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Meng Chen

Publications and source records attributed to Meng Chen.

At least 127 records · Page 7Linked to original sources
arXiv2020

TTDM: A Travel Time Difference Model for Next Location Prediction

Next location prediction is of great importance for many location-based applications and provides essential intelligence to business and governments. In existing studies, a common approach to next location prediction is to learn the sequential transitions with massive historical trajectories based on conditional probability. Unfortunately, due to the time and space complexity, these methods (e.g., Markov models) only use the just passed locations to predict next locations, without considering all the passed locations in the trajectory. In this paper, we seek to enhance the prediction performance by considering the travel time from all the passed locations in the query trajectory to a candidate next location. In particular, we propose a novel method, called Travel Time Difference Model (TTDM), which exploits the difference between the shortest travel time and the actual travel time to predict next locations. Further, we integrate the TTDM with a Markov model via a linear interpolation to yield a joint model, which computes the probability of reaching each possible next location and returns the top-rankings as results. We have conducted extensive experiments on two real datasets: the vehicle passage record (VPR) data and the taxi trajectory data. The experimental results demonstrate significant improvements in prediction accuracy over existing solutions. For example, compared with the Markov model, the top-1 accuracy improves by 40% on the VPR data and by 15.6% on the Taxi data.

cs.AI↗
arXiv2020

PCNN: Deep Convolutional Networks for Short-term Traffic Congestion Prediction

Traffic problems have seriously affected people's life quality and urban development, and forecasting the short-term traffic congestion is of great importance to both individuals and governments. However, understanding and modeling the traffic conditions can be extremely difficult, and our observations from real traffic data reveal that (1) similar traffic congestion patterns exist in the neighboring time slots and on consecutive workdays; (2) the levels of traffic congestion have clear multiscale properties. To capture these characteristics, we propose a novel method named PCNN based on deep Convolutional Neural Network, modeling Periodic traffic data for short-term traffic congestion prediction. PCNN has two pivotal procedures: time series folding and multi-grained learning. It first temporally folds the time series and constructs a two-dimensional matrix as the network input, such that both the real-time traffic conditions and past traffic patterns are well considered; then with a series of convolutions over the input matrix, it is able to model the local temporal dependency and multiscale traffic patterns. In particular, the global trend of congestion can be addressed at the macroscale; whereas more details and variations of the congestion can be captured at the microscale. Experimental results on a real-world urban traffic dataset confirm that folding time series data into a two-dimensional matrix is effective and PCNN outperforms the baselines significantly for the task of short-term congestion prediction.

eess.SP↗
arXiv2020

TraLFM: Latent Factor Modeling of Traffic Trajectory Data

The widespread use of positioning devices (e.g., GPS) has given rise to a vast body of human movement data, often in the form of trajectories. Understanding human mobility patterns could benefit many location-based applications. In this paper, we propose a novel generative model called TraLFM via latent factor modeling to mine human mobility patterns underlying traffic trajectories. TraLFM is based on three key observations: (1) human mobility patterns are reflected by the sequences of locations in the trajectories; (2) human mobility patterns vary with people; and (3) human mobility patterns tend to be cyclical and change over time. Thus, TraLFM models the joint action of sequential, personal and temporal factors in a unified way, and brings a new perspective to many applications such as latent factor analysis and next location prediction. We perform thorough empirical studies on two real datasets, and the experimental results confirm that TraLFM outperforms the state-of-the-art methods significantly in these applications.

cs.SI↗
arXiv2020

Addendum to "The Noether inequality for algebraic threefolds"

In this short note, we give a refinement of our previous work (arXiv:1803.05553) stating that for a projective $3$-fold $X$ of general type with either $p_g(X)\leq 4$ or $p_g(X)\geq 11$, $$\text{vol}(X)\geq \frac{4}{3}p_g(X)-{\frac{10}{3}}.$$

math.AG↗
arXiv2019

On the anti-canonical geometry of weak $\mathbb{Q}$-Fano threefolds, II

By a canonical (resp. terminal) weak $\mathbb{Q}$-Fano $3$-fold we mean a normal projective one with at worst canonical (resp. terminal) singularities on which the anti-canonical divisor is $\mathbb{Q}$-Cartier, nef and big. For a canonical weak $\mathbb{Q}$-Fano $3$-fold $V$, we show that there exists a terminal weak $\mathbb{Q}$-Fano $3$-fold $X$, being birational to $V$, such that the $m$-th anti-canonical map defined by $|-mK_{X}|$ is birational for all $m\geq 52$. As an intermediate result, we show that for any $K$-Mori fiber space $Y$ of a canonical weak $\mathbb{Q}$-Fano $3$-fold, the $m$-th anti-canonical map defined by $|-mK_{Y}|$ is birational for all $m\geq 52$.

math.AG↗
arXiv2019

The Noether inequality for algebraic threefolds (With an Appendix by János Kollár)

We establish the Noether inequality for projective $3$-folds. More precisely, we prove that the inequality $${\rm vol}(X)\geq \tfrac{4}{3}p_g(X)-{\tfrac{10}{3}}$$ holds for all projective $3$-folds $X$ of general type with either $p_g(X)\leq 4$ or $p_g(X)\geq 21$, where $p_g(X)$ is the geometric genus and ${\rm vol}(X)$ is the canonical volume. This inequality is optimal due to known examples found by M. Kobayashi in 1992.

math.AG↗
arXiv2019

Mappa Mundi: An Interactive Artistic Mind Map Generator with Artificial Imagination

