Temporal Knowledge Graph (TKG) reasoning has attracted increasing attention due to its enormous potential value, and the critical issue is how to model the complex temporal structure information effectively.Recent studies use the method of encoding graph snapshots into hidden vector space and then performing heuristic deductions, which perform well on the task of entity prediction.However, these approaches cannot predict when an event will occur, and have the following limitations: 1) there are many facts not related to the query that can confuse the model; 2) there exists information forgetting caused by long-term evolutionary processes.To this end, we propose a Graph Hawkes Transformer (GHT) for both TKG entity prediction and time prediction tasks in the future time.In GHT, there are two variants of Transformer, which capture the instantaneous structural information and temporal evolution information, respectively, and a new relational continuous-time encoding function to facilitate feature evolution with the Hawkes process.Extensive experiments on four public datasets demonstrate its superior performance, especially on long-term evolutionary tasks.

Temporal knowledge graph (TKG) reasoning is a crucial task that has gained increasing research interest in recent years.Most existing methods focus on reasoning at past timestamps to complete the missing facts, and there are only a few works of reasoning on known TKGs to forecast future facts.Compared with the completion task, the forecasting task is more difficult and faces two main challenges: (1) how to effectively model the time information to handle future timestamps?(2) how to make inductive inference to handle previously unseen entities that emerge over time?To address these challenges, we propose the first reinforcement learning method for forecasting.Specifically, the agent travels on historical knowledge graph snapshots to search for the answer.Our method defines a relative time encoding function to capture the timespan information, and we design a novel time-shaped reward based on Dirichlet distribution to guide the model learning.Furthermore, we propose a novel representation method for unseen entities to improve the inductive inference ability of the model.We evaluate our method for this link prediction task at future timestamps.Extensive experiments on four benchmark datasets demonstrate substantial performance improvement meanwhile with higher explainability, less calculation, and fewer parameters when compared with existing stateof-the-art methods.

In this paper, we propose a design method for 3-D higher order ambisonics (3-D HOA) encoding matrices which offers the possibility to impose spatial stop-bands in the directivity patterns of all the spherical-harmonic audio channels while keeping the transformed audio channels still compatible with the 3-D HOA reproduction sound format. This might be useful as an encoding technique which suppresses interfering signals from specific directions in a 3-D HOA recording, or in other situations where certain spatial areas should be suppressed. The design method is adapted from recent work on the optimization of spherical microphone array beamforming. Using the proposed optimization method and the spherical harmonics mathematics framework, the relationship between several design factors, e.g., distortions in the desired response, the dynamic range of matrix coefficients, can be analyzed and illustrated as function of frequency. Based on the proposed optimization formulation, additional constraints can also be easily included and solved. In some of the formulations, the processing can be applied as a matrix multiplication to recorded spherical harmonics coefficients, that is, already encoded 3-D HOA format signals. The modified signals can be of the same or a lower spherical harmonics order. For a full optimization that gives a globally optimal solution, on the other hand, the processing must be applied to the microphone signals themselves. Numerical and experimental results validate the proposed method.

This paper presents a method for the localization of reflectors in an acoustic environment, using robust beamforming techniques and a cylindrical microphone array, for which an intuitive and highly efficient three-step procedure is proposed. First, the directions of ar rival (DOAs) corresponding to the sound source and reflectors are estimated by a robust Minimum Variance Distortionless Response (MVDR) beamformer. Next, signals originating from the estimated DOAs are extracted by a robust superdirective beamformer, from which time differences of arrival (TDOAs) of major reflections are estimated by crosscorrelation analysis. Finally, by using additional information about the position of the direct sound source relative to the array, the positions of the reflective boundaries of the room can be inferred. Experiments based on real measurements carried out in a moderately reverberant room show the effectiveness of this method.

Methods of 3D direction of arrival (DOA) estimation, coherent source detection and reflective surface localization are studied, based on recordings by a spherical microphone array. First, the spherical harmonics domain minimum variance distortionless response (EB-MVDR) beamformer is employed for the localization of broadband coherent sources, which is characterized by simpler frequency focusing matrices than the corresponding element-space implementation, and by a higher resolution than conventional spherical array beamformers. After the DOA estimation step, the source signals are extracted by EB-MVDRs. Then, by computing the crosscorrelation functions between the extracted signals, the coherent sources are detected and their time differences of arrival (TDOA) are estimated. Given the positions of the array and the reference source, and the estimated DOA and TDOA of the coherent sources, the positions of the major reflectors can be inferred. Experimental results in a real room validate the proposed method.

