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Xiaoli Li

Publications and source records attributed to Xiaoli Li.

162 records · Page 9Linked to original sources

Interact and Decide: Medley of Sub-Attention Networks for Effective Group Recommendation

This paper proposes Medley of Sub-Attention Networks (MoSAN), a new novel neural architecture for the group recommendation task. Group-level recommendation is known to be a challenging task, in which intricate group dynamics have to be considered. As such, this is to be contrasted with the standard recommendation problem where recommendations are personalized with respect to a single user. Our proposed approach hinges upon the key intuition that the decision making process (in groups) is generally dynamic, i.e., a user's decision is highly dependent on the other group members. All in all, our key motivation manifests in a form of an attentive neural model that captures fine-grained interactions between group members. In our MoSAN model, each sub-attention module is representative of a single member, which models a user's preference with respect to all other group members. Subsequently, a Medley of Sub-Attention modules is then used to collectively make the group's final decision. Overall, our proposed model is both expressive and effective. Via a series of extensive experiments, we show that MoSAN not only achieves state-of-the-art performance but also improves standard baselines by a considerable margin.

cs.AI↗

HyperML: A Boosting Metric Learning Approach in Hyperbolic Space for Recommender Systems

This paper investigates the notion of learning user and item representations in non-Euclidean space. Specifically, we study the connection between metric learning in hyperbolic space and collaborative filtering by exploring Mobius gyrovector spaces where the formalism of the spaces could be utilized to generalize the most common Euclidean vector operations. Overall, this work aims to bridge the gap between Euclidean and hyperbolic geometry in recommender systems through metric learning approach. We propose HyperML (Hyperbolic Metric Learning), a conceptually simple but highly effective model for boosting the performance. Via a series of extensive experiments, we show that our proposed HyperML not only outperforms their Euclidean counterparts, but also achieves state-of-the-art performance on multiple benchmark datasets, demonstrating the effectiveness of personalized recommendation in hyperbolic geometry.

cs.IR↗

Error analysis of the SAV-MAC scheme for the Navier-Stokes equations

An efficient numerical scheme based on the scalar auxiliary variable (SAV) and marker and cell scheme (MAC) is constructed for the Navier-Stokes equations. A particular feature of the scheme is that the nonlinear term is treated explicitly while being unconditionally energy stable. A rigorous error analysis is carried out to show that both velocity and pressure approximations are second-order accurate in time and space. Numerical experiments are presented to verify the theoretical results.

math.NA↗

Stability and Error estimates of the SAV Fourier-spectral method for the Phase Field Crystal Equation

We consider fully discrete schemes based on the scalar auxiliary variable (SAV) approach and stabilized SAV approach in time and the Fourier-spectral method in space for the phase field crystal (PFC) equation. Unconditionally energy stability is established for both first- and second-order fully discrete schemes. In addition to the stability, we also provide a rigorous error estimate which shows that our second-order in time with Fourier-spectral method in space converges with order $O(Δt^2+N^{-m})$, where $Δt$, $N$ and $m$ are time step size, number of Fourier modes in each direction, and regularity index in space, respectively. We also present numerical experiments to verify our theoretical results and demonstrate the robustness and accuracy of the schemes.

math.AP↗

On a SAV-MAC scheme for the Cahn-Hilliard-Navier-Stokes Phase Field Model

We construct a numerical scheme based on the scalar auxiliary variable (SAV) approach in time and the MAC discretization in space for the Cahn-Hilliard-Navier-Stokes phase field model, and carry out stability and error analysis. The scheme is linear, second-order, unconditionally energy stable and can be implemented very efficiently. We establish second-order error estimates both in time and space for phase field variable, chemical potential, velocity and pressure in different discrete norms. We also provide numerical experiments to verify our theoretical results and demonstrate the robustness and accuracy of the our scheme.

