Joint multiple dictionary learning for tensor sparse coding

Traditional dictionary learning algorithms are used for finding a sparse representation on high dimensional data by transforming samples into a one-dimensional (1D) vector. This 1D model loses the inherent spatial structure property of data. An alternative solution is to employ Tensor Decomposition for dictionary learning on their original structural form —a tensor— by learning multiple dictionaries along each mode and the corresponding sparse representation in respect to the Kronecker product of these dictionaries. To learn tensor dictionaries along each mode, all the existing methods update each dictionary iteratively in an alternating manner. Because atoms from each mode dictionary jointly make contributions to the sparsity of tensor, existing works ignore atoms correlations between different mode dictionaries by treating each mode dictionary independently. In this paper, we propose a joint multiple dictionary learning method for tensor sparse coding, which explores atom correlations for sparse representation and updates multiple atoms from each mode dictionary simultaneously. In this algorithm, the Frequent-Pattern Tree (FP-tree) mining algorithm is employed to exploit frequent atom patterns in the sparse representation. Inspired by the idea of K-SVD, we develop a new dictionary update method that jointly updates elements in each pattern. Experimental results demonstrate our method outperforms other tensor based dictionary learning algorithms

Tensor regression based on linked multiway parameter analysis

Classical regression methods take vectors as covariates and estimate the corresponding vectors of regression parameters. When addressing regression problems on covariates of more complex form such as multi-dimensional arrays (i.e. tensors), traditional computational models can be severely compromised by ultrahigh dimensionality as well as complex structure. By exploiting the special structure of tensor covariates, the tensor regression model provides a promising solution to reduce the model’s dimensionality to a manageable level, thus leading to efficient estimation. Most of the existing tensor-based methods independently estimate each individual regression problem based on tensor decomposition which allows the simultaneous projections of an input tensor to more than one direction along each mode. As a matter of fact, multi-dimensional data are collected under the same or very similar conditions, so that data share some common latent components but can also have their own independent parameters for each regression task. Therefore, it is beneficial to analyse regression parameters among all the regressions in a linked way. In this paper, we propose a tensor regression model based on Tucker Decomposition, which identifies not only the common components of parameters across all the regression tasks, but also independent factors contributing to each particular regression task simultaneously. Under this paradigm, the number of independent parameters along each mode is constrained by a sparsity-preserving regulariser. Linked multiway parameter analysis and sparsity modeling further reduce the total number of parameters, with lower memory cost than their tensor-based counterparts. The effectiveness of the new method is demonstrated on real data sets

Utilization of Dynamic and Static Sensors for Monitoring Infrastructures

Infrastructures, including bridges, tunnels, sewers, and telecommunications, may be exposed to environmental-induced or traffic-induced deformation and vibrations. Some infrastructures, such as bridges and roadside upright structures, may be sensitive to vibration and displacement where several different types of dynamic and static sensors may be used for their measurement of sensitivity to environmental-induced loads, like wind and earthquake, and traffic-induced loads, such as passing trucks. Remote sensing involves either in situ, on-site, or airborne sensing where in situ sensors, such as strain gauges, displacement transducers, velometers, and accelerometers, are considered conventional but more durable and reliable. With data collected by accelerometers, time histories may be obtained, transformed, and then analyzed to determine their modal frequencies and shapes, while with displacement and strain transducers, structural deflections and internal stress distribution may be measured, respectively. Field tests can be used to characterize the dynamic and static properties of the infrastructures and may be further used to show their changes due to damage. Additionally, representative field applications on bridge dynamic testing, seismology, and earthborn/construction vibration are explained. Sensor data can be analyzed to establish the trend and ensure optimal structural health. At the end, five case studies on bridges and industry facilities are demonstrated in this chapter

Phase-matched locally chiral light for global control of chiral light-matter interaction

Locally chiral light is an emerging tool for probing and controlling molecular chirality. It can generate large and freely adjustable enantioselectivities in purely electric-dipole effects, offering its major advantages over traditional chiral light. However, the existing types of locally chiral light are phase-mismatched, and thus the global efficiencies are greatly reduced compared with the maximum single-point efficiencies or even vanish. Here, we propose a scheme to generate phase-matched locally chiral light. To confirm this advantage, we numerically show the robust highly efficient global control of enantiospecific electronic state transfer of methyloxirane at nanoseconds. Our work potentially constitutes the starting point for developing more efficient chiroptical techniques for the studies of chiral molecules.Comment: 5 pages, 3figures, 1 supplment documen

