Related papers: Comparison of PCA with ICA from data distribution …
We present an adaptation of the standard Grassberger-Proccacia (GP) algorithm for estimating the Correlation Dimension of a time series in a non subjective manner. The validity and accuracy of this approach is tested using different types…
The particle-in-cell numerical method of plasma physics balances a trade-off between computational cost and intrinsic noise. Inference on data produced by these simulations generally consists of binning the data to recover the particle…
In several application domains, high-dimensional observations are collected and then analysed in search for naturally occurring data clusters which might provide further insights about the nature of the problem. In this paper we describe a…
This article establishes a new and comprehensive estimation and inference theory for principal component analysis (PCA) under the weak factor model that allow for cross-sectional dependent idiosyncratic components under the nearly minimal…
The article discusses selected problems related to both principal component analysis (PCA) and factor analysis (FA). In particular, both types of analysis were compared. A vector interpretation for both PCA and FA has also been proposed.…
Differences between computer simulation of dynamical systems and laboratory experiments are common in teaching and research in engineering. Normally, numerical inaccuracy and the non-ideal behaviour of the devices involved in the experiment…
We seek to narrow the gap between parametric and nonparametric modelling of stationary time series processes. The approach is inspired by recent advances in focused inference and model selection techniques. The paper generalises and extends…
We consider the relative abilities and limitations of computationally efficient algorithms for learning in the presence of noise, under two well-studied and challenging adversarial noise models for learning Boolean functions: malicious…
This paper is concerned by the statistical analysis of data sets whose elements are random histograms. For the purpose of learning principal modes of variation from such data, we consider the issue of computing the PCA of histograms with…
This paper studies the complexity of the stochastic gradient algorithm for PCA when the data are observed in a streaming setting. We also propose an online approach for selecting the learning rate. Simulation experiments confirm the…
Independent Component Analysis (ICA) is a technique for unsupervised exploration of multi-channel data that is widely used in observational sciences. In its classic form, ICA relies on modeling the data as linear mixtures of non-Gaussian…
We present the first experimental realization of a ratchet cellular automaton (RCA) which has been recently suggested as an alternative approach for performing logical operations with interacting (quasi) particles. Our study was performed…
Principal component analysis (PCA) is a key statistical technique for multivariate data analysis. For large data sets the common approach to PCA computation is based on the standard NIPALS-PCA algorithm, which unfortunately suffers from…
Dimensionality reduction techniques have found great success in a wide range of fields requiring analysis of high-dimensional datasets. Time-lagged independent components analysis (TICA), which finds independent components (TICs) with…
The analysis of pulsar timing data, especially in pulsar timing array (PTA) projects, has encountered practical difficulties: evaluating the likelihood and/or correlation-based statistics can become prohibitively computationally expensive…
The concepts of information transfer and causal effect have received much recent attention, yet often the two are not appropriately distinguished and certain measures have been suggested to be suitable for both. We discuss two existing…
Dimension reduction is useful for exploratory data analysis. In many applications, it is of interest to discover variation that is enriched in a "foreground" dataset relative to a "background" dataset. Recently, contrastive principal…
Factor analysis has proven to be a relevant tool for extracting tissue time-activity curves (TACs) in dynamic PET images, since it allows for an unsupervised analysis of the data. Reliable and interpretable results are possible only if…
The linked cell list algorithm is an essential part of molecular simulation software, both molecular dynamics and Monte Carlo. Though it scales linearly with the number of particles, there has been a constant interest in increasing its…
Principal components analysis (PCA) is a fundamental algorithm in data analysis. Its memory-restricted online versions are useful in many modern applications, where the data are too large to fit in memory, or when data arrive as a stream of…