math.AP↗

High-Efficiency Second Harmonic Generation of Low-Temporal-Coherent Light Pulse

The nonlinear frequency conversion of low-temporal-coherent light holds a variety of applications and has attracted considerable interest. However, its physical mechanism remains relatively unexplored, and the conversion efficiency and bandwidth are extremely insufficient. Here, considering the instantaneous broadband characteristic, we establish a model of second harmonic generation (SHG) of low-temporal-coherent pulse, and reveal its differences from the coherent conditions. It is found that the second harmonic (SH) of low-temporal-coherent light is produced by not only the degenerate SH processes but also crossed sum-frequency processes. On the basis of this, we propose a method for realizing low-temporal-coherent SHG with high efficiency and broad bandwidth, and experimentally demonstrate a conversion efficiency up to 70% with a bandwidth of 3.1 THz (2.9 nm centered at 528 nm). To the best of our knowledge, this is the highest efficiency and broadest bandwidth of low-temporal-coherent SHG, and its efficiency is almost the same with that of the narrowband coherent condition. Furthermore, the spectral evolution characteristics of the broadband low-temporal-coherent pulse in SHG process are revealed in experiments, that the SH power spectral density (PSD) is proportional to the self-convolution of the fundamental wave PSD, which is greatly different from that of the coherent process. Our research opens a door for the study of the low-coherent nonlinear optical processes.

physics.optics↗

The fast scalar auxiliary variable approach with unconditional energy stability for nonlocal Cahn-Hilliard equation

Comparing with the classical local gradient flow and phase field models, the nonlocal models such as nonlocal Cahn-Hilliard equations equipped with nonlocal diffusion operator can describe more practical phenomena for modeling phase transitions. In this paper, we construct an accurate and efficient scalar auxiliary variable approach for the nonlocal Cahn-Hilliard equation with general nonlinear potential. The first contribution is that we have proved the unconditional energy stability for nonlocal Cahn-Hilliard model and its semi-discrete schemes carefully and rigorously. Secondly, what we need to focus on is that the non-locality of the nonlocal diffusion term will lead the stiffness matrix to be almost full matrix which generates huge computational work and memory requirement. For spatial discretizaion by finite difference method, we find that the discretizaition for nonlocal operator will lead to a block-Toeplitz-Toeplitz-block (BTTB) matrix by applying four transformation operators. Based on this special structure, we present a fast procedure to reduce the computational work and memory requirement. Finally, several numerical simulations are demonstrated to verify the accuracy and efficiency of our proposed schemes.

math.AP↗

Energy Stability and Convergence of SAV Block-centered Finite Difference Method for Gradient Flows

We present in this paper construction and analysis of a block-centered finite difference method for the spatial discretization of the scalar auxiliary variable Crank-Nicolson scheme (SAV/CN-BCFD) for gradient flows, and show rigorously that scheme is second-order in both time and space in various discrete norms. When equipped with an adaptive time strategy, the SAV/CN-BCFD scheme is accurate and extremely efficient. Numerical experiments on typical Allen-Cahn and Cahn-Hilliard equations are presented to verify our theoretical results and to show the robustness and accuracy of the SAV/CN-BCFD scheme.

math.NA↗

Enhanced magnetic properties in ZnCoAlO caused by exchangecoupling to Co nanoparticles

Wereport the results of a sequence of magnetisation and magneto-optical studies on laser ablated thin films of ZnCoAlO and ZnCoO that contain a small amount of metallic cobalt. The results are compared to those expected when all the magnetization is due to isolated metallic clusters of cobalt and with an oxide sample that is almost free from metallic inclusions. Using a variety of direct magnetic measurements and also magnetic circular dichroism we find that there is ferromagnetism within both the oxide and the metallic inclusions, and furthermore that these magnetic components are exchange-coupled when aluminium is included. This enhances both the coercive field and the remanence. Hence the presence of a controlled quantity of metallic nanoparticles in ZnAlO can improve the magnetic response of the oxide, thus giving great advantages for applications in spintronics.