Solving High-dimensional Parametric Elliptic Equation Using Tensor Neural Network

In this paper, we introduce a tensor neural network based machine learning method for solving the elliptic partial differential equations with random coefficients in a bounded physical domain. With the help of tensor product structure, we can transform the high-dimensional integrations of tensor neural network functions to one-dimensional integrations which can be computed with the classical quadrature schemes with high accuracy. The complexity of its calculation can be reduced from the exponential scale to a polynomial scale. The corresponding machine learning method is designed for solving high-dimensional parametric elliptic equations. Some numerical examples are provided to validate the accuracy and efficiency of the proposed algorithms.Comment: 22 pages, 25 figures. arXiv admin note: substantial text overlap with arXiv:2311.0273

Tensor LRR and sparse coding-based subspace clustering

Subspace clustering groups a set of samples from a union of several linear subspaces into clusters, so that the samples in the same cluster are drawn from the same linear subspace. In the majority of the existing work on subspace clustering, clusters are built based on feature information, while sample correlations in their original spatial structure are simply ignored. Besides, original high-dimensional feature vector contains noisy/redundant information, and the time complexity grows exponentially with the number of dimensions. To address these issues, we propose a tensor low-rank representation (TLRR) and sparse coding-based (TLRRSC) subspace clustering method by simultaneously considering feature information and spatial structures. TLRR seeks the lowest rank representation over original spatial structures along all spatial directions. Sparse coding learns a dictionary along feature spaces, so that each sample can be represented by a few atoms of the learned dictionary. The affinity matrix used for spectral clustering is built from the joint similarities in both spatial and feature spaces. TLRRSC can well capture the global structure and inherent feature information of data, and provide a robust subspace segmentation from corrupted data. Experimental results on both synthetic and real-world data sets show that TLRRSC outperforms several established state-of-the-art methods

Maximum Entropy Heterogeneous-Agent Mirror Learning

Multi-agent reinforcement learning (MARL) has been shown effective for cooperative games in recent years. However, existing state-of-the-art methods face challenges related to sample inefficiency, brittleness regarding hyperparameters, and the risk of converging to a suboptimal Nash Equilibrium. To resolve these issues, in this paper, we propose a novel theoretical framework, named Maximum Entropy Heterogeneous-Agent Mirror Learning (MEHAML), that leverages the maximum entropy principle to design maximum entropy MARL actor-critic algorithms. We prove that algorithms derived from the MEHAML framework enjoy the desired properties of the monotonic improvement of the joint maximum entropy objective and the convergence to quantal response equilibrium (QRE). The practicality of MEHAML is demonstrated by developing a MEHAML extension of the widely used RL algorithm, HASAC (for soft actor-critic), which shows significant improvements in exploration and robustness on three challenging benchmarks: Multi-Agent MuJoCo, StarCraftII, and Google Research Football. Our results show that HASAC outperforms strong baseline methods such as HATD3, HAPPO, QMIX, and MAPPO, thereby establishing the new state of the art. See our project page at https://sites.google.com/view/mehaml

Enantioselective switch on radiations of dissipative chiral molecules

Enantiodetection is an important and challenging task across natural science. Nowadays, some chiroptical methods of enantiodetection based on decoherence-free cyclic three-level models of chiral molecules can reach the ultimate limit of the enantioselectivities in the molecular responses. They are thus more efficient than traditional chiroptical methods. However, decoherence is inevitable and can severely reduce enantioselectivities in these advanced chiroptical methods, so they only work well in the weak decoherence region. Here, we propose an enantioselective switch on the radiation of dissipative chiral molecules and develop a novel chiroptical method of enantiodetection working well in all decoherence regions. In our scheme, radiation is turned on for the selected enantiomer and simultaneously turned off for its mirror image by designing the electromagnetic fields well based on dissipative cyclic three-level models. The enantiomeric excess of a chiral mixture is determined by comparing its emissions in two cases, where the radiations of two enantiomers are turned off respectively. The corresponding enantioselectivities reach the ultimate limit in all decoherence regions, offering our scheme advantages over other chiroptical methods in enantiodetection. Our work potentially constitutes the starting point for developing more efficient chiroptical techniques for enantiodection in all decoherence regions