Related papers: Principal Amalgamation Analysis for Microbiome Dat…

Traditional principal component analysis (PCA) is well known in high-dimensional data analysis, but it requires to express data by a matrix with observations to be continuous. To overcome the limitations, a new method called flexible PCA…

Data augmentation (DA) is a key factor in medical image analysis, such as in prostate cancer (PCa) detection on magnetic resonance images. State-of-the-art computer-aided diagnosis systems still rely on simplistic spatial transformations to…

Scientific studies in the last two decades have established the central role of the microbiome in disease and health. Differential abundance analysis seeks to identify microbial taxa associated with sample groups defined by a factor such as…

The human microbiome plays an important role in human health and disease status. Next generating sequencing technologies allow for quantifying the composition of the human microbiome. Clustering these microbiome data can provide valuable…

Microbiome data are complex in nature, involving high dimensionality, compositionally, zero inflation, and taxonomic hierarchy. Compositional data reside in a simplex that does not admit the standard Euclidean geometry. Most existing…

Recent work has extended the invariance principle for out-of-distribution (OOD) generalization from Euclidean to graph data, where challenges arise due to complex structures and diverse distribution shifts in node attributes and topology.…

Tabular data, widely used in various applications such as industrial control systems, finance, and supply chain, often contains complex interrelationships among its attributes. Data disentanglement seeks to transform such data into latent…

Data augmentation (DA) is indispensable in modern machine learning and deep neural networks. The basic idea of DA is to construct new training data to improve the model's generalization by adding slightly disturbed versions of existing data…

Principal Component Analysis (PCA) is a well known procedure to reduce intrinsic complexity of a dataset, essentially through simplifying the covariance structure or the correlation structure. We introduce a novel algebraic, model-based…

Sparse principal component analysis (sparse PCA) is a widely used technique for dimensionality reduction in multivariate analysis, addressing two key limitations of standard PCA. First, sparse PCA can be implemented in high-dimensional low…

In this paper we analyze approximate methods for undertaking a principal components analysis (PCA) on large data sets. PCA is a classical dimension reduction method that involves the projection of the data onto the subspace spanned by the…

We present a technique to perform dimensionality reduction on data that is subject to uncertainty. Our method is a generalization of traditional principal component analysis (PCA) to multivariate probability distributions. In comparison to…

Dimension reduction techniques usually lose information in the sense that reconstructed data are not identical to the original data. However, we argue that it is possible to have reconstructed data identically distributed as the original…

Matching methods are widely used to reduce confounding effects in observational studies, but conventional approaches often treat all covariates as equally important, which can result in poor performance when covariates differ in their…

Phylogenetic analysis of DNA or other data commonly gives rise to a collection or sample of inferred evolutionary trees. Principal Components Analysis (PCA) cannot be applied directly to collections of trees since the space of evolutionary…

Satellite imagery analysis plays a pivotal role in remote sensing; however, information loss due to cloud cover significantly impedes its application. Although existing deep cloud removal models have achieved notable outcomes, they scarcely…

Despite the rapid development of computational hardware, the treatment of large and high dimensional data sets is still a challenging problem. This paper provides a twofold contribution to the topic. First, we propose a Gaussian Mixture…

There has been a growing acknowledgement of the involvement of the gut microbiome - the collection of microbes that reside in our gut - in regulating our mood and behaviour. This phenomenon is referred to as the microbiome-gut-brain axis.…

The statistical analysis of tree structured data is a new topic in statistics with wide application areas. Some Principal Component Analysis (PCA) ideas were previously developed for binary tree spaces. In this study, we extend these ideas…

In certain fields where compositional data are studied, the compositional components, called parts, can be combined into certain subsets, called amalgamations, that are based on domain knowledge. Furthermore, these subsets can form a…