Related papers: Worst-Case Linear Discriminant Analysis as Scalabl…
We study a weighted generalization of the fractional cut-covering problem, which we relate to the maximum cut problem via antiblocker and gauge duality. This relationship allows us to introduce a semidefinite programming (SDP) relaxation…
Linear discriminant analysis (LDA) is a typical method for classification problems with large dimensions and small samples. There are various types of LDA methods that are based on the different types of estimators for the covariance…
Tensor classification has become increasingly crucial in statistics and machine learning, with applications spanning neuroimaging, computer vision, and recommendation systems. However, the high dimensionality of tensors presents significant…
Semidefinite programs (SDP) are important in learning and combinatorial optimization with numerous applications. In pursuit of low-rank solutions and low complexity algorithms, we consider the Burer--Monteiro factorization approach for…
Non-commutative polynomial optimization (NPO) problems seek to minimize the state average of a polynomial of some operator variables, subject to polynomial constraints, over all states and operators, as well as the Hilbert spaces where…
This paper presents two novel algorithms for approximately projecting symmetric matrices onto the Positive Semidefinite (PSD) cone using Randomized Numerical Linear Algebra (RNLA). Classical PSD projection methods rely on full-rank…
Annotation-efficient segmentation of the numerous mitochondria instances from various electron microscopy (EM) images is highly valuable for biological and neuroscience research. Although unsupervised domain adaptation (UDA) methods can…
In practical machine learning applications, it is often challenging to assign accurate labels to data, and increasing the number of labeled instances is often limited. In such cases, Weakly Supervised Learning (WSL), which enables training…
We propose an efficient approach to semidefinite spectral clustering (SSC), which addresses the Frobenius normalization with the positive semidefinite (p.s.d.) constraint for spectral clustering. Compared with the original Frobenius norm…
Determination of the most economic strategies for supply and transmission of electricity is a daunting computational challenge. Due to theoretical barriers, so-called NP-hardness, the amount of effort to optimize the schedule of generating…
In recent years, many estimation problems in robotics have been shown to be solvable to global optimality using their semidefinite relaxations. However, the runtime complexity of off-the-shelf semidefinite programming (SDP) solvers is up to…
Semidefinite programming (SDP) is a fundamental class of convex optimization problems with diverse applications in mathematics, engineering, machine learning, and related disciplines. This paper investigates the application of the…
Covariance and Hessian matrices have been analyzed separately in the literature for classification problems. However, integrating these matrices has the potential to enhance their combined power in improving classification performance. We…
This paper proposes an incremental solution to Fast Subclass Discriminant Analysis (fastSDA). We present an exact and an approximate linear solution, along with an approximate kernelized variant. Extensive experiments on eight image…
The sensor network localization, SNL, problem in embedding dimension r, consists of locating the positions of wireless sensors, given only the distances between sensors that are within radio range and the positions of a subset of the…
Optimal power flow (OPF) is an important problem in the operation of electric power systems. Due to the OPF problem's non-convexity, there may exist multiple local optima. Certifiably obtaining the global solution is important for certain…
Topology optimization of frame structures under free-vibration eigenvalue constraints constitutes a challenging nonconvex polynomial optimization problem with disconnected feasible sets. In this article, we first formulate it as a…
Optimization problems constrained by high-dimensional, time-dependent partial differential equations require repeated forward and sensitivity solves, making high-fidelity optimization computationally prohibitive in many-query design and…
This paper studies the problem of stability of a parameterized delay differential equations (DDE see equation (0.1)). After discretizing the DDE (0.1), we show that the problem can be equivalently casted into a semi-definite programming…
The placement problem in Very Large-Scale Integration (VLSI) circuits is a critical step in chip design. Its primary goal is to optimize the wirelength of circuit components within a confined area while adhering to nonoverlapping…