A Two-stage Classification Method for High-dimensional Data and Point Clouds

High-dimensional data classification is a fundamental task in machine learning and imaging science. In this paper, we propose a two-stage multiphase semi-supervised classification method for classifying high-dimensional data and unstructured point clouds. To begin with, a fuzzy classification method such as the standard support vector machine is used to generate a warm initialization. We then apply a two-stage approach named SaT (smoothing and thresholding) to improve the classification. In the first stage, an unconstraint convex variational model is implemented to purify and smooth the initialization, followed by the second stage which is to project the smoothed partition obtained at stage one to a binary partition. These two stages can be repeated, with the latest result as a new initialization, to keep improving the classification quality. We show that the convex model of the smoothing stage has a unique solution and can be solved by a specifically designed primal-dual algorithm whose convergence is guaranteed. We test our method and compare it with the state-of-the-art methods on several benchmark data sets. The experimental results demonstrate clearly that our method is superior in both the classification accuracy and computation speed for high-dimensional data and point clouds.Comment: 21 pages, 4 figure

Quenched large deviation principles for random projections of ℓpn\ell_p^n balls

Let $(k_n)_{n \in \mathbb{N}}$ be a sequence of positive integers growing to infinity at a sublinear rate, $k_n \rightarrow \infty$ and $k_n/n \rightarrow 0$ as $n \rightarrow \infty$. Given a sequence of $n$-dimensional random vectors $\{Y^{(n)}\}_{n \in \mathbb{N}}$ belonging to a certain class, which includes uniform distributions on suitably scaled $\ell_p^n$-balls or $\ell_p^n$-spheres, $p \geq 2$, and product distributions with sub-Gaussian marginals, we study the large deviations behavior of the corresponding sequence of $k_n$-dimensional orthogonal projections $n^{-1/2} \boldsymbol{a}_{n,k_n} Y^{(n)}$, where $\boldsymbol{a}_{n,k_n}$ is an $(n \times k_n)$-dimensional projection matrix lying in the Stiefel manifold of orthonormal $k_n$-frames in $\mathbb{R}^n$. For almost every sequence of projection matrices, we establish a large deviation principle (LDP) for the corresponding sequence of projections, with a fairly explicit rate function that does not depend on the sequence of projection matrices. As corollaries, we also obtain quenched LDPs for sequences of $\ell_2$-norms and $\ell_\infty$-norms of the coordinates of the projections. Past work on LDPs for projections with growing dimension has mainly focused on the annealed setting, where one also averages over the random projection matrix, chosen from the Haar measure, in which case the coordinates of the projection are exchangeable. The quenched setting lacks such symmetry properties, and gives rise to significant new challenges in the setting of growing projection dimension. Along the way, we establish new Gaussian approximation results on the Stiefel manifold that may be of independent interest. Such LDPs are of relevance in asymptotic convex geometry, statistical physics and high-dimensional statistics.Comment: 53 page

Central limit theorem for the complex eigenvalues of Gaussian random matrices

We establish a central limit theorem for the counting function of the eigenvalues of a matrix of real Gaussian random variables.Comment: 11 page

Data-driven discovery of dimensionless numbers and scaling laws from experimental measurements

Dimensionless numbers and scaling laws provide elegant insights into the characteristic properties of physical systems. Classical dimensional analysis and similitude theory fail to identify a set of unique dimensionless numbers for a highly-multivariable system with incomplete governing equations. In this study, we embed the principle of dimensional invariance into a two-level machine learning scheme to automatically discover dominant and unique dimensionless numbers and scaling laws from data. The proposed methodology, called dimensionless learning, can reduce high-dimensional parametric spaces into descriptions involving just a few physically-interpretable dimensionless parameters, which significantly simplifies the process design and optimization of the system. We demonstrate the algorithm by solving several challenging engineering problems with noisy experimental measurements (not synthetic data) collected from the literature. The examples include turbulent Rayleigh-Benard convection, vapor depression dynamics in laser melting of metals, and porosity formation in 3D printing. We also show that the proposed approach can identify dimensionally-homogeneous differential equations with minimal parameters by leveraging sparsity-promoting techniques

An Investigation of Cyberinfrastructure Adoption in University Libraries

This study aims to understand factors that affect university libraries’ adoption of cyberinfrastructure for big data sharing and reuse. A cyberinfrastructure adoption model which contains 10 factors has been developed based on the technology-organization-environment (TOE) framework and the literature regarding tradeoffs of applying cyberinfrastructure. This paper describes the proposed cyberinfrastructure adoption model and explains the survey in-struments. The next steps of the study are also presented

Quantum Circuit Implementation and Resource Analysis of LBlock and LiCi

Due to Grover's algorithm, any exhaustive search attack of block ciphers can achieve a quadratic speed-up. To implement Grover,s exhaustive search and accurately estimate the required resources, one needs to implement the target ciphers as quantum circuits. Recently, there has been increasing interest in quantum circuits implementing lightweight ciphers. In this paper we present the quantum implementations and resource estimates of the lightweight ciphers LBlock and LiCi. We optimize the quantum circuit implementations in the number of gates, required qubits and the circuit depth, and simulate the quantum circuits on ProjectQ. Furthermore, based on the quantum implementations, we analyze the resources required for exhaustive key search attacks of LBlock and LiCi with Grover's algorithm. Finally, we compare the resources for implementing LBlock and LiCi with those of other lightweight ciphers.Comment: 29 pages,21 figure

What Makes Good Open-Vocabulary Detector: A Disassembling Perspective

Open-vocabulary detection (OVD) is a new object detection paradigm, aiming to localize and recognize unseen objects defined by an unbounded vocabulary. This is challenging since traditional detectors can only learn from pre-defined categories and thus fail to detect and localize objects out of pre-defined vocabulary. To handle the challenge, OVD leverages pre-trained cross-modal VLM, such as CLIP, ALIGN, etc. Previous works mainly focus on the open vocabulary classification part, with less attention on the localization part. We argue that for a good OVD detector, both classification and localization should be parallelly studied for the novel object categories. We show in this work that improving localization as well as cross-modal classification complement each other, and compose a good OVD detector jointly. We analyze three families of OVD methods with different design emphases. We first propose a vanilla method,i.e., cropping a bounding box obtained by a localizer and resizing it into the CLIP. We next introduce another approach, which combines a standard two-stage object detector with CLIP. A two-stage object detector includes a visual backbone, a region proposal network (RPN), and a region of interest (RoI) head. We decouple RPN and ROI head (DRR) and use RoIAlign to extract meaningful features. In this case, it avoids resizing objects. To further accelerate the training time and reduce the model parameters, we couple RPN and ROI head (CRR) as the third approach. We conduct extensive experiments on these three types of approaches in different settings. On the OVD-COCO benchmark, DRR obtains the best performance and achieves 35.8 Novel AP$_{50}$, an absolute 2.8 gain over the previous state-of-the-art (SOTA). For OVD-LVIS, DRR surpasses the previous SOTA by 1.9 AP$_{50}$ in rare categories. We also provide an object detection dataset called PID and provide a baseline on PID

Practical Computation of the Charge Mobility in Molecular Semiconductors Using Transient Localization Theory

We describe a practical and flexible procedure to compute the charge carrier mobility in the transient localization regime. The method is straightforward to implement and computationally very inexpensive. We highlight the practical steps and provide sample computer codes. To demonstrate the flexibility of the method and generalize the theory, the correlation between the fluctuations of the transfer integrals is assessed. The method can be transparently linked with the results of electronic structure calculations and can therefore be used to extract the charge mobility at no additional cost