Related papers: Nonlinear Data Integration via Kernel Methods for …

Kernel-based subspace clustering, which addresses the nonlinear structures in data, is an evolving area of research. Despite noteworthy progressions, prevailing methodologies predominantly grapple with limitations relating to (i) the…

Dimensionality reduction is an important step in processing the hyperspectral images (HSI) to overcome the curse of dimensionality problem. Linear dimensionality reduction methods such as Independent component analysis (ICA) and Linear…

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…

Subspace clustering aims to group data points into multiple clusters of which each corresponds to one subspace. Most existing subspace clustering approaches assume that input data lie on linear subspaces. In practice, however, this…

An increasing number of systems are being designed by gathering significant amounts of data and then optimizing the system parameters directly using the obtained data. Often this is done without analyzing the dataset structure. As task…

Linear dimensionality reduction techniques, notably principal component analysis, are widely used in climate data analysis as a means to aid in the interpretation of datasets of high dimensionality. These linear methods may not be…

Multi-source data fusion, in which multiple data sources are jointly analyzed to obtain improved information, has considerable research attention. For the datasets of multiple medical institutions, data confidentiality and…

Principal component analysis (PCA) is widely used for feature extraction and dimensionality reduction, with documented merits in diverse tasks involving high-dimensional data. Standard PCA copes with one dataset at a time, but it is…

Domain specific (dis-)similarity or proximity measures used e.g. in alignment algorithms of sequence data, are popular to analyze complex data objects and to cover domain specific data properties. Without an underlying vector space these…

Contrastive Learning (CL) has shown promising performance in collaborative filtering. The key idea is to generate augmentation-invariant embeddings by maximizing the Mutual Information between different augmented views of the same instance.…

Conventional research attributes the improvements of generalization ability of deep neural networks either to powerful optimizers or the new network design. Different from them, in this paper, we aim to link the generalization ability of a…

The state-of-the-art dimensionality reduction approaches largely rely on complicated optimization procedures. On the other hand, closed-form approaches requiring merely eigen-decomposition do not have enough sophistication and nonlinearity.…

In this paper, we present a kernel subspace clustering method that can handle non-linear models. In contrast to recent kernel subspace clustering methods which use predefined kernels, we propose to learn a low-rank kernel matrix, with which…

Linear dimensionality reduction methods are a cornerstone of analyzing high dimensional data, due to their simple geometric interpretations and typically attractive computational properties. These methods capture many data features of…

High-Dimensional and Incomplete (HDI) data is commonly encountered in big data-related applications like social network services systems, which are concerning the limited interactions among numerous nodes. Knowledge acquisition from HDI…

Methodologies for multidimensionality reduction aim at discovering low-dimensional manifolds where data ranges. Principal Component Analysis (PCA) is very effective if data have linear structure. But fails in identifying a possible…

Because of high dimensionality, correlation among covariates, and noise contained in data, dimension reduction (DR) techniques are often employed to the application of machine learning algorithms. Principal Component Analysis (PCA), Linear…

Integrative analysis of multiple heterogeneous datasets has become standard practice in many research fields, especially in single-cell genomics and medical informatics. Existing approaches oftentimes suffer from limited power in capturing…

We study non-linear data-dimension reduction. We are motivated by the classical linear framework of Principal Component Analysis. In nonlinear case, we introduce instead a new kernel-Principal Component Analysis, manifold and feature space…

Research in modern data-driven dynamical systems is typically focused on the three key challenges of high dimensionality, unknown dynamics, and nonlinearity. The dynamic mode decomposition (DMD) has emerged as a cornerstone for modeling…