the looptop region when plasmoids intermittently arrive at the shock by combining magnetohydrodynamics simulations with a particle kinetic model. As plasmoids interact with the shock, the looptop region exhibits various compressible structures that modulate the production of energetic electrons. The energetic electron population varies rapidly in both time and space. The number of 5$-$10 keV electrons correlates well with the area with compression, while that of $>$50 keV electrons shows good correlation with strong compression area but only moderate correlation with shock parameters. We further examine the impacts of the first plasmoid, which marks the transition from a quasi-steady shock front to a distorted and dynamical shock. The number of energetic electrons is reduced by $\sim 20\%$ at 15$-$25 keV and nearly 40\% for 25$-$50 keV, while the number of 5$-$10 keV electrons increases. In addition, the electron energy spectrum above 10 keV evolves softer with time. We also find double or even multiple distinct sources can develop in the looptop region when the plasmoids move across the shock. Our simulations have strong implications to the interpretation of nonthermal looptop sources, as well as the commonly observed fast temporal variations in flare emissions, including the quasi-periodic pulsations.Comment: accepted for publication in ApJ

Giant Magneto-Optical Sch\"{a}fer-Hubert Effect in Two-Dimensional van der Waals Antiferromagnets \textit{M}PS3_3 (\textit{M}=Mn, Fe, Ni)

The recent discovery of long-range magnetic order in atomically thin films has triggered particular interest in two-dimensional (2D) van der Waals (vdW) magnetic materials. In this paper, we perform a systematic theoretical study of the magneto-optical Sch\"{a}fer-Hubert effect (MOSHE) in 2D vdW antiferromagnetic \textit{M}PS$_3$ (\textit{M} = Mn, Fe, Ni) with multifold intralayer and interlayer magnetic orders. The formula for evaluating the MOSHE in 2D magnets is derived by considering the influence of a non-magnetic substrate. The MOSHE of monolayer and bilayer \textit{M}PS$_3$ are considerably large ($>2^{\circ}$), originating from the strong anisotropy of in-plane optical conductivity. The Sch\"{a}fer-Hubert rotation angles are surprisingly insensitive to the orientations of the N\'{e}el vector, while the Sch\"{a}fer-Hubert ellipticities are identified to be a good criterion to distinguish different interlayer magnetic orders. Our work establishes a theoretical framework for exploring novel 2D vdW magnets and facilitates the promising applications of the 2D \textit{M}PS$_3$ family in antiferromagnetic nanophotonic devices