We present a novel real-time, collaborative, and interactive AI painting system, Mappa Mundi, for artistic Mind Map creation. The system consists of a voice-based input interface, an automatic topic expansion module, and an image projection module. The key innovation is to inject Artificial Imagination into painting creation by considering lexical and phonological similarities of language, learning and inheriting artist's original painting style, and applying the principles of Dadaism and impossibility of improvisation. Our system indicates that AI and artist can collaborate seamlessly to create imaginative artistic painting and Mappa Mundi has been applied in art exhibition in UCCA, Beijing

cs.AI↗
arXiv2019

Kernel-based collocation methods for heat transport on evolving surfaces

We propose algorithms for solving convective-diffusion partial differential equations (PDEs), which model surfactant concentration and heat transport on evolving surfaces, based on intrinsic kernel-based meshless collocation methods. The algorithms can be classified into two categories: one collocates PDEs directly and analytically, and the other approximates surface differential operators by meshless pseudospectral approaches. The former is specifically designed to handle PDEs on evolving surfaces defined by parametric equations, and the latter works on surface evolutions based on point clouds. After some convergence studies and comparisons, we demonstrate that the proposed method can solve challenging PDEs posed on surfaces with high curvatures with discontinuous initial conditions with correct physics.

math.NA↗
arXiv2019

From Knowledge Map to Mind Map: Artificial Imagination

Imagination is one of the most important factors which makes an artistic painting unique and impressive. With the rapid development of Artificial Intelligence, more and more researchers try to create painting with AI technology automatically. However, lacking of imagination is still a main problem for AI painting. In this paper, we propose a novel approach to inject rich imagination into a special painting art Mind Map creation. We firstly consider lexical and phonological similarities of seed word, then learn and inherit original painting style of the author, and finally apply Dadaism and impossibility of improvisation principles into painting process. We also design several metrics for imagination evaluation. Experimental results show that our proposed method can increase imagination of painting and also improve its overall quality.

cs.CL↗
arXiv2018

On an open problem of characterizing the birationality of 4K

We answer an open problem raised by Chen and Zhang in 2008 and prove that, for any minimal projective 3-fold $X$ of general type with the geometric genus $\geq 5$, $X$ is birationally fibred by a pencil of $(1,2)$-surfaces (i.e. $c_1^2=1$, $p_g=2$) if and only if the $4$-canonical map $φ_{4,X}$ is non-birational. The statement does not hold for those with the geometric genus $\leq 4$ according to our examples.

math.AG↗
arXiv2017

On minimal 3-folds of general type with maximal pluricanonical section index

Let $X$ be a minimal projective 3-fold of general type. The pluricanonical section index $δ(X)$ is defined to be the minimal integer $m$ so that $P_{m}(X)\geq 2$. According to Chen-Chen, one has either $1\leq δ(X)\leq 15$ or $δ(X)=18$. This note aims to intensively study those with maximal such index. A direct corollary is that the $57$th canonical map of every minimal 3-fold of general type is stably birational.

math.AG↗
arXiv2017

Lie Algebrized Gaussians for Image Representation

We present an image representation method which is derived from analyzing Gaussian probability density function (\emph{pdf}) space using Lie group theory. In our proposed method, images are modeled by Gaussian mixture models (GMMs) which are adapted from a globally trained GMM called universal background model (UBM). Then we vectorize the GMMs based on two facts: (1) components of image-specific GMMs are closely grouped together around their corresponding component of the UBM due to the characteristic of the UBM adaption procedure; (2) Gaussian \emph{pdf}s form a Lie group, which is a differentiable manifold rather than a vector space. We map each Gaussian component to the tangent vector space (named Lie algebra) of Lie group at the manifold position of UBM. The final feature vector, named Lie algebrized Gaussians (LAG) is then constructed by combining the Lie algebrized Gaussian components with mixture weights. We apply LAG features to scene category recognition problem and observe state-of-the-art performance on 15Scenes benchmark.

cs.CV↗
arXiv2015

Characterization of the 4-canonical birationality of algebraic 3-folds, II

For nonsingular projective 3-folds $X$ (of general type) whose geometric genus $p_g=h^0(X, K_X)$ is $\geq 5$, the birationality of the fourth canonical map $φ_{4,X}=Φ_{|4K_X|}$ was characterized by D.-Q. Zhang and the first author in 2008. This paper aims at characterizing the birationality of $φ_{4,X}$ for those $X$ with $p_g=4$.

math.AG↗
arXiv2015

On the anti-canonical geometry of $\mathbb{Q}$-Fano 3-folds

For a $\mathbb{Q}$-Fano 3-fold $X$ on which $K_X$ is a canonical divisor, we investigate the geometry induced from the linear system $|-mK_X|$ in this paper and prove that the anti-$m$-canonical map $φ_{-m}$ is birational onto its image for all $m\geq 39$. By a weak $\mathbb{Q}$-Fano 3-fold $X$ we mean a projective one with at worst terminal singularities on which $-K_X$ is $\mathbb{Q}$-Cartier, nef and big. For weak $\mathbb{Q}$-Fano 3-folds, we prove that $φ_{-m}$ is birational onto its image for all $m\geq 97$.

math.AG↗
arXiv2014

Explicit birational geometry of 3-folds and 4-folds of general type, III

Nonsingular projective 3-folds $V$ of general type can be naturally classified into 18 families according to the {\it pluricanonical section index} $δ(V):=\text{min}\{m|P_m\geq 2\}$ since $1\leq δ(V)\leq 18$ due to our previous series (I, II). Based on our further classification to 3-folds with $δ(V)\geq 13$ and an intensive geometrical investigation to those with $δ(V)\leq 12$, we prove that $\text{Vol}(V) \geq \frac{1}{1680}$ and that the pluricanonical map $Φ_{m}$ is birational for all $m \geq 61$, which greatly improves known results. An optimal birationality of $Φ_m$ for the case $δ(V)=2$ is obtained. As an effective application, we study projective 4-folds of general type with $p_g\geq 2$ in the last section.

math.AG↗