Related papers: Subspace Determination through Local Intrinsic Dim…

Accurate estimation of Intrinsic Dimensionality (ID) is of crucial importance in many data mining and machine learning tasks, including dimensionality reduction, outlier detection, similarity search and subspace clustering. However, since…

This paper reconsiders common benchmarking approaches to nearest neighbor search. It is shown that the concept of local intrinsic dimensionality (LID) allows to choose query sets of a wide range of difficulty for real-world datasets.…

The local intrinsic dimension (LID) of data is a fundamental quantity in signal processing and learning theory, but quantifying the LID of high-dimensional, complex data has been a historically challenging task. Recent works have discovered…

Intrinsic dimensionality (ID) is one of the most fundamental characteristics of multi-dimensional data point clouds. Knowing ID is crucial to choose the appropriate machine learning approach as well as to understand its behavior and…

Local Intrinsic Dimensionality (LID) has shown strong potential for identifying anomalies and outliers in high-dimensional data across a wide range of real-world applications, including landslide failure detection in granular media. Early…

Robust local feature representations are essential for spatial intelligence tasks such as robot navigation and augmented reality. Establishing reliable correspondences requires descriptors that provide both high discriminative power and…

One of the founding paradigms of machine learning is that a small number of variables is often sufficient to describe high-dimensional data. The minimum number of variables required is called the intrinsic dimension (ID) of the data.…

Most of the existing methods for estimating the local intrinsic dimension of a data distribution do not scale well to high-dimensional data. Many of them rely on a non-parametric nearest neighbors approach which suffers from the curse of…

High-dimensional data commonly lies on low-dimensional submanifolds, and estimating the local intrinsic dimension (LID) of a datum -- i.e. the dimension of the submanifold it belongs to -- is a longstanding problem. LID can be understood as…

The theory of Local Intrinsic Dimensionality (LID) has become a valuable tool for characterizing local complexity within and across data manifolds, supporting a range of data mining and machine learning tasks. Accurate LID estimation…

We consider the problems of classification and intrinsic dimension estimation on image data. A new subspace based classifier is proposed for supervised classification or intrinsic dimension estimation. The distribution of the data in each…

The notion of local intrinsic dimensionality (LID) is an important advancement in data dimensionality analysis, with applications in data mining, machine learning and similarity search problems. Existing distance-based LID estimators were…

The intrinsic dimensionality refers to the ``true'' dimensionality of the data, as opposed to the dimensionality of the data representation. For example, when attributes are highly correlated, the intrinsic dimensionality can be much lower…

The manifold hypothesis asserts that data of interest in high-dimensional ambient spaces, such as image data, lies on unknown low-dimensional submanifolds. Diffusion models (DMs) -- which operate by convolving data with progressively larger…

We introduce a dimension reduction method for visualizing the clustering structure obtained from a finite mixture of Gaussian densities. Information on the dimension reduction subspace is obtained from the variation on group means and,…

Discovering and clustering subspaces in high-dimensional data is a fundamental problem of machine learning with a wide range of applications in data mining, computer vision, and pattern recognition. Earlier methods divided the problem into…

Subspace clustering refers to the task of finding a multi-subspace representation that best fits a collection of points taken from a high-dimensional space. This paper introduces an algorithm inspired by sparse subspace clustering (SSC) [In…

Analyzing large volumes of high-dimensional data is an issue of fundamental importance in data science, molecular simulations and beyond. Several approaches work on the assumption that the important content of a dataset belongs to a…

Local intrinsic dimension (LID) estimation methods have received a lot of attention in recent years thanks to the progress in deep neural networks and generative modeling. In opposition to old non-parametric methods, new methods use…

This paper introduces a new clustering technique, called {\em dimensional clustering}, which clusters each data point by its latent {\em pointwise dimension}, which is a measure of the dimensionality of the data set local to that point.…