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Methodologies for multidimensionality reduction aim at discovering low-dimensional manifolds where data ranges. Principal Component Analysis (PCA) is very effective if data have linear structure. But fails in identifying a possible…
STEM XEDS spectrum images can be drastically denoised by application of the principal component analysis (PCA). This paper looks inside the PCA workflow step by step on an example of a complex semiconductor structure consisting of a number…
Unsupervised learning makes manifest the underlying structure of data without curated training and specific problem definitions. However, the inference of relationships between data points is frustrated by the `curse of dimensionality' in…
Despite the advances of deep learning in specific tasks using images, the principled assessment of image fidelity and similarity is still a critical ability to develop. As it has been shown that Mean Squared Error (MSE) is insufficient for…
A general framework for principal component analysis (PCA) in the presence of heteroskedastic noise is introduced. We propose an algorithm called HeteroPCA, which involves iteratively imputing the diagonal entries of the sample covariance…
Principal manifolds are defined as lines or surfaces passing through ``the middle'' of data distribution. Linear principal manifolds (Principal Components Analysis) are routinely used for dimension reduction, noise filtering and data…
High-fidelity 3D anatomical reconstruction is a prerequisite for downstream clinical tasks such as preoperative planning, radiotherapy target delineation, and orthopedic implant design. We present Med-PU, a knowledge-driven framework that…
Principle Component Analysis PCA is a classical feature extraction and data representation technique widely used in pattern recognition. It is one of the most successful techniques in face recognition. But it has drawback of high…
Surface normal integration is a fundamental problem in computer vision, dealing with the objective of reconstructing a surface from its corresponding normal map. Existing approaches require an iterative global optimization to jointly…
Machine learning (ML) methods have proved to be a very successful tool in physical sciences, especially when applied to experimental data analysis. Artificial intelligence is particularly good at recognizing patterns in high dimensional…
When the dimension of data is comparable to or larger than the number of data samples, Principal Components Analysis (PCA) may exhibit problematic high-dimensional noise. In this work, we propose an Empirical Bayes PCA method that reduces…
The concept of quantum correlation matrix for observables leads to the application of the PCA (Principal Component Analysis) also for quantum system in Hilbert space. It is shown that, in the case of a 2x2 spin system where the observables…
Digital analysis of mammographic images is a complementary tool to clinical evaluation, commonly used to identify tumors and/or microcalcifications in mammograms. Recent mammographic equipment, can automatically classify them using this…
Intraoperative observation of tissue internal structure is often difficult. Hence, real-time soft tissue deformation is essential for the localization of tumor and other internal structures. We propose a method to simulate the internal…
The high-dimensional feature space of the hyperspectral imagery poses major challenges to the processing and analysis of the hyperspectral data sets. In such a case, dimensionality reduction is necessary to decrease the computational…
High-dimensional image data often require dimensionality reduction before further analysis. This paper provides a purely analytical comparison of two linear techniques-Principal Component Analysis (PCA) and Singular Value Decomposition…
Generalization of time series prediction remains an important open issue in machine learning, wherein earlier methods have either large generalization error or local minima. We develop an analytically solvable, unsupervised learning scheme…
We discuss the problem of estimating the number of principal components in Principal Com- ponents Analysis (PCA). Despite of the importance of the problem and the multitude of solutions proposed in the literature, it comes as a surprise…
Realistic microscale domains are an essential step towards making modern multiscale simulations more applicable to computational materials engineering. For this purpose, 3D computed tomography scans can be very expensive or technically…
This paper reviews the current state-of-the-art in the simulation of the mechanical behavior of polycrystalline materials by means of computational homogenization. The key ingredients of this modelling strategy are presented in detail…