Related papers: On pattern classification with weighted dimensions

For any finite point set in $D$-dimensional space equipped with the 1-norm, we present random linear embeddings to $k$-dimensional space, with a new metric, having the following properties. For any pair of points from the point set that are…

In general, the clustering problem is NP-hard, and global optimality cannot be established for non-trivial instances. For high-dimensional data, distance-based methods for clustering or classification face an additional difficulty, the…

Distance queries are a basic tool in data analysis. They are used for detection and localization of change for the purpose of anomaly detection, monitoring, or planning. Distance queries are particularly useful when data sets such as…

We propose an iterative scheme for feature-based positioning using a new weighted dissimilarity measure with the goal of reducing the impact of large errors among the measured or modeled features. The weights are computed from the…

In the field of node representation learning the task of interpreting latent dimensions has become a prominent, well-studied research topic. The contribution of this work focuses on appraising the interpretability of another…

This work presents the design, implementation and validation of learning techniques based on the kNN scheme for gesture detection in prosthetic control. To cope with high computational demands in instance-based prediction, methods of…

Generalization is a central aspect of learning theory. Here, we propose a framework that explores an auxiliary task-dependent notion of generalization, and attempts to quantitatively answer the following question: given two sets of patterns…

Dimensionality is a major concern in analyzing large data sets. Some well known dimension reduction methods are for example principal component analysis (PCA), invariant coordinate selection (ICS), sliced inverse regression (SIR), sliced…

Complex, high-dimensional data is ubiquitous across many scientific disciplines, including machine learning, biology, and the social sciences. One of the primary methods of visualizing these datasets is with two-dimensional scatter plots…

Multidimensional scaling is an important dimension reduction tool in statistics and machine learning. Yet few theoretical results characterizing its statistical performance exist, not to mention any in high dimensions. By considering a…

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…

Feature representation is an important aspect of remote-sensing based image classification. While deep convolutional neural networks are able to effectively amalgamate information, large numbers of parameters often make learned features…

Three important properties of a classification machinery are: (i) the system preserves the core information of the input data; (ii) the training examples convey information about unseen data; and (iii) the system is able to treat…

Data visualization and dimension reduction for regression between a general metric space-valued response and Euclidean predictors is proposed. Current Fr\'ech\'et dimension reduction methods require that the response metric space be…

We propose a novel algorithm for the task of supervised discriminative distance learning by nonlinearly embedding vectors into a low dimensional Euclidean space. We work in the challenging setting where supervision is with constraints on…

In the context of kernel methods, the similarity between data points is encoded by the kernel function which is often defined thanks to the Euclidean distance, a common example being the squared exponential kernel. Recently, other distances…

Safe use of Deep Neural Networks (DNNs) requires careful testing. However, deployed models are often trained further to improve in performance. As rigorous testing and evaluation is expensive, triggers are in need to determine the degree of…

Existing theories on deep nonparametric regression have shown that when the input data lie on a low-dimensional manifold, deep neural networks can adapt to the intrinsic data structures. In real world applications, such an assumption of…

This paper examines the quantization methods used in large-scale data analysis models and their hyperparameter choices. The recent surge in data analysis scale has significantly increased computational resource requirements. To address…

Distances are pervasive in machine learning. They serve as similarity measures, loss functions, and learning targets; it is said that a good distance measure solves a task. When defining distances, the triangle inequality has proven to be a…