Related papers: Layers and stability
In image classification, visual separability between different object categories is highly uneven, and some categories are more difficult to distinguish than others. Such difficult categories demand more dedicated classifiers. However,…
Determining the number of clusters present in a dataset is an important problem in cluster analysis. Conventional clustering techniques generally assume this parameter to be provided up front. %user supplied. %Recently, robustness of any…
A new hierarchy of separability conditions for bipartite states is obtained. All the conditions in the hierarchy are necessary for separability. The conditions are expressed in terms of higher powers of the density operator of the bipartite…
Interpretability of Deep Neural Networks has become a major area of exploration. Although these networks have achieved state of the art accuracy in many tasks, it is extremely difficult to interpret and explain their decisions. In this work…
Large surveys of the local Universe have shown that galaxies with different intrinsic properties, such as colour, luminosity and morphological type display a range of clustering amplitudes. Galaxies are therefore not faithful tracers of the…
The primary goal in cluster analysis is to discover natural groupings of objects. The field of cluster analysis is crowded with diverse methods that make special assumptions about data and address different scientific aims. Despite its…
We introduce a spectral hierarchy of cosmic-web classifications obtained by applying simple scale-weighting kernels to the density field before performing a standard eigenvalue-based web classification. This unifies and extends several…
Superclusters are a convenient way to partition and characterize the large scale structure of the Universe. In this Letter we explore the advantages of defining superclusters as watershed basins in the divergence velocity field. We apply…
The mass spectra of gas-phase clusters in cluster beams have a rich structure where the relative heights of the peaks compared to peaks corresponding to clusters of neighbor sizes reveal the stability of the clusters as a function of the…
Using the APM cluster data we investigate whether the dynamical status of clusters is related to the large-scale structure of the Universe. We find that cluster substructure is strongly correlated with the tendency of clusters to be aligned…
Layered stable (multivariate) distributions and processes are defined and studied. A layered stable process combines stable trends of two different indices, one of them possibly Gaussian. More precisely, in short time, it is close to a…
Star clusters have hierarchical patterns in space and time, suggesting formation processes in the densest regions of a turbulent interstellar medium. Clusters also have hierarchical substructure when they are young, which makes them all…
Traditional Multi-level Hierarchical Classification (MLHC) classifiers often rely on backbone models with $n$ independent output layers. This structure tends to overlook the hierarchical relationships between classes, leading to…
Clusters of galaxies are the most recently assembled, massive, bound structures in the Universe. As predicted by General Relativity, given their masses, clusters strongly deform space-time in their vicinity. Clusters act as some of the most…
Galaxies and clusters embedded in the large-scale structure of the Universe are observed to align in preferential directions. Galaxy alignment has been established as a potential probe for cosmological information, but the application of…
We propose a nearest neighbor based clustering algorithm that results in a naturally defined hierarchy of clusters. In contrast to the agglomerative and divisive hierarchical clustering algorithms, our approach is not dependent on the…
Clustering analysis identifies samples as groups based on either their mutual closeness or homogeneity. In order to detect clusters in arbitrary shapes, a novel and generic solution based on boundary erosion is proposed. The clusters are…
Graph vertices are often organized into groups that seem to live fairly independently of the rest of the graph, with which they share but a few edges, whereas the relationships between group members are stronger, as shown by the large…
We build upon Ordering Points To Identify Clustering Structure (OPTICS), a hierarchical clustering algorithm well-known to be a robust data-miner, in order to produce Halo-OPTICS, an algorithm designed for the automatic detection and…
A large amount of research on Convolutional Neural Networks has focused on flat Classification in the multi-class domain. In the real world, many problems are naturally expressed as problems of hierarchical classification, in which the…