相关论文: Principal Inertia Components and Applications

Motivation: Although principal component analysis is frequently applied to reduce the dimensionality of matrix data, the method is sensitive to noise and bias and has difficulty with comparability and interpretation. These issues are…

Classical Principal Component Analysis (PCA) approximates data in terms of projections on a small number of orthogonal vectors. There are simple procedures to efficiently compute various functions of the data from the PCA approximation. The…

We initiate a study of the composition properties of interactive differentially private mechanisms. An interactive differentially private mechanism is an algorithm that allows an analyst to adaptively ask queries about a sensitive dataset,…

Principal component analysis (PCA) is by far the most widespread tool for unsupervised learning with high-dimensional data sets. Its application is popularly studied for the purpose of exploratory data analysis and online process…

The success of machine learning models relies heavily on effectively representing high-dimensional data. However, ensuring data representations capture human-understandable concepts remains difficult, often requiring the incorporation of…

Principal component analysis (PCA) is a standard tool for dimensional reduction of a set of $n$ observations (samples), each with $p$ variables. In this paper, using a matrix perturbation approach, we study the nonasymptotic relation…

In this work we investigate the Principal Component Analysis (PCA) sensitivity to the velocity power spectrum in high opacity regimes of the interstellar medium (ISM). For our analysis we use synthetic Position-Position-Velocity (PPV) cubes…

We introduce a class of copulas that we call Principal Component Copulas (PCCs). This class combines the strong points of copula-based techniques with principal component analysis (PCA), which results in flexibility when modelling tail…

Principal Component Analysis (PCA) is one of the most commonly used statistical methods for data exploration, and for dimensionality reduction wherein the first few principal components account for an appreciable proportion of the…

Principal component analysis is an important pattern recognition and dimensionality reduction tool in many applications. Principal components are computed as eigenvectors of a maximum likelihood covariance $\widehat{\Sigma}$ that…

It is shown that Principal Component Analysis (PCA) applied to event-by-event single-particle distributions in A-A collisions allows establishing the most optimal basis for anisotropic flow studies from data itself, in contrast to manual…

In this work we analyze principle component analysis (PCA) as a deterministic input-output system. We show that the relative information loss induced by reducing the dimensionality of the data after performing the PCA is the same as in…

In many areas of engineering and sciences, decision rules and control strategies are usually designed based on nominal values of relevant system parameters. To ensure that a control strategy or decision rule will work properly when the…

Principal component analysis (PCA) is a longstanding and well-studied approach for dimension reduction. It rests upon the assumption that the underlying signal in the data has low rank, and thus can be well-summarized using a small number…

We describe an experiment on an underdamped mechanical oscillator used as an information engine. The system is equivalent to an inertial Brownian particle confined in a harmonic potential whose center is controlled by a feedback protocol…

In the 21st century, many of the crucial scientific and technical issues facing humanity can be understood as problems associated with understanding, modelling, and ultimately controlling complex systems: systems comprised of a large number…

The Partial Information Decomposition (PID) [arXiv:1004.2515] provides a theoretical framework to characterize and quantify the structure of multivariate information sharing. A new method (Idep) has recently been proposed for computing a…

The design of a statistical signal processing privacy problem is studied where the private data is assumed to be observable. In this work, an agent observes useful data $Y$, which is correlated with private data $X$, and wants to disclose…

Recently a class of generalized information measures was defined on sets of items parametrized by submodular functions. In this paper, we propose and study various notions of independence between sets with respect to such information…

Consider a pair of random variables $(X,Y)$ distributed according to a given joint distribution $p_{XY}$. A curator wishes to maximally disclose information about $Y$, while limiting the information leakage incurred on $X$. Adopting mutual…