Related papers: On dimension folding of matrix- or array-valued st…
Low-dimensional embeddings for data from disparate sources play critical roles in multi-modal machine learning, multimedia information retrieval, and bioinformatics. In this paper, we propose a supervised dimensionality reduction method…
Sufficient dimension reduction is a powerful tool to extract core information hidden in the high-dimensional data and has potentially many important applications in machine learning tasks. However, the existing nonlinear sufficient…
Manifold learning (ML), known also as non-linear dimension reduction, is a set of methods to find the low dimensional structure of data. Dimension reduction for large, high dimensional data is not merely a way to reduce the data; the new…
In this paper, we propose a dimension reduction method specifically designed for tensor-structured feature data in deep neural networks. The method is implemented as a hidden layer, called the TensorProjection layer, which transforms input…
We present an incremental, scalable and efficient dimension reduction technique for tensors that is based on sparse random linear coding. Data is stored in a compactified representation with fixed size, which makes memory requirements low…
An analysis of high-dimensional data can offer a detailed description of a system but is often challenged by the curse of dimensionality. General dimensionality reduction techniques can alleviate such difficulty by extracting a few…
Molecular simulations produce very high-dimensional data-sets with millions of data points. As analysis methods are often unable to cope with so many dimensions, it is common to use dimensionality reduction and clustering methods to reach a…
We propose a novel linear discriminant analysis approach for the classification of high-dimensional matrix-valued data that commonly arises from imaging studies. Motivated by the equivalence of the conventional linear discriminant analysis…
Dimension reduction provides a useful tool for analyzing high dimensional data. The recently developed \textit{Envelope} method is a parsimonious version of the classical multivariate regression model through identifying a minimal reducing…
Modern technology often generates data with complex structures in which both response and explanatory variables are matrix-valued. Existing methods in the literature are able to tackle matrix-valued predictors but are rather limited for…
Dimensionality reduction (DR) algorithms compress high-dimensional data into a lower dimensional representation while preserving important features of the data. DR is a critical step in many analysis pipelines as it enables visualisation,…
Despite the prominence of neural network approaches in the field of recommender systems, simple methods such as matrix factorization with quadratic loss are still used in industry for several reasons. These models can be trained with…
The statistical problem of estimating the effective dimension-reduction (EDR) subspace in the multi-index regression model with deterministic design and additive noise is considered. A new procedure for recovering the directions of the EDR…
Multidimensional scaling is an important dimension reduction tool in statistics and machine learning. Yet few theoretical results characterizing its statistical performance exist, not to mention any in high dimensions. By considering a…
Considering the case where the response variable is a categorical variable and the predictor is a random function, two novel functional sufficient dimensional reduction (FSDR) methods are proposed based on mutual information and square loss…
The application of standard sufficient dimension reduction methods for reducing the dimension space of predictors without losing regression information requires inverting the covariance matrix of the predictors. This has posed a number of…
An envelope is a targeted dimension reduction subspace for simultaneously achieving dimension reduction and improving parameter estimation efficiency. While many envelope methods have been proposed in recent years, all envelope methods…
A new deep learning-based electroencephalography (EEG) signal analysis framework is proposed. While deep neural networks, specifically convolutional neural networks (CNNs), have gained remarkable attention recently, they still suffer from…
It is a standard assumption that datasets in high dimension have an internal structure which means that they in fact lie on, or near, subsets of a lower dimension. In many instances it is important to understand the real dimension of the…
Dimension reduction plays a pivotal role in analysing high-dimensional data. However, observations with missing values present serious difficulties in directly applying standard dimension reduction techniques. As a large number of dimension…