cond-mat.mtrl-sci↗

Fast procedures for Caputo fractional derivative and its applications to ordinary and partial differential equations

In this paper, we develop fast procedures for solving linear systems arising from discretization of ordinary and partial differential equations with Caputo fractional derivative w.r.t time variable. First, we consider a finite difference scheme to solve a two-sided fractional ordinary equation. Furthermore, we present a fast solution technique to accelerate Toeplitz matrix-vector multiplications arising from finite difference discretization. This fast solution technique is based on a fast Fourier transform and depends on the special structure of coefficient matrices, and it helps to reduce the computational work from $O(N^{3})$ required by traditional methods to $O(Nlog^{2}N)$ and the memory requirement from $O(N^{2})$ to $O(N)$ without using any lossy compression, where $N$ is the number of unknowns. Two finite difference schemes to solve time fractional hyperbolic equations with different fractional order $γ$ are considered. We present a fast solution technique depending on the special structure of coefficient matrices by rearranging the order of unknowns. It helps to reduce the computational work from $O(N^2M)$ required by traditional methods to $O(N$log$^{2}N)$ and the memory requirement from $O(NM)$ to $O(N)$ without using any lossy compression, where $N=τ^{-1}$ and $τ$ is the size of time step, $M=h^{-1}$ and $h$ is the size of space step. Importantly, a fast method is employed to solve the classical time fractional diffusion equation with a lower coast at $O(MN$log$^2N)$, where the direct method requires an overall computational complexity of $O(N^2M)$. Moreover, the applicability and accuracy of the scheme are demonstrated by numerical experiments to support our theoretical analysis.

math.AP↗

Pruning Convolutional Neural Networks for Image Instance Retrieval

In this work, we focus on the problem of image instance retrieval with deep descriptors extracted from pruned Convolutional Neural Networks (CNN). The objective is to heavily prune convolutional edges while maintaining retrieval performance. To this end, we introduce both data-independent and data-dependent heuristics to prune convolutional edges, and evaluate their performance across various compression rates with different deep descriptors over several benchmark datasets. Further, we present an end-to-end framework to fine-tune the pruned network, with a triplet loss function specially designed for the retrieval task. We show that the combination of heuristic pruning and fine-tuning offers 5x compression rate without considerable loss in retrieval performance.

cs.CV↗

A novel second order finite difference discrete scheme for fractal mobile/immobile transport model based on equivalent transformative Caputo formulation

In this article, we present a new second order finite difference discrete scheme for fractal mobile/immobile transport model based on equivalent transformative Caputo formulation. The new transformative formulation takes the singular kernel away to make the integral calculation more efficient. Furthermore, this definition is also effective where $α$ is a positive integer. Besides, the T-Caputo derivative also helps to increase the convergence rate of the discretization of $α$-order($0<α<1$) Caputo derivative from $O(τ^{2-α})$ to $O(τ^{3-α})$, where $τ$ is the time step. For numerical analysis, a Crank-Nicholson finite difference scheme to solve fractal mobile/immobile transport model is introduced and analyzed. The unconditional stability and a priori estimates of the scheme are given rigorously. Moreover, the applicability and accuracy of the scheme are demonstrated by numerical experiments to support our theoretical analysis.

