Related papers: Order-Preserving Dimension Reduction for Multimoda…

High-dimensional vector embeddings are widely used in retrieval systems, but they often suffer from noise, the curse of dimensionality, and slow runtime. However, dimensionality reduction (DR) is rarely applied due to its tendency to…

Dimensionality reduction is a topic of recent interest. In this paper, we present the classification constrained dimensionality reduction (CCDR) algorithm to account for label information. The algorithm can account for multiple classes as…

Metric embeddings traditionally study how to map $n$ items to a target metric space such that distance lengths are not heavily distorted; but what if we only care to preserve the relative order of the distances (and not their length)? In…

Image ranking is to rank images based on some known ranked images. In this paper, we propose an improved linear ordinal distance metric learning approach based on the linear distance metric learning model. By decomposing the distance metric…

Dimensionality reduction (DR) on the manifold includes effective methods which project the data from an implicit relational space onto a vectorial space. Regardless of the achievements in this area, these algorithms suffer from the lack of…

A $k$-nearest neighbor ($k$NN) query determines the $k$ nearest points, using distance metrics, from a specific location. An all $k$-nearest neighbor (A$k$NN) query constitutes a variation of a $k$NN query and retrieves the $k$ nearest…

Ordinal embedding aims at finding a low dimensional representation of objects from a set of constraints of the form "item $j$ is closer to item $i$ than item $k$". Typically, each object is mapped onto a point vector in a low dimensional…

Dimensionality reduction methods are unsupervised approaches which learn low-dimensional spaces where some properties of the initial space, typically the notion of "neighborhood", are preserved. Such methods usually require propagation on…

Dense high dimensional vectors are becoming increasingly vital in fields such as computer vision, machine learning, and large language models (LLMs), serving as standard representations for multimodal data. Now the dimensionality of these…

With the development of feature extraction technique, one sample always can be represented by multiple features which locate in high-dimensional space. Multiple features can re ect various perspectives of one same sample, so there must be…

Metric learning methods for dimensionality reduction in combination with k-Nearest Neighbors (kNN) have been extensively deployed in many classification, data embedding, and information retrieval applications. However, most of these…

Moment-based distributionally robust optimization (DRO) provides an optimization framework to integrate statistical information with traditional optimization approaches. Under this framework, one assumes that the underlying joint…

One of the goals of NASA funded project at IBM T. J. Watson Research Center was to build an index for similarity searching satellite images, which were characterized by high-dimensional feature image texture vectors. Reviewed is our effort…

Deep metric learning (DML) aims to automatically construct task-specific distances or similarities of data, resulting in a low-dimensional representation. Several significant metric-learning methods have been proposed. Nonetheless, no…

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…

The goal of image ordinal estimation is to estimate the ordinal label of a given image with a convolutional neural network. Existing methods are mainly based on ordinal regression and particularly focus on modeling the ordinal mapping from…

While high-dimensional embedding vectors are being increasingly employed in various tasks like Retrieval-Augmented Generation and Recommendation Systems, popular dimensionality reduction (DR) methods such as PCA and UMAP have rarely been…

The objective of ordinal embedding is to find a Euclidean representation of a set of abstract items, using only answers to triplet comparisons of the form "Is item $i$ closer to the item $j$ or item $k$?". In recent years, numerous…

Metric embeddings are a widely used method in algorithm design, where generally a ``complex'' metric is embedded into a simpler, lower-dimensional one. Historically, the theoretical computer science community has focused on bi-Lipschitz…

Quantum computing is a promising candidate for accelerating machine learning tasks. Limited by the control accuracy of current quantum hardware, reducing the consumption of quantum resources is the key to achieving quantum advantage. Here,…