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Compared to point estimates calculated by standard neural networks, Bayesian neural networks (BNN) provide probability distributions over the output predictions and model parameters, i.e., the weights. Training the weight distribution of a…
A difficult problem in clustering is how to handle data with a manifold structure, i.e. data that is not shaped in the form of compact clouds of points, forming arbitrary shapes or paths embedded in a high-dimensional space. In this work we…
We are interested in how quantum data can allow for practical solutions to otherwise difficult computational problems. A notoriously difficult phenomenon from quantum many-body physics is the emergence of many-body localization (MBL). So…
Multi-label classification (MLC) studies the problem where each instance is associated with multiple relevant labels, which leads to the exponential growth of output space. MLC encourages a popular framework named label compression (LC) for…
Classifying the topology of closed curves is a central problem in low dimensional topology with applications beyond mathematics spanning protein folding, polymer physics and even magnetohydrodynamics. The central problem is how to determine…
One of the simplest and most effective classical machine learning algorithms is the $k$-nearest neighbors algorithm ($k$NN) which classifies an unknown test state by finding the $k$ nearest neighbors from a set of $M$ train states. Here we…
In this paper, we consider unsupervised partitioning problems, such as clustering, image segmentation, video segmentation and other change-point detection problems. We focus on partitioning problems based explicitly or implicitly on the…
For manifold learning, it is assumed that high-dimensional sample/data points are embedded on a low-dimensional manifold. Usually, distances among samples are computed to capture an underlying data structure. Here we propose a metric…
The human visual system is able to recognize objects despite transformations that can drastically alter their appearance. To this end, much effort has been devoted to the invariance properties of recognition systems. Invariance can be…
Manifold structure learning is often used to exploit geometric information among data in semi-supervised feature learning algorithms. In this paper, we find that local discriminative information is also of importance for semi-supervised…
The cross-media retrieval problem has received much attention in recent years due to the rapid increasing of multimedia data on the Internet. A new approach to the problem has been raised which intends to match features of different…
Modified Hamiltonians are used in the field of geometric numerical integration to show that symplectic schemes for Hamiltonian systems are accurate over long times. For nonlinear systems the series defining the modified Hamiltonian usually…
Similarity/Distance measures play a key role in many machine learning, pattern recognition, and data mining algorithms, which leads to the emergence of metric learning field. Many metric learning algorithms learn a global distance function…
Multi-task learning (MTL) improves prediction performance in different contexts by learning models jointly on multiple different, but related tasks. Network data, which are a priori data with a rich relational structure, provide an…
Computing the similarity between two data points plays a vital role in many machine learning algorithms. Metric learning has the aim of learning a good metric automatically from data. Most existing studies on metric learning for…
Multi-Objective Learning Model Predictive Control is a novel data-driven control scheme which improves a linear system's closed-loop performance with respect to several convex control objectives over iterations of a repeated task. At each…
We present a geometric formulation of the Multiple Kernel Learning (MKL) problem. To do so, we reinterpret the problem of learning kernel weights as searching for a kernel that maximizes the minimum (kernel) distance between two convex…
Few-shot learning aims to learn classifiers for new classes with only a few training examples per class. Most existing few-shot learning approaches belong to either metric-based meta-learning or optimization-based meta-learning category,…
KNN classification is an improvisational learning mode, in which they are carried out only when a test data is predicted that set a suitable K value and search the K nearest neighbors from the whole training sample space, referred them to…
Image classification is an essential part of computer vision which assigns a given input image to a specific category based on the similarity evaluation within given criteria. While promising classifiers can be obtained through deep…