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The matching of multiple objects (e.g. shapes or images) is a fundamental problem in vision and graphics. In order to robustly handle ambiguities, noise and repetitive patterns in challenging real-world settings, it is essential to take…
We present an asymptotically faster algorithm for solving linear systems in well-structured 3-dimensional truss stiffness matrices. These linear systems arise from linear elasticity problems, and can be viewed as extensions of graph…
Scenario-based stochastic optimal control problems suffer from the curse of dimensionality as they can easily grow to six and seven figure sizes. First-order methods are suitable as they can deal with such large-scale problems, but may fail…
Hierarchical optimization refers to problems with interdependent decision variables and objectives, such as minimax and bilevel formulations. While various algorithms have been proposed, existing methods and analyses lack adaptivity in…
Hyperdimensional Computing (HDC), a technique inspired by cognitive models of computation, has been proposed as an efficient and robust alternative basis for machine learning. HDC programs are often manually written in low-level and target…
The Analytic Hierarchy Process (AHP) is a much discussed method in ranking business alternatives based on empirical and judgemental information. We focus here upon the key component of deducing efficient vectors for a reciprocal matrix of…
Hyperdimensional Computing (HDC), also known as Vector-Symbolic Architectures (VSA), is a promising framework for the development of cognitive architectures and artificial intelligence systems, as well as for technical applications and…
In this paper, we introduce novel fast matrix inversion algorithms that leverage triangular decomposition and recurrent formalism, incorporating Strassen's fast matrix multiplication. Our research places particular emphasis on triangular…
Many modern multiclass and multilabel problems are characterized by increasingly large output spaces. For these problems, label embeddings have been shown to be a useful primitive that can improve computational and statistical efficiency.…
Redundant robots are desired to execute multitasks with different priorities simultaneously. The task priorities are necessary to be transitioned for complex task scheduling of whole-body control (WBC). Many methods focused on guaranteeing…
Randomized numerical linear algebra is proved to bridge theoretical advancements to offer scalable solutions for approximating tensor decomposition. This paper introduces fast randomized algorithms for solving the fixed Tucker-rank problem…
Deep neural networks have become the standard approach to building reliable Natural Language Processing (NLP) applications, ranging from Neural Machine Translation (NMT) to dialogue systems. However, improving accuracy by increasing the…
We consider classification tasks in the regime of scarce labeled training data in high dimensional feature space, where specific expert knowledge is also available. We propose a new hybrid optimization algorithm that solves the elastic-net…
We present novel algorithmic solutions together with implementation details utilizing non-Abelian symmetries in order to boost the current limits of tensor network state algorithms on high performance computing infrastructure. In our…
We present an unsupervised data processing workflow that is specifically designed to obtain a fast conformational clustering of long molecular dynamics simulation trajectories. In this approach we combine two dimensionality reduction…
In many modern data sets, High dimension low sample size (HDLSS) data is prevalent in many fields of studies. There has been an increased focus recently on using machine learning and statistical methods to mine valuable information out of…
We propose a novel Hybrid High-Order method for the Cahn-Hilliard problem with convection. The proposed method is valid in two and three space dimensions, and it supports arbitrary approximation orders on general meshes containing…
This paper studies an accelerated fitted value iteration (FVI) algorithm to solve high-dimensional Markov decision processes (MDPs). FVI is an approximate dynamic programming algorithm that has desirable theoretical properties. However, it…
Nonnegative matrix factorization is the following problem: given a nonnegative input matrix $V$ and a factorization rank $K$, compute two nonnegative matrices, $W$ with $K$ columns and $H$ with $K$ rows, such that $WH$ approximates $V$ as…
Given a matrix $M$ (not necessarily nonnegative) and a factorization rank $r$, semi-nonnegative matrix factorization (semi-NMF) looks for a matrix $U$ with $r$ columns and a nonnegative matrix $V$ with $r$ rows such that $UV$ is the best…