Related papers: Tangent phylogenetic PCA
We propose a new approach to analyze data that naturally lie on manifolds. We focus on a special class of manifolds, called direct product manifolds, whose intrinsic dimension could be very high. Our method finds a low-dimensional…
Phylogenetic Diversity (PD) is a prominent quantitative measure of the biodiversity of a collection of present-day species (taxa). This measure is based on the evolutionary distance among the species in the collection. Loosely speaking, if…
Quantum simulations constructing probability tensors of biological multi-taxa in phylogenetic trees are proposed, in terms of positive trace preserving maps, describing evolving systems of quantum walks with multiple walkers. Basic…
Conventional domain adaptation typically transfers knowledge from a source domain to a stationary target domain. However, in many real-world cases, target data usually emerge sequentially and have continuously evolving distributions.…
Principal component analysis (PCA) is a longstanding and well-studied approach for dimension reduction. It rests upon the assumption that the underlying signal in the data has low rank, and thus can be well-summarized using a small number…
Principal component analysis (PCA) is a well-known linear dimension-reduction method that has been widely used in data analysis and modeling. It is an unsupervised learning technique that identifies a suitable linear subspace for the input…
Principal component analysis (PCA) is a classical and ubiquitous method for reducing data dimensionality, but it is suboptimal for heterogeneous data that are increasingly common in modern applications. PCA treats all samples uniformly so…
In this paper, we propose a novel approach named by Discriminative Principal Component Analysis which is abbreviated as Discriminative PCA in order to enhance separability of PCA by Linear Discriminant Analysis (LDA). The proposed method…
Sparse principal component analysis (PCA) and sparse canonical correlation analysis (CCA) are two essential techniques from high-dimensional statistics and machine learning for analyzing large-scale data. Both problems can be formulated as…
Even with the rise in popularity of over-parameterized models, simple dimensionality reduction and clustering methods, such as PCA and k-means, are still routinely used in an amazing variety of settings. A primary reason is the combination…
Many applications, such as photon-limited imaging and genomics, involve large datasets with noisy entries from exponential family distributions. It is of interest to estimate the covariance structure and principal components of the…
Data analysis often requires methods that are invariant with respect to specific transformations, such as rotations in case of images or shifts in case of images and time series. While principal component analysis (PCA) is a widely-used…
This paper develops a novel method to estimate a latent factor model for a large target panel with missing observations by optimally using the information from auxiliary panel data sets. We refer to our estimator as target-PCA. Transfer…
Phylogenetic comparative methods are new in our field and are shrouded, for most linguists, in at least a little mystery. Yet the path that led to their discovery in comparative biology is so similar to the methodological history of…
Data integration is the problem of combining multiple data groups (studies, cohorts) and/or multiple data views (variables, features). This task is becoming increasingly important in many disciplines due to the prevalence of large and…
We propose kernel PCA as a method for analyzing the dependence structure of multivariate extremes and demonstrate that it can be a powerful tool for clustering and dimension reduction. Our work provides some theoretical insight into the…
We consider multi-class classification problems for high dimensional data. Following the idea of reduced-rank linear discriminant analysis (LDA), we introduce a new dimension reduction tool with a flavor of supervised principal component…
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…
Canonical correlation analysis (CCA) is a standard tool for studying associations between two data sources; however, it is not designed for data with count or proportion measurement types. In addition, while CCA uncovers common signals, it…
Despite the fact that they do not consider the temporal nature of data, classic dimensionality reduction techniques, such as PCA, are widely applied to time series data. In this paper, we introduce a factor decomposition specific for time…