Related papers: Breaking the curse of dimensionality with Isolatio…

The curse of dimensionality in the realm of association rules is twofold. Firstly, we have the well known exponential increase in computational complexity with increasing item set size. Secondly, there is a \emph{related curse} concerned…

The curse of dimensionality has remained a challenge for a wide variety of algorithms in data mining, clustering, classification and privacy. Recently, it was shown that an increasing dimensionality makes the data resistant to effective…

Large scale online kernel learning aims to build an efficient and scalable kernel-based predictive model incrementally from a sequence of potentially infinite data points. A current key approach focuses on ways to produce an approximate…

Integration is affected by the curse of dimensionality and quickly becomes intractable as the dimensionality of the problem grows. We propose a randomized algorithm that, with high probability, gives a constant-factor approximation of a…

Real-world datasets are often of high dimension and effected by the curse of dimensionality. This hinders their comprehensibility and interpretability. To reduce the complexity feature selection aims to identify features that are crucial to…

We consider the problem of estimating a structured multivariate density, subject to Markov conditions implied by an undirected graph. In the worst case, without Markovian assumptions, this problem suffers from the curse of dimensionality.…

As annotations of data can be scarce in large-scale practical problems, leveraging unlabelled examples is one of the most important aspects of machine learning. This is the aim of semi-supervised learning. To benefit from the access to…

The characteristics of data like distribution and heterogeneity, become more complex and counterintuitive as dimensionality increases. This phenomenon is known as curse of dimensionality, where common patterns and relationships (e.g.,…

In this work we study the validity of the so-called curse of dimensionality for indexing of databases for similarity search. We perform an asymptotic analysis, with a test model based on a sequence of metric spaces $(\Omega_d)$ from which…

Modern vector databases enable efficient retrieval over high-dimensional neural embeddings, powering applications from web search to retrieval-augmented generation. However, classical theory predicts such tasks should suffer from the curse…

Kernelized Stein discrepancy (KSD), though being extensively used in goodness-of-fit tests and model learning, suffers from the curse-of-dimensionality. We address this issue by proposing the sliced Stein discrepancy and its scalable and…

We offer a theoretical validation of the curse of dimensionality in the pivot-based indexing of datasets for similarity search, by proving, in the framework of statistical learning, that in high dimensions no pivot-based indexing scheme can…

Artificial intelligence, particularly the subfield of machine learning, has seen a paradigm shift towards data-driven models that learn from and adapt to data. This has resulted in unprecedented advancements in various domains such as…

Two-step approaches combining pre-trained large language model embeddings and anomaly detectors demonstrate strong performance in text anomaly detection by leveraging rich semantic representations. However, high-dimensional dense embeddings…

We suggest that the curse of dimensionality affecting the similarity-based search in large datasets is a manifestation of the phenomenon of concentration of measure on high-dimensional structures. We prove that, under certain geometric…

This paper presents a new insight into improving the performance of Stochastic Neighbour Embedding (t-SNE) by using Isolation kernel instead of Gaussian kernel. Isolation kernel outperforms Gaussian kernel in two aspects. First, the use of…

In high-dimensional data analysis the curse of dimensionality reasons that points tend to be far away from the center of the distribution and on the edge of high-dimensional space. Contrary to this, is that projected data tends to clump at…

Spectral clustering and diffusion maps are celebrated dimensionality reduction algorithms built on eigen-elements related to the diffusive structure of the data. The core of these procedures is the approximation of a Laplacian through a…

The failure of the Euclidean norm to reliably distinguish between nearby and distant points in high dimensional space is well-known. This phenomenon of distance concentration manifests in a variety of data distributions, with iid or…

A recent proposal of data dependent similarity called Isolation Kernel/Similarity has enabled SVM to produce better classification accuracy. We identify shortcomings of using a tree method to implement Isolation Similarity; and propose a…