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Li Chen

Publications and source records attributed to Li Chen.

At least 541 records · Page 30Linked to original sources
arXiv2020

Fast Dynamic Cuts, Distances and Effective Resistances via Vertex Sparsifiers

We present a general framework of designing efficient dynamic approximate algorithms for optimization on undirected graphs. In particular, we develop a technique that, given any problem that admits a certain notion of vertex sparsifiers, gives data structures that maintain approximate solutions in sub-linear update and query time. We illustrate the applicability of our paradigm to the following problems. (1) A fully-dynamic algorithm that approximates all-pair maximum-flows/minimum-cuts up to a nearly logarithmic factor in $\tilde{O}(n^{2/3})$ amortized time against an oblivious adversary, and $\tilde{O}(m^{3/4})$ time against an adaptive adversary. (2) An incremental data structure that maintains $O(1)$-approximate shortest path in $n^{o(1)}$ time per operation, as well as fully dynamic approximate all-pair shortest path and transshipment in $\tilde{O}(n^{2/3+o(1)})$ amortized time per operation. (3) A fully-dynamic algorithm that approximates all-pair effective resistance up to an $(1+ε)$ factor in $\tilde{O}(n^{2/3+o(1)} ε^{-O(1)})$ amortized update time per operation. The key tool behind result (1) is the dynamic maintenance of an algorithmic construction due to Madry [FOCS' 10], which partitions a graph into a collection of simpler graph structures (known as j-trees) and approximately captures the cut-flow and metric structure of the graph. The $O(1)$-approximation guarantee of (2) is by adapting the distance oracles by [Thorup-Zwick JACM `05]. Result (3) is obtained by invoking the random-walk based spectral vertex sparsifier by [Durfee et al. STOC `19] in a hierarchical manner, while carefully keeping track of the recourse among levels in the hierarchy.

cs.DS↗
arXiv2020

Besov class via heat semigroup on Dirichlet spaces I: Sobolev type inequalities

We introduce heat semigroup-based Besov classes in the general framework of Dirichlet spaces. General properties of those classes are studied and quantitative regularization estimates for the heat semigroup in this scale of spaces are obtained. As a highlight of the paper, we obtain a far reaching $L^p$-analogue, $p \ge 1$, of the Sobolev inequality that was proved for $p=2$ by N. Varopoulos under the assumption of ultracontractivity for the heat semigroup. The case $p=1$ is of special interest since it yields isoperimetric type inequalities.

math.FA↗
arXiv2020

Frozen Patterns of Impacted Droplets: From Conical Tips to Toroidal Shapes

We report frozen patterns for the water droplets impacting on a cold substrate through fast-speed images. These patterns can be manipulated by several physical parameters (the droplet size, falling height, and substrate temperature), and the scaling analysis has a remarkable agreement with the phase diagram. The observed double-concentric toroidal shape is attributed to the correlation between the impacting dynamics and freezing process, as confirmed by the spatiotemporal evolution of the droplet temperature, the identified timescale associated with the morphology and solidification ($t_{inn}\simeq τ_{sol}$), and the ice front-advection model. These results for frozen patterns provide insight into the complex interplay of the rapid impacting hydrodynamics, the transient heat transfer, and the intricate solidification process.

physics.flu-dyn↗
arXiv2020

User Validation of Recommendation Serendipity Metrics

Though it has been recognized that recommending serendipitous (i.e., surprising and relevant) items can be helpful for increasing users' satisfaction and behavioral intention, how to measure serendipity in the offline environment is still an open issue. In recent years, a number of metrics have been proposed, but most of them were based on researchers' assumptions due to the serendipity's subjective nature. In order to validate these metrics' actual performance, we collected over 10,000 users' real feedback data and compared with the metrics' results. It turns out the user profile based metrics, especially content-based ones, perform better than those based on item popularity, in terms of estimating the unexpectedness facet of recommendations. Moreover, the full metrics, which involve the unexpectedness component, relevance, timeliness, and user curiosity, can more accurately indicate the recommendation's serendipity degree, relative to those that just involve some of them. The application of these metrics to several recommender algorithms further consolidates their practical usage, because the comparison results are consistent with those from user evaluation. Thus, this work is constructive for filling the gap between offline measurement and user study on recommendation serendipity.

