Related papers: ToMAToMP: Robust and Multi-Parameter Topological C…

Testing Deep Learning (DL)-based systems is an open challenge. Although it is relatively easy to find inputs that cause a DL model to misbehave, the grouping of inputs by features that make the DL model under test fail is largely…

In this work we present a clustering technique called \textit{multi-level conformal clustering (MLCC)}. The technique is hierarchical in nature because it can be performed at multiple significance levels which yields greater insight into…

We study clustering properties of networks of single integrator nodes over a directed graph, in which the nodes converge to steady-state values. These values define clustering groups of nodes, which depend on interaction topology, edge…

This study presents a novel approach utilizing cluster means to address the non-differentiability issue arising from multiple eigenvalues in eigenfrequency and bandgap optimization. By constructing symmetric functions of repeated…

Topology optimization (TO) is a method of deriving an optimal design that satisfies a given load and boundary conditions within a design domain. This method enables effective design without initial design, but has been limited in use due to…

Living systems exhibit complex yet organized behavior on multiple spatiotemporal scales. To investigate the nature of multiscale coordination in living systems, one needs a meaningful and systematic way to quantify the complex dynamics, a…

Dynamic community detection methods often lack effective mechanisms to ensure temporal consistency, hindering the analysis of network evolution. In this paper, we propose a novel deep graph clustering framework with temporal consistency…

Many clustering schemes have been proposed for ad hoc networks. A systematic classification of these clustering schemes enables one to better understand and make improvements. In mobile ad hoc networks, the movement of the network nodes may…

In recent years, topology optimization (TO) has gained widespread attention as a powerful structural design method. However, its application remains challenging due to the deep expertise and extensive development effort required.…

Robust topology optimization (RTO), as a class of topology optimization problems, identifies a design with the best average performance while reducing the response sensitivity to input uncertainties, e.g. load uncertainty. Solving RTO is…

Machine learning models for repeated measurements are limited. Using topological data analysis (TDA), we present a classifier for repeated measurements which samples from the data space and builds a network graph based on the data topology.…

We formulate a novel technique for the detection of functional clusters in discrete event data. The advantage of this algorithm is that no prior knowledge of the number of functional groups is needed, as our procedure progressively combines…

Different algorithms can be used for clustering purposes with data sets. On of these algorithms, uses topological features extracted from the data set to base the clusters on. The complexity of this algorithm is however exponential in the…

Spectral clustering is one of the most prominent clustering approaches. The distance-based similarity is the most widely used method for spectral clustering. However, people have already noticed that this is not suitable for multi-scale…

Shooting methods are an efficient approach to solving nonlinear optimal control problems. As they use local optimization, they exhibit favorable convergence when initialized with a good warm-start but may not converge at all if provided…

Persistent homology is a natural tool for probing the topological characteristics of weighted graphs, essentially focusing on their $0$-dimensional homology. While this area has been substantially studied, we present a new approach to…

Topological methods can provide a way of proposing new metrics and methods of scrutinising data, that otherwise may be overlooked. In this work, a method of quantifying the shape of data, via a topic called topological data analysis will be…

We present Topological Point Cloud Clustering (TPCC), a new method to cluster points in an arbitrary point cloud based on their contribution to global topological features. TPCC synthesizes desirable features from spectral clustering and…

Deep learning has been recently applied to a multitude of computer vision and medical image analysis problems. Although recent research efforts have improved the state of the art, most of the methods cannot be easily accessed, compared or…

Topological methods, including persistent homology, are powerful tools for analysis of high-dimensional data sets but these methods rely almost exclusively on thresholding techniques. In noisy data sets, thresholding does not always allow…