arXiv subjects

Zeqin Lin

Publications and source records attributed to Zeqin Lin.

4 recordsLinked to original sources

arXiv2026

Multi-kernel spectral clustering: Entrywise eigenvector perturbation bounds and exact recovery

Kernel spectral clustering with a single bandwidth can be inadequate for data exhibiting multiple characteristic pairwise-distance scales, a problem particularly prevalent in the high-dimensional regime. We address this issue through a multi-kernel formulation that aggregates kernels with different bandwidths. The bandwidths are selected as prescribed empirical quantiles of the pairwise squared distances, thereby capturing the relevant distance scales without requiring prior population-scale information. We develop a rigorous theoretical analysis of the resulting method under a general high-dimensional, multi-scale mixture model with heterogeneous cluster centers and covariance geometries. We construct a blockwise constant, low-rank informative approximation to the empirical multi-kernel matrix and establish row-wise $\ell_{2,\infty}$ perturbation bounds for its leading spectral components, as well as for the associated normalized Laplacian matrix. These bounds yield observation-level control of the spectral embedding, which is more informative than conventional global eigenspace perturbation estimates. Under suitable eigen-gap and cluster-separation conditions, we show that approximate $K$-means applied to the multi-kernel spectral embedding achieves exact recovery with high probability.

stat.ML↗

arXiv2024

Eigenvector overlaps in large sample covariance matrices and nonlinear shrinkage estimators

Consider a data matrix $Y = [\mathbf{y}_1, \cdots, \mathbf{y}_N]$ of size $M \times N$, where the columns are independent observations from a random vector $\mathbf{y}$ with zero mean and population covariance $\Sigma$. Let $\mathbf{u}_i$ and $\mathbf{v}_j$ denote the left and right singular vectors of $Y$, respectively. This study investigates the eigenvector/singular vector overlaps $\langle {\mathbf{u}_i, D_1 \mathbf{u}_j} \rangle$, $\langle {\mathbf{v}_i, D_2 \mathbf{v}_j} \rangle$ and $\langle {\mathbf{u}_i, D_3 \mathbf{v}_j} \rangle$, where $D_k$ are general deterministic matrices with bounded operator norms. We establish the convergence in probability of these eigenvector overlaps toward their deterministic counterparts with explicit convergence rates, when the dimension $M$ scales proportionally with the sample size $N$. Building on these findings, we offer a more precise characterization of the loss for Ledoit and Wolf's nonlinear shrinkage estimators of the population covariance $\Sigma$.

math.ST↗

arXiv2024

Asymptotic distribution of spiked eigenvalues in the large signal-plus-noise models

Consider large signal-plus-noise data matrices of the form $S + \Sigma^{1/2} X$, where $S$ is a low-rank deterministic signal matrix and the noise covariance matrix $\Sigma$ can be anisotropic. We establish the asymptotic joint distribution of its spiked singular values when the dimensionality and sample size are comparably large and the signals are supercritical under general assumptions concerning the structure of $(S, \Sigma)$ and the distribution of the random noise $X$. It turns out that the asymptotic distributions exhibit nonuniversality in the sense of dependence on the distributions of the entries of $X$, which contrasts with what has previously been established for the spiked sample eigenvalues in the context of spiked population models. Such a result yields the asymptotic distribution of the sample spiked eigenvalues associated with mixture models. We also explore the application of these findings in detecting mean heterogeneity of data matrices.

math.ST↗

arXiv2021

M-FasterSeg: An Efficient Semantic Segmentation Network Based on Neural Architecture Search

Image semantic segmentation technology is one of the key technologies for intelligent systems to understand natural scenes. As one of the important research directions in the field of visual intelligence, this technology has broad application scenarios in the fields of mobile robots, drones, smart driving, and smart security. However, in the actual application of mobile robots, problems such as inaccurate segmentation semantic label prediction and loss of edge information of segmented objects and background may occur. This paper proposes an improved structure of a semantic segmentation network based on a deep learning network that combines self-attention neural network and neural network architecture search methods. First, a neural network search method NAS (Neural Architecture Search) is used to find a semantic segmentation network with multiple resolution branches. In the search process, combine the self-attention network structure module to adjust the searched neural network structure, and then combine the semantic segmentation network searched by different branches to form a fast semantic segmentation network structure, and input the picture into the network structure to get the final forecast result. The experimental results on the Cityscapes dataset show that the accuracy of the algorithm is 69.8%, and the segmentation speed is 48/s. It achieves a good balance between real-time and accuracy, can optimize edge segmentation, and has a better performance in complex scenes. Good robustness is suitable for practical application.

cs.CV↗