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With the recent surge in big data analytics for hyper-dimensional data there is a renewed interest in dimensionality reduction techniques for machine learning applications. In order for these methods to improve performance gains and…
Explicit topology optimization methods have received ever-increasing interest in recent years. In particular, a 188-line Matlab code of the two-dimensional (2D) Moving Morphable Component (MMC)-based topology optimization method was…
Structural optimization (topology, shapes, sizing) is an important tool for facilitating the emergence of new concepts in structural design. Normally, topology optimization is carried out at the early stage of design and then shape and…
When performing classification tasks, raw high dimensional features often contain redundant information, and lead to increased computational complexity and overfitting. In this paper, we assume the data samples lie on a single underlying…
We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework…
Representation learning is currently a very hot topic in modern machine learning, mostly due to the great success of the deep learning methods. In particular low-dimensional representation which discriminates classes can not only enhance…
Cross-modal image-text retrieval is challenging because of the diverse possible associations between content from different modalities. Traditional methods learn a single-vector embedding to represent semantics of each sample, but struggle…
Embedding high-dimensional data onto a low-dimensional manifold is of both theoretical and practical value. In this paper, we propose to combine deep neural networks (DNN) with mathematics-guided embedding rules for high-dimensional data…
The knapsack problem (KP) and its multidimensional version (MKP) are basic problems in combinatorial optimization. In this paper we consider their multiobjective extension (MOKP and MOMKP), for which the aim is to obtain or to approximate…
Self-supervised monocular depth estimation (MDE) has gained popularity for obtaining depth predictions directly from videos. However, these methods often produce scale invariant results, unless additional training signals are provided.…
Dimension reduction (DR) techniques such as t-SNE, UMAP, and TriMAP have demonstrated impressive visualization performance on many real world datasets. One tension that has always faced these methods is the trade-off between preservation of…
Classical nonlinear dimensionality reduction (NLDR) techniques like t-SNE, Isomap, and LLE excel at creating low-dimensional embeddings for data visualization but fundamentally lack the ability to map these embeddings back to the original…
We first show that the commonly used dimensionality reduction (DR) methods such as t-SNE and LargeVis poorly capture the global structure of the data in the low dimensional embedding. We show this via a number of tests for the DR methods…
Multimodality is one of the biggest difficulties for optimization as local optima are often preventing algorithms from making progress. This does not only challenge local strategies that can get stuck. It also hinders meta-heuristics like…
This work presents a highly optimized computational framework for the Discrete Dipole Approximation, a numerical method for calculating the optical properties associated with a target of arbitrary geometry that is widely used in…
Benders decomposition is a widely used method for solving large optimization problems, but its performance is often hindered by the repeated solution of subproblems. We propose a flexible and modular algorithmic framework for accelerating…
Composite convex optimization models arise in several applications, and are especially prevalent in inverse problems with a sparsity inducing norm and in general convex optimization with simple constraints. The most widely used algorithms…
The continuing advances of omic technologies mean that it is now more tangible to measure the numerous features collectively reflecting the molecular properties of a sample. When multiple omic methods are used, statistical and computational…
The paper presents a new method for shape and topology optimization based on an efficient and scalable boundary integral formulation for elasticity. To optimize topology, our approach uses iterative extraction of isosurfaces of a…
Nonlinear dimensionality reduction methods provide a valuable means to visualize and interpret high-dimensional data. However, many popular methods can fail dramatically, even on simple two-dimensional manifolds, due to problems such as…