Related papers: A Survey: Potential Dimensionality Reduction Metho…
Data reconciliation (DR) and Principal Component Analysis (PCA) are two popular data analysis techniques in process industries. Data reconciliation is used to obtain accurate and consistent estimates of variables and parameters from…
Capturing patterns of variation present in a dataset is important in exploratory data analysis and unsupervised learning. Contrastive dimension reduction methods, such as contrastive principal component analysis (cPCA), find patterns unique…
Principal Component Analysis (PCA) is a ubiquitous tool with many applications in machine learning including feature construction, subspace embedding, and outlier detection. In this paper, we present an algorithm for computing the top…
Principal component analysis (PCA) is a widely used dimension reduction technique in machine learning and multivariate statistics. To improve the interpretability of PCA, various approaches to obtain sparse principal direction loadings have…
One of the central issues of several machine learning applications on real data is the choice of the input features. Ideally, the designer should select only the relevant, non-redundant features to preserve the complete information…
We propose MNPCA, a novel non-linear generalization of (2D)$^2${PCA}, a classical linear method for the simultaneous dimension reduction of both rows and columns of a set of matrix-valued data. MNPCA is based on optimizing over separate…
Dimensionality reduction (DR) methods are commonly used for analyzing and visualizing multidimensional data. However, when data is a live streaming feed, conventional DR methods cannot be directly used because of their computational…
Data dimension reduction (DDR) is all about mapping data from high dimensions to low dimensions, various techniques of DDR are being used for image dimension reduction like Random Projections, Principal Component Analysis (PCA), the…
Poor scaling of dynamics simulations with number of dimensions is currently a major limiting factor in the simulation of photochemical processes. In this work, we investigate ways to reduce the dimensionality of many-atom systems with a…
Revisiting PCA for Time Series Reduction in Temporal Dimension; Jiaxin Gao, Wenbo Hu, Yuntian Chen; Deep learning has significantly advanced time series analysis (TSA), enabling the extraction of complex patterns for tasks like…
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,…
Many statistical estimation techniques for high-dimensional or functional data are based on a preliminary dimension reduction step, which consists in projecting the sample $\bX_1, \hdots, \bX_n$ onto the first $D$ eigenvectors of the…
Scalability of statistical estimators is of increasing importance in modern applications and dimension reduction is often used to extract relevant information from data. A variety of popular dimension reduction approaches can be framed as…
Dimensionality reduction is critical across various domains of science including neuroscience. Probabilistic Principal Component Analysis (PPCA) is a prominent dimensionality reduction method that provides a probabilistic approach unlike…
Dimensionality reduction is an effective method for learning high-dimensional data, which can provide better understanding of decision boundaries in human-readable low-dimensional subspace. Linear methods, such as principal component…
Principal components analysis (PCA) is a classical method for the reduction of dimensionality of data in the form of n observations (or cases) of a vector with p variables. For a simple model of factor analysis type, it is proved that…
Principal Component Analysis (PCA) is a classical method for reducing the dimensionality of data by projecting them onto a subspace that captures most of their variation. Effective use of PCA in modern applications requires understanding…
Mining useful clusters from high dimensional data has received significant attention of the computer vision and pattern recognition community in the recent years. Linear and non-linear dimensionality reduction has played an important role…
Sequential or online dimensional reduction is of interests due to the explosion of streaming data based applications and the requirement of adaptive statistical modeling, in many emerging fields, such as the modeling of energy end-use…
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…