Related papers: An Experimental Study of Dimension Reduction Metho…
Predictive modeling from high-dimensional genomic data is often preceded by a dimension reduction step, such as principal components analysis (PCA). However, the application of PCA is not straightforward for multi-source data, wherein…
This paper proposes new ANOVA-based approximations of functions and emulators of high-dimensional models using either available derivatives or local stochastic evaluations of such models. Our approach makes use of sensitivity indices to…
We present local discriminative Gaussian (LDG) dimensionality reduction, a supervised dimensionality reduction technique for classification. The LDG objective function is an approximation to the leave-one-out training error of a local…
We consider reduction of dimension for nonlinear dynamical systems. We demonstrate that in some cases, one can reduce a nonlinear system of equations into a single equation for one of the state variables, and this can be useful for…
Establishing a low-dimensional representation of the data leads to efficient data learning strategies. In many cases, the reduced dimension needs to be explicitly stated and estimated from the data. We explore the estimation of dimension in…
Traditional machine learning assumes that training and test sets are derived from the same distribution; however, this assumption does not always hold in practical applications. This distribution disparity can lead to severe performance…
The growing number of dimensionality reduction methods available for data visualization has recently inspired the development of quality assessment measures, in order to evaluate the resulting low-dimensional representation independently…
Conventional unsupervised domain adaptation (UDA) studies the knowledge transfer between a limited number of domains. This neglects the more practical scenario where data are distributed in numerous different domains in the real world. The…
Modeling strong gravitational lenses is computationally expensive for the complex data from modern and next-generation cosmic surveys. Deep learning has emerged as a promising approach for finding lenses and predicting lensing parameters,…
This paper studies the dimension effect of the linear discriminant analysis (LDA) and the regularized linear discriminant analysis (RLDA) classifiers for large dimensional data where the observation dimension $p$ is of the same order as the…
Many engineering processes can be accurately modelled using partial differential equations (PDEs), but high dimensionality and non-convexity of the resulting systems pose limitations on their efficient optimisation. In this work, a model…
In many classification problems, we want a classifier that is robust to a range of non-semantic transformations. For example, a human can identify a dog in a picture regardless of the orientation and pose in which it appears. There is…
Dimensional reduction~(DR) maps high-dimensional data into a lower dimensions latent space with minimized defined optimization objectives. The DR method usually falls into feature selection~(FS) and feature projection~(FP). FS focuses on…
Retrieval-Augmented Generation (RAG) has emerged as a powerful paradigm for grounding large language models in external knowledge sources, improving the precision of agents responses. However, high-dimensional language model embeddings,…
Dimensionality reduction has become an important research topic as demand for interpreting high-dimensional datasets has been increasing rapidly in recent years. There have been many dimensionality reduction methods with good performance in…
The current study proposes a dimension reduction method, stepwise support vector machine (SVM), to reduce the dimensions of large p small n datasets. The proposed method is compared with other dimension reduction methods, namely, the…
Dimension reduction is the process of embedding high-dimensional data into a lower dimensional space to facilitate its analysis. In the Euclidean setting, one fundamental technique for dimension reduction is to apply a random linear map to…
Linear discriminant analysis (LDA) is a typical method for classification problems with large dimensions and small samples. There are various types of LDA methods that are based on the different types of estimators for the covariance…
We present a novel approach for the construction of ensemble classifiers based on dimensionality reduction. Dimensionality reduction methods represent datasets using a small number of attributes while preserving the information conveyed by…
Multispectral imaging is an important technique for improving the readability of written or printed text where the letters have faded, either due to deliberate erasing or simply due to the ravages of time. Often the text can be read simply…