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Wenjing Li

Publications and source records attributed to Wenjing Li.

51 records · Page 3Linked to original sources
arXiv2021

Neural Network Ensembles: Theory, Training, and the Importance of Explicit Diversity

Ensemble learning is a process by which multiple base learners are strategically generated and combined into one composite learner. There are two features that are essential to an ensemble's performance, the individual accuracies of the component learners and the overall diversity in the ensemble. The right balance of learner accuracy and ensemble diversity can improve the performance of machine learning tasks on benchmark and real-world data sets, and recent theoretical and practical work has demonstrated the subtle trade-off between accuracy and diversity in an ensemble. In this paper, we extend the extant literature by providing a deeper theoretical understanding for assessing and improving the optimality of any given ensemble, including random forests and deep neural network ensembles. We also propose a training algorithm for neural network ensembles and demonstrate that our approach provides improved performance when compared to both state-of-the-art individual learners and ensembles of state-of-the-art learners trained using standard loss functions. Our key insight is that it is better to explicitly encourage diversity in an ensemble, rather than merely allowing diversity to occur by happenstance, and that rigorous theoretical bounds on the trade-off between diversity and learner accuracy allow one to know when an optimal arrangement has been achieved.

cs.LG↗
arXiv2021

Projection Neural Network for a Class of Sparse Regression Problems with Cardinality Penalty

In this paper, we consider a class of sparse regression problems, whose objective function is the summation of a convex loss function and a cardinality penalty. By constructing a smoothing function for the cardinality function, we propose a projected neural network and design a correction method for solving this problem. The solution of the proposed neural network is unique, global existent, bounded and globally Lipschitz continuous. Besides, we prove that all accumulation points of the proposed neural network have a common support set and a unified lower bound for the nonzero entries. Combining the proposed neural network with the correction method, any corrected accumulation point is a local minimizer of the considered sparse regression problem. Moreover, we analyze the equivalent relationship on the local minimizers between the considered sparse regression problem and another regression sparse problem. Finally, some numerical experiments are provided to show the efficiency of the proposed neural networks in solving some sparse regression problems in practice.

cs.NE↗
arXiv2021

Effective Metagraph-based Life Pattern Clustering with Big Human Mobility Data

Life pattern clustering is essential for abstracting the groups' characteristics of daily mobility patterns and activity regularity. Based on millions of GPS records, this paper proposed a framework on the life pattern clustering which can efficiently identify the groups have similar life pattern. The proposed method can retain original features of individual life pattern data without aggregation. Metagraph-based data structure is proposed for presenting the diverse life pattern. Spatial-temporal similarity includes significant places semantics, time sequential properties and frequency are integrated into this data structure, which captures the uncertainty of an individual and the diversities between individuals. Non-negative-factorization-based method was utilized for reducing the dimension. The results show that our proposed method can effectively identify the groups have similar life pattern and takes advantages in computation efficiency and robustness comparing with the traditional method. We revealed the representative life pattern groups and analyzed the group characteristics of human life patterns during different periods and different regions. We believe our work will help in future infrastructure planning, services improvement and policies making related to urban and transportation, thus promoting a humanized and sustainable city.

cs.CY↗
arXiv2017

Conflict-free connection numbers of line graphs

A path in an edge-colored graph is called \emph{conflict-free} if it contains at least one color used on exactly one of its edges. An edge-colored graph $G$ is \emph{conflict-free connected} if for any two distinct vertices of $G$, there is a conflict-free path connecting them. For a connected graph $G$, the \emph{conflict-free connection number} of $G$, denoted by $cfc(G)$, is defined as the minimum number of colors that are required to make $G$ conflict-free connected. In this paper, we investigate the conflict-free connection numbers of connected claw-free graphs, especially line graphs. We first show that for an arbitrary connected graph $G$, there exists a positive integer $k$ such that $cfc(L^k(G))\leq 2$. Secondly, we get the exact value of the conflict-free connection number of a connected claw-free graph, especially a connected line graph. Thirdly, we prove that for an arbitrary connected graph $G$ and an arbitrary positive integer $k$, we always have $cfc(L^{k+1}(G))\leq cfc(L^k(G))$, with only the exception that $G$ is isomorphic to a star of order at least~$5$ and $k=1$. Finally, we obtain the exact values of $cfc(L^k(G))$, and use them as an efficient tool to get the smallest nonnegative integer $k_0$ such that $cfc(L^{k_0}(G))=2$.

math.CO↗
arXiv2017

Tight Nordhaus-Gaddum-type upper bound for total-rainbow connection number of graphs

