Related papers: Ultrametric embedding: application to data fingerp…

The depinning of an elastic line interacting with a quenched disorder is studied for long range interactions, applicable to crack propagation or wetting. An ultrametric distance is introduced instead of the Euclidean distance, allowing for…

'Big' high-dimensional data are commonly analyzed in low-dimensions, after performing a dimensionality-reduction step that inherently distorts the data structure. For the same purpose, clustering methods are also often used. These methods…

Unsupervised machine learning, and in particular data clustering, is a powerful approach for the analysis of datasets and identification of characteristic features occurring throughout a dataset. It is gaining popularity across scientific…

The embedded sensors in widely used smartphones and other wearable devices make the data of human activities more accessible. However, recognizing different human activities from the wearable sensor data remains a challenging research…

Dictionary learning and sparse coding have been widely studied as mechanisms for unsupervised feature learning. Unsupervised learning could bring enormous benefit to the processing of hyperspectral images and to other remote sensing data…

Consider a high-dimensional data set, in which for every data-point there is incomplete information. Each object in the data set represents a real entity, which is described by a point in high-dimensional space. We model the lack of…

This article provides an overview on the statistical modeling of complex data as increasingly encountered in modern data analysis. It is argued that such data can often be described as elements of a metric space that satisfies certain…

Effective representation of data is crucial in various machine learning tasks, as it captures the underlying structure and context of the data. Embeddings have emerged as a powerful technique for data representation, but evaluating their…

How best to quantify the information of an object, whether natural or artifact, is a problem of wide interest. A related problem is the computability of an object. We present practical examples of a new way to address this problem. By…

Metric embedding has become a common technique in the design of algorithms. Its applicability is often dependent on how high the embedding's distortion is. For example, embedding finite metric space into trees may require linear distortion…

A number of topics involving metrics and measures are discussed, including some of the special structure associated with ultrametrics.

We propose a method for the unsupervised clustering of hyperspectral images based on spatially regularized spectral clustering with ultrametric path distances. The proposed method efficiently combines data density and geometry to…

Today, huge amounts of data are being collected with spatial and temporal components from sources such as meteorological, satellite imagery etc. Efficient visualisation as well as discovery of useful knowledge from these datasets is…

We study the problem of supervised learning a metric space under discriminative constraints. Given a universe $X$ and sets ${\cal S}, {\cal D}\subset {X \choose 2}$ of similar and dissimilar pairs, we seek to find a mapping $f:X\to Y$, into…

We study two aspects of information semantics: (i) the collection of all relationships, (ii) tracking and spotting anomaly and change. The first is implemented by endowing all relevant information spaces with a Euclidean metric in a common…

Clustering algorithms are one of the main analytical methods to detect patterns in unlabeled data. Existing clustering methods typically treat samples in a dataset as points in a metric space and compute distances to group together similar…

A classic problem in unsupervised learning and data analysis is to find simpler and easy-to-visualize representations of the data that preserve its essential properties. A widely-used method to preserve the underlying hierarchical structure…

We propose a method to reconstruct and cluster incomplete high-dimensional data lying in a union of low-dimensional subspaces. Exploring the sparse representation model, we jointly estimate the missing data while imposing the intrinsic…

We study the problem of fitting an ultrametric distance to a dissimilarity graph in the context of hierarchical cluster analysis. Standard hierarchical clustering methods are specified procedurally, rather than in terms of the cost function…

Many datasets exhibit a well-defined structure that can be exploited to design faster search tools, but it is not always clear when such acceleration is possible. Here, we introduce a framework for similarity search based on characterizing…