Related papers: Local Doubling Dimension of Point Sets
In this paper, we consider the following query problem: given two weighted point sets $A$ and $B$ in the Euclidean space $\mathbb{R}^d$, we want to quickly determine that whether their earth mover's distance (EMD) is larger or smaller than…
Density based spatial clustering of points in $\mathbb{R}^n$ has a myriad of applications in a variety of industries. We generalise this problem to the density based clustering of lines in high-dimensional spaces, keeping in mind there…
Many real networks are embedded in space, where in some of them the links length decay as a power law distribution with distance. Indications that such systems can be characterized by the concept of dimension were found recently. Here, we…
In this article we construct a maximal set of kernels for a multi-parameter linear scale-space that allow us to construct trees for classification and recognition of one-dimensional continuous signals similar the Gaussian linear scale-space…
We investigate the problem of finding reverse nearest neighbors efficiently. Although provably good solutions exist for this problem in low or fixed dimensions, to this date the methods proposed in high dimensions are mostly heuristic. We…
Modern datasets are characterized by a large number of features that may conceal complex dependency structures. To deal with this type of data, dimensionality reduction techniques are essential. Numerous dimensionality reduction methods…
Modern datasets often contain high-dimensional features exhibiting complex dependencies. To effectively analyze such data, dimensionality reduction methods rely on estimating the dataset's intrinsic dimension (id) as a measure of its…
We introduce two practical properties of hierarchical clustering methods for (possibly asymmetric) network data: excisiveness and linear scale preservation. The latter enforces imperviousness to change in units of measure whereas the former…
Deep hashing has shown to be a complexity-efficient solution for the Approximate Nearest Neighbor search problem in high dimensional space. Many methods usually build the loss function from pairwise or triplet data points to capture the…
Datasets with non-trivial large scale topology can be hard to embed in low-dimensional Euclidean space with existing dimensionality reduction algorithms. We propose to model topologically complex datasets using vector bundles, in such a way…
Real world-datasets characterized by discrete features are ubiquitous: from categorical surveys to clinical questionnaires, from unweighted networks to DNA sequences. Nevertheless, the most common unsupervised dimensional reduction methods…
We consider the problem of clustering a set of high-dimensional data points into sets of low-dimensional linear subspaces. The number of subspaces, their dimensions, and their orientations are unknown. We propose a simple and low-complexity…
Localization in challenging, natural environments such as forests or woodlands is an important capability for many applications from guiding a robot navigating along a forest trail to monitoring vegetation growth with handheld sensors. In…
An unsupervised, iterative point-set registration algorithm for an unlabeled (i.e. correspondence between points is unknown) N-dimensional Euclidean point-cloud is proposed. It is based on linear least squares, and considers all possible…
Multidimensional scaling is a statistical process that aims to embed high dimensional data into a lower-dimensional space; this process is often used for the purpose of data visualisation. Common multidimensional scaling algorithms tend to…
High dimensional data can have a surprising property: pairs of data points may be easily separated from each other, or even from arbitrary subsets, with high probability using just simple linear classifiers. However, this is more of a rule…
Graph clustering is a fundamental problem that has been extensively studied both in theory and practice. The problem has been defined in several ways in literature and most of them have been proven to be NP-Hard. Due to their high practical…
In this paper, we consider the problem of assessing local clustering in complex networks. Various definitions for this measure have been proposed for the cases of networks having weighted edges, but less attention has been paid to both…
The concept of dimension is essential to grasp the complexity of data. A naive approach to determine the dimension of a dataset is based on the number of attributes. More sophisticated methods derive a notion of intrinsic dimension (ID)…
This paper extends the proof of density of neural networks in the space of continuous (or even measurable) functions on Euclidean spaces to functions on compact sets of probability measures. By doing so the work parallels a more then a…