cs.HC↗
arXiv2020

Large-scale Real-time Personalized Similar Product Recommendations

Similar product recommendation is one of the most common scenes in e-commerce. Many recommendation algorithms such as item-to-item Collaborative Filtering are working on measuring item similarities. In this paper, we introduce our real-time personalized algorithm to model product similarity and real-time user interests. We also introduce several other baseline algorithms including an image-similarity-based method, item-to-item collaborative filtering, and item2vec, and compare them on our large-scale real-world e-commerce dataset. The algorithms which achieve good offline results are also tested on the online e-commerce website. Our personalized method achieves a 10% improvement on the add-cart number in the real-world e-commerce scenario.

cs.IR↗
arXiv2020

Content Adaptive and Error Propagation Aware Deep Video Compression

Recently, learning based video compression methods attract increasing attention. However, the previous works suffer from error propagation due to the accumulation of reconstructed error in inter predictive coding. Meanwhile, the previous learning based video codecs are also not adaptive to different video contents. To address these two problems, we propose a content adaptive and error propagation aware video compression system. Specifically, our method employs a joint training strategy by considering the compression performance of multiple consecutive frames instead of a single frame. Based on the learned long-term temporal information, our approach effectively alleviates error propagation in reconstructed frames. More importantly, instead of using the hand-crafted coding modes in the traditional compression systems, we design an online encoder updating scheme in our system. The proposed approach updates the parameters for encoder according to the rate-distortion criterion but keeps the decoder unchanged in the inference stage. Therefore, the encoder is adaptive to different video contents and achieves better compression performance by reducing the domain gap between the training and testing datasets. Our method is simple yet effective and outperforms the state-of-the-art learning based video codecs on benchmark datasets without increasing the model size or decreasing the decoding speed.

eess.IV↗
arXiv2020

A Systematic Analysis of the Phase Lags Associated with the Type-C Quasi-periodic Oscillation in GRS 1915+105

We present a systematic analysis of the phase lags associated with the type-C QPOs in GRS 1915+105 using RXTE data. Our sample comprises of 620 RXTE observations with type-C QPOs ranging from ~0.4 Hz to ~6.3 Hz. Based on our analysis, we confirm that the QPO phase lags decrease with QPO frequency, and change sign from positive to negative at a QPO frequency of ~2 Hz. In addition, we find that the slope of this relation is significantly different between QPOs below and above 2 Hz. The relation between the QPO lags and QPO rms can be well fitted with a broken line: as the QPO lags go from negative to positive, the QPO rms first increases, reaching its maximum at around zero lag, and then decreases. The phase-lag behaviour of the subharmonic of the QPO is similar to that of the QPO fundamental, where the subharmonic lags decrease with subharmonic frequency and change sign from positive to negative at a subharmonic frequency of ~1 Hz; on the contrary, the second harmonic of the QPO shows a quite different phase-lag behaviour, where all the second harmonics show hard lags that remain more or less constant. For both the QPO and its (sub)harmonics, the slope of the lag-energy spectra shows a similar evolution with frequency as the average phase lags. This suggests that the lag-energy spectra drives the average phase lags. We discuss the possibility for the change in lag sign, and the physical origin of the QPO lags.

astro-ph.HE↗
arXiv2020

The Neumann problem for a class of mixed complex Hessian equations

In this paper, we consider the Neumann problem of a class of mixed complex Hessian equations, and establish the global C^1 estimates a nd reduce the global second derivative estimate to the estimate of double normal second derivatives on the boundary. In particular, we can prove the global C^2 estimates and the existence theorems when k=n.

math.AP↗
arXiv2020

Global existence, asymptotic behavior, and pattern formation driven by the parametrization of a nonlocal Fisher-KPP problem

