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We consider the problem of identifying patterns in a data set that exhibit anomalous behavior, often referred to as anomaly detection. Similarity-based anomaly detection algorithms detect abnormally large amounts of similarity or…

To measure node importance, network scientists employ centrality scores that typically take a microscopic or macroscopic perspective, relying on node features or global network structure. However, traditional centrality measures such as…

Principal component analysis (PCA) is not only a fundamental dimension reduction method, but is also a widely used network anomaly detection technique. Traditionally, PCA is performed in a centralized manner, which has poor scalability for…

Principal component analysis (PCA) is one of the most fundamental tools in machine learning with broad use as a dimensionality reduction and denoising tool. In the later setting, while PCA is known to be effective at subspace recovery and…

A key measure that has been used extensively in analyzing complex networks is the degree of a node (the number of the node's neighbors). Because of its discrete nature, when the degree measure was used in analyzing weighted networks,…

A general asymptotic framework is developed for studying consis- tency properties of principal component analysis (PCA). Our frame- work includes several previously studied domains of asymptotics as special cases and allows one to…

Principal component analysis (PCA) is a well-known tool in multivariate statistics. One significant challenge in using PCA is the choice of the number of components. In order to address this challenge, we propose an exact distribution-based…

Principal component analysis (PCA) is a dimensionality reduction method in data analysis that involves diagonalizing the covariance matrix of the dataset. Recently, quantum algorithms have been formulated for PCA based on diagonalizing a…

Model-independent analysis (MIA) methods are generally useful for analysing complex systems in which relationships between the observables are non-trivial and noise is present. Principle Component Analysis (PCA) is one of MIA methods…

The degree distribution is an important characteristic of complex networks. In many data analysis applications, the networks should be represented as fixed-length feature vectors and therefore the feature extraction from the degree…

Principal component analysis (PCA) is a widely used dimension reduction method, but its performance is known to be non-robust to outliers. Recently, product-PCA (PPCA) has been shown to possess the efficiency-loss free ordering-robustness…

The safety and robustness of the network have attracted the attention of people from all walks of life, and the damage of several key nodes will lead to extremely serious consequences. In this paper, we proposed the clustering H-index…

Principal Component analysis (PCA) is a useful statistical technique that is commonly used for multivariate analysis of correlated variables. It is usually applied as a dimension reduction method: the top principal components (PCs)…

We propose a novel Decentralized Differentially Private Power Method (D-DP-PM) for performing Principal Component Analysis (PCA) in networked multi-agent settings. Unlike conventional decentralized PCA approaches where each agent accesses…

Whether class labels in a given data set correspond to meaningful clusters is crucial for the evaluation of clustering algorithms using real-world data sets. This property can be quantified by separability measures. The central aspects of…

Blind source separation, particularly through independent component analysis (ICA), is widely utilized across various signal processing domains for disentangling underlying components from observed mixed signals, owing to its fully…

Principal components (PCA) and hierarchical clustering are two of the most heavily used techniques for analyzing the differences between nucleic acid sequence samples sampled from a given environment. However, a classical application of…

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 (PCA) is a standard dimensionality reduction technique used in various research and applied fields. From an algorithmic point of view, classical PCA can be formulated in terms of operations on a multivariate…

Principal component analysis (PCA) is a foundational tool in modern data analysis, and a crucial step in PCA is selecting the number of components to keep. However, classical selection methods (e.g., scree plots, parallel analysis, etc.)…