A graph is said to be \emph{total-colored} if all the edges and the vertices of the graph are colored. A total-colored graph is \emph{total-rainbow connected} if any two vertices of the graph are connected by a path whose edges and internal vertices have distinct colors. For a connected graph $G$, the \emph{total-rainbow connection number} of $G$, denoted by $trc(G)$, is the minimum number of colors required in a total-coloring of $G$ to make $G$ total-rainbow connected. In this paper, we first characterize the graphs having large total-rainbow connection numbers. Based on this, we obtain a Nordhaus-Gaddum-type upper bound for the total-rainbow connection number. We prove that if $G$ and $\overline{G}$ are connected complementary graphs on $n$ vertices, then $trc(G)+trc(\overline{G})\leq 2n$ when $n\geq 6$ and $trc(G)+trc(\overline{G})\leq 2n+1$ when $n=5$. Examples are given to show that the upper bounds are sharp for $n\geq 5$. This completely solves a conjecture in [Y. Ma, Total rainbow connection number and complementary graph, Results in Mathematics 70(1-2)(2016), 173-182].

math.CO↗
arXiv2016

The $k$-proper index of complete bipartite and complete multipartite graphs

Let $G$ be a nontrivial connected graph of order $n$ with an edge-coloring $c:E(G)\rightarrow\{1,2,\dots,t\}$,$t\in\mathbb{N}$, where adjacent edges may be colored with the same color. A tree $T$ in $G$ is a \emph{proper tree} if no two adjacent edges of it are assigned the same color. Let $k$ be a fixed integer with $2\leq k\leq n$. For a vertex subset $S\subseteq V(G)$ with $|S|\geq 2$, a tree is called an \emph{$S$-tree} if it connects $S$ in $G$ . A \emph{$k$-proper coloring} of $G$ is an edge-coloring of $G$ having the property that for every set $S$ of $k$ vertices of $G$, there exists a proper $S$-tree $T$ in $G$. The minimum number of colors that are needed in a $k$-proper coloring of $G$ is defined as the \emph{$k$-proper index} of $G$, denoted by $px_k(G)$. In this paper, we determine the 3-proper index of all complete bipartite and complete multipartite graphs and partially determine the $k$-proper index of them for $k\geq 4$.

math.CO↗
arXiv2016

Nordhaus-Gaddum-type theorem for total proper connection number of graphs

A graph is said to be \emph{total-colored} if all the edges and the vertices of the graph are colored. A path $P$ in a total-colored graph $G$ is called a \emph{total-proper path} if $(i)$ any two adjacent edges of $P$ are assigned distinct colors; $(ii)$ any two adjacent internal vertices of $P$ are assigned distinct colors; $(iii)$ any internal vertex of $P$ is assigned a distinct color from its incident edges of $P$. The total-colored graph $G$ is \emph{total-proper connected} if any two distinct vertices of $G$ are connected by a total-proper path. The \emph{total-proper connection number} of a connected graph $G$, denoted by $tpc(G)$, is the minimum number of colors that are required to make $G$ total-proper connected. In this paper, we first characterize the graphs $G$ on $n$ vertices with $tpc(G)=n-1$. Based on this, we obtain a Nordhaus-Gaddum-type result for total-proper connection number. We prove that if $G$ and $\overline{G}$ are connected complementary graphs on $n$ vertices, then $6\leq tpc(G)+tpc(\overline{G})\leq n+2$. Examples are given to show that the lower bound is sharp for $n\geq 4$. The upper bound is reached for $n\geq 5$ if and only if $G$ or $\overline{G}$ is the tree with maximum degree $n-2$.

math.CO↗
arXiv2016

3-Rainbow index and forbidden subgraphs

A tree in an edge-colored connected graph $G$ is called \emph{a rainbow tree} if no two edges of it are assigned the same color. For a vertex subset $S\subseteq V(G)$, a tree is called an \emph{$S$-tree} if it connects $S$ in $G$. A \emph{$k$-rainbow coloring} of $G$ is an edge-coloring of $G$ having the property that for every set $S$ of $k$ vertices of $G$, there exists a rainbow $S$-tree in $G$. The minimum number of colors that are needed in a $k$-rainbow coloring of $G$ is the \emph{$k$-rainbow index} of $G$, denoted by $rx_k(G)$. The \emph{Steiner distance $d(S)$} of a set $S$ of vertices of $G$ is the minimum size of an $S$-tree $T$. The \emph{$k$-Steiner diameter $sdiam_k(G)$} of $G$ is defined as the maximum Steiner distance of $S$ among all sets $S$ with $k$ vertices of $G$. In this paper, we focus on the 3-rainbow index of graphs and find all finite families $\mathcal{F}$ of connected graphs, for which there is a constant $C_\mathcal{F}$ such that, for every connected $\mathcal{F}$-free graph $G$, $rx_3(G)\leq sdiam_3(G)+C_\mathcal{F}$.

math.CO↗
arXiv2016

Magnetic fingerprint of interfacial coupling between CoFe and nanoscale ferroelectric domain walls

Magnetoelectric coupling in ferromagnet/multiferroic systems is often manifested in the exchange bias effect, which may have combined contributions from multiple sources, such as domain walls, chemical defects or strain. In this study we magnetically "fingerprint" the coupling behavior of CoFe grown on epitaxial BiFeO3 (BFO) thin films by magnetometry and first-order-reversal-curves (FORC). The contribution to exchange bias from 71°, 109° and charged ferroelectric domain walls (DWs) was elucidated by the FORC distribution. CoFe samples grown on BFO with 71° DWs only exhibit an enhancement of the coercivity, but little exchange bias. Samples grown on BFO with 109° DWs and mosaic DWs exhibit a much larger exchange bias, with the main enhancement attributed to 109° and charged DWs. Based on the Malozemoff random field model, a varying-anisotropy model is proposed to account for the exchange bias enhancement. This work sheds light on the relationship between the exchange bias effect of the CoFe/BFO heterointerface and the ferroelectric DWs, and provides a path for multiferroic device analysis and design.

