Related papers: Multidimensional Scaling for Interval Data: INTERS…

Irregular features disrupt the desired classification. In this paper, we consider aggressively modifying scales of features in the original space according to the label information to form well-separated clusters in low-dimensional space.…

Generalized dimensions of multifractal measures are usually seen as static objects, related to the scaling properties of suitable partition functions, or moments of measures of cells. When these measures are invariant for the flow of a…

The kernel matrix used in kernel methods encodes all the information required for solving complex nonlinear problems defined on data representations in the input space using simple, but implicitly defined, solutions. Spectral analysis on…

Dimensionality reduction is often used as an initial step in data exploration, either as preprocessing for classification or regression or for visualization. Most dimensionality reduction techniques to date are unsupervised; they do not…

In his article "Powerlist: A Structure for Parallel Recursion" Jayadev Misra wrote: "Many data parallel algorithms Fast Fourier Transform, Batcher's sorting schemes and prefix sum -exhibit recursive structure. We propose a data structure,…

Manifold learning is used for dimensionality reduction, with the goal of finding a projection subspace to increase and decrease the inter- and intraclass variances, respectively. However, a bottleneck for subspace learning methods often…

In the mean field (or random link) model there are $n$ points and inter-point distances are independent random variables. For $0 < \ell < \infty$ and in the $n \to \infty$ limit, let $\delta(\ell) = 1/n \times$ (maximum number of steps in a…

Dimension reduction is often the first step in statistical modeling or prediction of multivariate spatial data. However, most existing dimension reduction techniques do not account for the spatial correlation between observations and do not…

Constant rescaling of a Riemannian metric appears in many computational settings, often through a global scale parameter that is introduced either explicitly or implicitly. Although this operation is elementary, its consequences are not…

Any traditional classification problem in general involves modelling individual classes and in turn classification by evaluating the similarity of the test set with the modelled classes. In this paper, we introduce another approach that…

Data types that lie in metric spaces but not in vector spaces are difficult to use within the usual regression setting, either as the response and/or a predictor. We represent the information in these variables using distance matrices which…

For a random variable $X$, we are interested in the blind extraction of its finest mutual independence pattern $\mu ( X )$. We introduce a specific kind of independence that we call dichotomic. If $\Delta ( X )$ stands for the set of all…

We present a new image scaling method both for downscaling and upscaling, running with any scale factor or desired size. The resized image is achieved by sampling a bivariate polynomial which globally interpolates the data at the new scale.…

Multimodal representation learning, exemplified by multimodal contrastive learning (MMCL) using image-text pairs, aims to learn powerful representations by aligning cues across modalities. This approach relies on the core assumption that…

The distance standard deviation, which arises in distance correlation analysis of multivariate data, is studied as a measure of spread. The asymptotic distribution of the empirical distance standard deviation is derived under the assumption…

Deep ResNets are recognized for achieving state-of-the-art results in complex machine learning tasks. However, the remarkable performance of these architectures relies on a training procedure that needs to be carefully crafted to avoid…

Multi-label classification is an important learning problem with many applications. In this work, we propose a principled similarity-based approach for multi-label learning called SML. We also introduce a similarity-based approach for…

There has been a great effort to transfer linear discriminant techniques that operate on vector data to high-order data, generally referred to as Multilinear Discriminant Analysis (MDA) techniques. Many existing works focus on maximizing…

The multimodal relevance metric is usually borrowed from the embedding ability of pretrained contrastive learning models for bimodal data, which is used to evaluate the correlation between cross-modal data (e.g., CLIP). However, the…

In cluster analysis, a common first step is to scale the data aiming to better partition them into clusters. Even though many different techniques have throughout many years been introduced to this end, it is probably fair to say that the…