The global boundedness and the hair trigger effect of solutions for the nonlinear nonlocal reaction-diffusion equation \begin{align*} u_t=Δu+μu^α(1-κJ*u^β),\quad\hbox{in} \;\mathbb R^N\times(0,\infty),\; N\geq 1 \end{align*} with $α\geq1$, $β,μ,κ>0$ and $u(x,0)=u_0(x)$ are investigated. Under appropriate assumptions on $J$, it is proved that for any nonnegative and bounded initial condition, if $α\in[1,α^*)$ with $α^*=1+β$ for $N=1,2$ and $α^*=1+\frac{2β}{N}$ for $N>2$, then the problem has a global bounded classical solution. Under further assumptions on the initial datum, the solutions satisfying $0\leq u(x,t)\leqκ^{-\frac1β}$ for any $(x,t)\in\mathbb R^N\times[0,+\infty)$ are shown to converge to $κ^{-\frac1β}$ uniformly on any compact subset of $\mathbb R^N$, which is known as the hair trigger effect. 1D numerical simulations of the above nonlocal reaction-diffusion equation are performed and the effect of several combinations of parameters and convolution kernels on the solution behavior is investigated. The results motivate a discussion about some conjectures arising from this model and further issues to be studied in this context. A formal deduction of the model from a mesoscopic formulation is provided as well.

math.AP↗
arXiv2020

Adversarial Example in Remote Sensing Image Recognition

With the wide application of remote sensing technology in various fields, the accuracy and security requirements for remote sensing images (RSIs) recognition are also increasing. In recent years, due to the rapid development of deep learning in the field of image recognition, RSI recognition models based on deep convolution neural networks (CNNs) outperform traditional hand-craft feature techniques. However, CNNs also pose security issues when they show their capability of accurate classification. By adding a very small variation of the adversarial perturbation to the input image, the CNN model can be caused to produce erroneous results with extremely high confidence, and the modification of the image is not perceived by the human eye. This added adversarial perturbation image is called an adversarial example, which poses a serious security problem for systems based on CNN model recognition results. This paper, for the first time, analyzes adversarial example problem of RSI recognition under CNN models. In the experiments, we used different attack algorithms to fool multiple high-accuracy RSI recognition models trained on multiple RSI datasets. The results show that RSI recognition models are also vulnerable to adversarial examples, and the models with different structures trained on the same RSI dataset also have different vulnerabilities. For each RSI dataset, the number of features also affects the vulnerability of the model. Many features are good for defensive adversarial examples. Further, we find that the attacked class of RSI has an attack selectivity property. The misclassification of adversarial examples of the RSIs are related to the similarity of the original classes in the CNN feature space. In addition, adversarial examples in RSI recognition are of great significance for the security of remote sensing applications, showing a huge potential for future research.

cs.CV↗
arXiv2020

Blurry Video Frame Interpolation

Existing works reduce motion blur and up-convert frame rate through two separate ways, including frame deblurring and frame interpolation. However, few studies have approached the joint video enhancement problem, namely synthesizing high-frame-rate clear results from low-frame-rate blurry inputs. In this paper, we propose a blurry video frame interpolation method to reduce motion blur and up-convert frame rate simultaneously. Specifically, we develop a pyramid module to cyclically synthesize clear intermediate frames. The pyramid module features adjustable spatial receptive field and temporal scope, thus contributing to controllable computational complexity and restoration ability. Besides, we propose an inter-pyramid recurrent module to connect sequential models to exploit the temporal relationship. The pyramid module integrates a recurrent module, thus can iteratively synthesize temporally smooth results without significantly increasing the model size. Extensive experimental results demonstrate that our method performs favorably against state-of-the-art methods.

cs.CV↗
arXiv2020

Algorithms for Deforming and Contracting Simply Connected Discrete Closed Manifolds (III)