math.AP↗

Learning Social Circles in Ego Networks based on Multi-View Social Graphs

In social network analysis, automatic social circle detection in ego-networks is becoming a fundamental and important task, with many potential applications such as user privacy protection or interest group recommendation. So far, most studies have focused on addressing two questions, namely, how to detect overlapping circles and how to detect circles using a combination of network structure and network node attributes. This paper asks an orthogonal research question, that is, how to detect circles based on network structures that are (usually) described by multiple views? Our investigation begins with crawling ego-networks from Twitter and employing classic techniques to model their structures by six views, including user relationships, user interactions and user content. We then apply both standard and our modified multi-view spectral clustering techniques to detect social circles in these ego-networks. Based on extensive automatic and manual experimental evaluations, we deliver two major findings: first, multi-view clustering techniques perform better than common single-view clustering techniques, which only use one view or naively integrate all views for detection, second, the standard multi-view clustering technique is less robust than our modified technique, which selectively transfers information across views based on an assumption that sparse network structures are (potentially) incomplete. In particular, the second finding makes us believe a direct application of standard clustering on potentially incomplete networks may yield biased results. We lightly examine this issue in theory, where we derive an upper bound for such bias by integrating theories of spectral clustering and matrix perturbation, and discuss how it may be affected by several network characteristics.

cs.SI↗

Incremental Minimax Optimization based Fuzzy Clustering for Large Multi-view Data

Incremental clustering approaches have been proposed for handling large data when given data set is too large to be stored. The key idea of these approaches is to find representatives to represent each cluster in each data chunk and final data analysis is carried out based on those identified representatives from all the chunks. However, most of the incremental approaches are used for single view data. As large multi-view data generated from multiple sources becomes prevalent nowadays, there is a need for incremental clustering approaches to handle both large and multi-view data. In this paper we propose a new incremental clustering approach called incremental minimax optimization based fuzzy clustering (IminimaxFCM) to handle large multi-view data. In IminimaxFCM, representatives with multiple views are identified to represent each cluster by integrating multiple complementary views using minimax optimization. The detailed problem formulation, updating rules derivation, and the in-depth analysis of the proposed IminimaxFCM are provided. Experimental studies on several real world multi-view data sets have been conducted. We observed that IminimaxFCM outperforms related incremental fuzzy clustering in terms of clustering accuracy, demonstrating the great potential of IminimaxFCM for large multi-view data analysis.

cs.AI↗

Variable-Length Hashing

Hashing has emerged as a popular technique for large-scale similarity search. Most learning-based hashing methods generate compact yet correlated hash codes. However, this redundancy is storage-inefficient. Hence we propose a lossless variable-length hashing (VLH) method that is both storage- and search-efficient. Storage efficiency is achieved by converting the fixed-length hash code into a variable-length code. Search efficiency is obtained by using a multiple hash table structure. With VLH, we are able to deliberately add redundancy into hash codes to improve retrieval performance with little sacrifice in storage efficiency or search complexity. In particular, we propose a block K-means hashing (B-KMH) method to obtain significantly improved retrieval performance with no increase in storage and marginal increase in computational cost.

cs.CV↗

Global strong solution to the density-dependent incompressible flow of liquid crystals

The initial-boundary value problem for the density-dependent incompressible flow of liquid crystals is studied in a three-dimensional bounded smooth domain. For the initial density away from vacuum, the existence and uniqueness is established for both the local strong solution with large initial data and the global strong solution with small data. It is also proved that when the strong solution exists, a weak solution with the same data must be equal to the unique strong solution.

math.AP↗

Local strong solution to the compressible magnetohydrodynamic flow with large data

The three-dimensional compressible magnetohydrodynamic (MHD) isentropic flow with zero magnetic diffusivity is studied. The vanishing magnetic diffusivity causes significant difficulties due to the loss of dissipation of the magnetic field. The existence and uniqueness of local in time strong solution with large initial data is established. The strong solution has weaker regularity than the classical solution. A generalized Lax-Milgram theorem and a Schauder-Tychonoff-type fixed point argument are applied with novel techniques and estimates for the strong solution.

math.AP↗

Global solution to the incompressible flow of liquid crystals

The initial boundary value problem for the three-dimensional incompressible flow of liquid crystals is considered in a bounded smooth domain. The existence and uniqueness is established for both the local strong solution with large initial data and the global strong solution with small data. It is also proved that when the strong solution exists, a weak solution must be equal to the unique strong solution with the same data.

math.AP↗