Spherical microphone array eigenbeam (EB)-ESPRIT gives an elegant closed-form solution for 3D broadband source localization based on the spherical harmonics (eigenbeam) framework. However, in practical implementations, there are still several issues not being rigorously studied, e.g. how to avoid the ill-conditioning of an EB-ESPRIT matrix, solve the ambiguity problem, handle a large number of sources, and localize coherent broadband sources, etc. In this work, we propose to use the condition number of the EB-ESPRIT matrix as a robustness measure, and to use Wigner-D weighting to avoid the ill-conditioning issue and improve the robustness. In addition, power spectrum testing, frequency smoothing, and manifold vector extension techniques are employed to address the ambiguity, coherent source localization, and large source number problems, respectively. Experimental results based on measurements taken with a real spherical microphone array in a room environment show the effectiveness of the proposed methods.

A robust minimum sidelobe beamforming approach based on the spherical harmonics framework for spherical microphone arrays is proposed. It minimizes the peaks of sidelobes while keeping the distortionless response in the look direction and maintaining the mainlobe width. A white noise gain constraint is also derived and employed to improve the robustness against array errors. The resulting beamformer can provide optimal tradeoff between the sidelobe level, the beamwidth and robustness, so it could be more practical than the existing spherical array Dolph-Chebyshev modal beamformer in the presence of array errors. The optimal modal beamforming problem is formulated as a tractable convex second-order cone programming program, which is more efficient than conventional element-space based approaches, since the dimension of array weight vectors can be significantly decreased by using the properties of spherical harmonics and Legendre polynomials. For the purpose of performance comparison, we also formulate current robust modal beamformers as equivalent optimization problems based on the proposed array model. Numerical results show the high flexibility and efficiency of the proposed beamforming approach.

Most of the existing spherical array modal beamformers are implemented in the frequency domain, where a block of snapshots is required to perform the discrete Fourier transform. In this paper, an approach to real-valued time-domain implementation of the modal beamformer for broadband spherical microphone arrays is presented. The microphone array data are converted to the spherical harmonics domain by using the discrete spherical Fourier transform, and then steered to the look direction followed by the pattern generation unit implemented using the filter-and-sum structure. We derive the expression for the array response, the beamformer output power against both isotropic noise and spatially white noise, and the mainlobe spatial response variation in terms of the finite impulse response (FIR) filters' tap weights. A multiple-constraint problem is then formulated to find the filters' tap weights with the aim of providing a suitable tradeoff among multiple conflicting performance measures such as directivity index, robustness, sidelobe level, and mainlobe response variation. Simulation and experimental results show good performance of the proposed time-domain broadband modal beamforming approach.

An approach to optimal array pattern synthesis based on spherical harmonics is presented. The array processing problem in the spherical harmonics domain is expressed with a matrix formulation. The beamformer weight vector design problem is written as a multiply constrained problem, so that the resulting beamformer can provide a suitable trade-off among multiple conflicting performance measures such as directivity index, robustness, array gain, sidelobe level, mainlobe width, and so on. The multiply constrained problem is formulated as a convex form of second-order cone programming which is computationally tractable. We show that the pure phase-mode spherical microphone array can be viewed as a minimum variance distortionless response (MVDR) beamformer in the spherical harmonics domain for the case of spherically isotropic noise. It is shown that our approach includes the delay-and-sum beamformer and a pure phase-mode beamformer as special cases, which leads to very flexible designs. Results of simulations and experimental data processing show good performance of the proposed array pattern synthesis approach. To simplify the analysis, the assumption of equidistant spatial sampling of the wavefield by microphones on a spherical surface is used and the aliasing effects due to noncontinuous spatial sampling are neglected.

A space domain optimal beamforming approach for spherical microphone arrays is presented, which is based on original microphone signals rather than spherical harmonics. A simple correlated multipath signal model is employed. The beamforming optimization criteria, including adaptive beamforming, multi-beam steering, sidelobe control, correlated interference cancellation and robustness control, are proposed and reformulated in a convex form of second order cone programming, which is computationally tractable. Using the spherical harmonics framework, we also prove that, given a perfect spatial sampling scheme, the conventional plan-wave decomposition (PWD) beamformer can be interpreted as a space domain minimum variance distortionless response (MVDR) beamformer under the condition of a spherically isotropic sound field.