In a recent paper, {\it Algorithms for Deforming and Contracting Simply Connected Discrete Closed Manifolds (II)}, we discussed two algorithms for deforming and contracting a simply connected discrete closed manifold into a discrete sphere. The first algorithm was a continuation of work that began in {\it Algorithms for Deforming and Contracting Simply Connected Discrete Closed Manifolds (I)}, the second algorithm contained a more direct treatment of contraction for discrete manifolds. In this paper, we clarify that we can use this same method on standard piecewise linear (PL) complexes on the triangulation of general smooth manifolds. Our discussion is based on triangulation techniques invented by Cairns, Whitehead, and Whitney more than half of a century ago. In this paper, we use PL or simplicial complexes to replace certain concepts of discrete manifolds in previous papers. Note that some details in the original papers related to discrete manifolds may also need to be slightly modified for this purpose. In this paper, we use the algorithmic procedure (a contraction process) to prove the following theorem: For a finite triangulation of a simply-connected closed and orientable 3-manifold $M$ in Euclidean space, if a (simply-connected closed) 2-cycle which was made by 2-cells of this triangulation separates $M$ into two connected components, then each of the components will also be simply-connected. In addition, we can algorithmically make $M$ to be homeomorphic to a 3-sphere. The relationship of the theorem to a generalized Jordan separation problem, the general Jordan-Schoenflies theorem, and other important problems are also discussed. This revision adds more figures and explanations as well as two more special cases. We will post the detailed algorithm/procedure for practical triangulations in the following papers.

math.GT↗
arXiv2020

Stable Sparse Subspace Embedding for Dimensionality Reduction

Sparse random projection (RP) is a popular tool for dimensionality reduction that shows promising performance with low computational complexity. However, in the existing sparse RP matrices, the positions of non-zero entries are usually randomly selected. Although they adopt uniform sampling with replacement, due to large sampling variance, the number of non-zeros is uneven among rows of the projection matrix which is generated in one trial, and more data information may be lost after dimension reduction. To break this bottleneck, based on random sampling without replacement in statistics, this paper builds a stable sparse subspace embedded matrix (S-SSE), in which non-zeros are uniformly distributed. It is proved that the S-SSE is stabler than the existing matrix, and it can maintain Euclidean distance between points well after dimension reduction. Our empirical studies corroborate our theoretical findings and demonstrate that our approach can indeed achieve satisfactory performance.

cs.LG↗
arXiv2020

Fast Kernel k-means Clustering Using Incomplete Cholesky Factorization

Kernel-based clustering algorithm can identify and capture the non-linear structure in datasets, and thereby it can achieve better performance than linear clustering. However, computing and storing the entire kernel matrix occupy so large memory that it is difficult for kernel-based clustering to deal with large-scale datasets. In this paper, we employ incomplete Cholesky factorization to accelerate kernel clustering and save memory space. The key idea of the proposed kernel $k$-means clustering using incomplete Cholesky factorization is that we approximate the entire kernel matrix by the product of a low-rank matrix and its transposition. Then linear $k$-means clustering is applied to columns of the transpose of the low-rank matrix. We show both analytically and empirically that the performance of the proposed algorithm is similar to that of the kernel $k$-means clustering algorithm, but our method can deal with large-scale datasets.

cs.LG↗
arXiv2020

On a class of reaction-diffusion equations with aggregation

In this paper, global-in-time existence and blow up results are shown for a reaction-diffusion equation appearing in the theory of aggregation phenomena (including chemotaxis). Properties of the corresponding steady-state problem are also presented. Moreover, the stability around constant equilibria and the non-existence of non-constant solutions are studied in certain cases.

math.AP↗
arXiv2020

Convolution Neural Network Architecture Learning for Remote Sensing Scene Classification

Remote sensing image scene classification is a fundamental but challenging task in understanding remote sensing images. Recently, deep learning-based methods, especially convolutional neural network-based (CNN-based) methods have shown enormous potential to understand remote sensing images. CNN-based methods meet with success by utilizing features learned from data rather than features designed manually. The feature-learning procedure of CNN largely depends on the architecture of CNN. However, most of the architectures of CNN used for remote sensing scene classification are still designed by hand which demands a considerable amount of architecture engineering skills and domain knowledge, and it may not play CNN's maximum potential on a special dataset. In this paper, we proposed an automatically architecture learning procedure for remote sensing scene classification. We designed a parameters space in which every set of parameters represents a certain architecture of CNN (i.e., some parameters represent the type of operators used in the architecture such as convolution, pooling, no connection or identity, and the others represent the way how these operators connect). To discover the optimal set of parameters for a given dataset, we introduced a learning strategy which can allow efficient search in the architecture space by means of gradient descent. An architecture generator finally maps the set of parameters into the CNN used in our experiments.

cs.CV↗