Related papers: spd-metrics-id: A Python Package for SPD-Aware Dis…
Domain specific (dis-)similarity or proximity measures used e.g. in alignment algorithms of sequence data, are popular to analyze complex data objects and to cover domain specific data properties. Without an underlying vector space these…
Latent fingerprint matching is a daunting task, primarily due to the poor quality of latent fingerprints. In this study, we propose a deep-learning based dense minutia descriptor (DMD) for latent fingerprint matching. A DMD is obtained by…
Classification in the sense of similarity is an important issue. In this paper, we study similarity classification in Topological Data Analysis. We define a pseudometric $d_{S}^{(p)}$ to measure the distance between barcodes generated by…
Similarity search is an important problem in information retrieval. This similarity is based on a distance. Symbolic representation of time series has attracted many researchers recently, since it reduces the dimensionality of these high…
Synthetic data are an attractive concept to enable privacy in data sharing. A fundamental question is how similar the privacy-preserving synthetic data are compared to the true data. Using metric privacy, an effective generalization of…
Independent parallel q-ary symmetric channels are a suitable transmission model for several applications. The proposed weighted-Hamming metric is tailored to this setting and enables optimal decoding performance. We show that some…
This paper presents evomap, a Python package for dynamic mapping. Mapping methods are widely used across disciplines to visualize relationships among objects as spatial representations, or maps. However, most existing statistical software…
We introduce a new distance-preserving compact representation of multi-dimensional point-sets. Given $n$ points in a $d$-dimensional space where each coordinate is represented using $B$ bits (i.e., $dB$ bits per point), it produces a…
We propose a novel measure of statistical depth, the metric spatial depth, for data residing in an arbitrary metric space. The measure assigns high (low) values for points located near (far away from) the bulk of the data distribution,…
Spatial approximations have been traditionally used in spatial databases to accelerate the processing of complex geometric operations. However, approximations are typically only used in a first filtering step to determine a set of candidate…
The sliced Wasserstein metric compares probability measures on $\mathbb{R}^d$ by taking averages of the Wasserstein distances between projections of the measures to lines. The distance has found a range of applications in statistics and…
This paper presents hep-aid, a modular Python library conceived for utilising, implementing, and developing parameter scan algorithms. Originally devised for sample-efficient, multi-objective active search approaches in computationally…
We present Safe Surgery by Identifying Pushouts (SSIP), an open-source lightweight Python package for automating surgery between qubit CSS codes. SSIP is flexible: it is capable of performing both external surgery, that is surgery between…
Metrics in Grassmannians, or distances between subspaces of same dimension, have many uses, and extending them to the Total Grassmannian of subspaces of different dimensions is an important problem, as usual extensions lack good properties…
Algebraic topology methods have recently played an important role for statistical analysis with complicated geometric structured data such as shapes, linked twist maps, and material data. Among them, \textit{persistent homology} is a…
Sphere decoding (SD) of polar codes is an efficient method to achieve the error performance of maximum likelihood (ML) decoding. But the complexity of the conventional sphere decoder is still high, where the candidates in a target sphere…
In this paper, we present new results on the Riemannian geometry of symmetric positive semi-definite (SPSD) matrices. First, based on an existing approximation of the geodesic path, we introduce approximations of the logarithmic and…
We introduce a new geometric framework for the set of symmetric positive-definite (SPD) matrices, aimed to characterize deformations of SPD matrices by individual scaling of eigenvalues and rotation of eigenvectors of the SPD matrices. To…
Surface metrology is the area of engineering concerned with the study of geometric variation in surfaces. This paper explores the potential for modern techniques from spatial statistics to act as generative models for geometric variation in…
Distance metric learning (DML) is an important task that has found applications in many domains. The high computational cost of DML arises from the large number of variables to be determined and the constraint that a distance metric has to…