cond-mat.mtrl-sci↗
arXiv2016

Rainbow vertex-connection and forbidden subgraphs

A path in a vertex-colored graph is called \emph{vertex-rainbow} if its internal vertices have pairwise distinct colors. A graph $G$ is \emph{rainbow vertex-connected} if for any two distinct vertices of $G$, there is a vertex-rainbow path connecting them. For a connected graph $G$, the \emph{rainbow vertex-connection number} of $G$, denoted by $rvc(G)$, is defined as the minimum number of colors that are required to make $G$ rainbow vertex-connected. In this paper, we find all the families $\mathcal{F}$ of connected graphs with $|\mathcal{F}|\in\{1,2\}$, for which there is a constant $k_\mathcal{F}$ such that, for every connected $\mathcal{F}$-free graph $G$, $rvc(G)\leq diam(G)+k_\mathcal{F}$, where $diam(G)$ is the diameter of $G$.

math.CO↗
arXiv2015

Hardness result for the total rainbow $k$-connection of graphs

A path in a total-colored graph is called \emph{total rainbow} if its edges and internal vertices have distinct colors. For an $\ell$-connected graph $G$ and an integer $k$ with $1\leq k \leq\ell$, the \emph{total rainbow $k$-connection number} of $G$, denoted by $trc_k(G)$, is the minimum number of colors used in a total coloring of $G$ to make $G$ \emph{total rainbow $k$-connected}, that is, any two vertices of $G$ are connected by $k$ internally vertex-disjoint total rainbow paths. In this paper, we study the computational complexity of total rainbow $k$-connection number of graphs. We show that it is NP-complete to decide whether $trc_k(G)=3$.

math.CO↗
arXiv2011

Second cohomology for finite groups of Lie type

Let $G$ be a simple, simply-connected algebraic group defined over $\mathbb{F}_p$. Given a power $q = p^r$ of $p$, let $G(\mathbb{F}_q) \subset G$ be the subgroup of $\mathbb{F}_q$-rational points. Let $L(λ)$ be the simple rational $G$-module of highest weight $λ$. In this paper we establish sufficient criteria for the restriction map in second cohomology $H^2(G,L(λ)) \rightarrow H^2(G(\mathbb{F}_q),L(λ))$ to be an isomorphism. In particular, the restriction map is an isomorphism under very mild conditions on $p$ and $q$ provided $λ$ is less than or equal to a fundamental dominant weight. Even when the restriction map is not an isomorphism, we are often able to describe $H^2(G(\mathbb{F}_q),L(λ))$ in terms of rational cohomology for $G$. We apply our techniques to compute $H^2(G(\mathbb{F}_q),L(λ))$ in a wide range of cases, and obtain new examples of nonzero second cohomology for finite groups of Lie type.

math.RT↗
arXiv2011

First cohomology for finite groups of Lie type: simple modules with small dominant weights

Let $k$ be an algebraically closed field of characteristic $p > 0$, and let $G$ be a simple, simply connected algebraic group defined over $\mathbb{F}_p$. Given $r \geq 1$, set $q=p^r$, and let $G(\mathbb{F}_q)$ be the corresponding finite Chevalley group. In this paper we investigate the structure of the first cohomology group $H^1(G(\mathbb{F}_q),L(λ))$ where $L(λ)$ is the simple $G$-module of highest weight $λ$. Under certain very mild conditions on $p$ and $q$, we are able to completely describe the first cohomology group when $λ$ is less than or equal to a fundamental dominant weight. In particular, in the cases we consider, we show that the first cohomology group has dimension at most one. Our calculations significantly extend, and provide new proofs for, earlier results of Cline, Parshall, Scott, and Jones, who considered the special case when $λ$ is a minimal nonzero dominant weight.

math.GR↗
arXiv2008

Cohomology of quantum groups: An analog of Kostant's Theorem

We prove the analog of Kostant's Theorem on Lie algebra cohomology in the context of quantum groups. We prove that Kostant's cohomology formula holds for quantum groups at a generic parameter $q$, recovering an earlier result of Malikov in the case where the underlying semisimple Lie algebra $\mathfrak{g} = \mathfrak{sl}(n)$. We also show that Kostant's formula holds when $q$ is specialized to an $\ell$-th root of unity for odd $\ell \ge h-1$ (where $h$ is the Coxeter number of $\mathfrak{g}$) when the highest weight of the coefficient module lies in the lowest alcove. This can be regarded as an extension of results of Friedlander-Parshall and Polo-Tilouine on the cohomology of Lie algebras of reductive algebraic groups in prime characteristic.

math.RT↗