Related papers: A spectral clustering-type algorithm for the consi…

We propose an algorithm to estimate the Hurst exponent of high-dimensional fractals, based on a generalized high-dimensional variance around a moving average low-pass filter. As working examples, we consider rough surfaces generated by the…

High-dimensional clustering analysis is a challenging problem in statistics and machine learning, with broad applications such as the analysis of microarray data and RNA-seq data. In this paper, we propose a new clustering procedure called…

The Hurst coefficient $H$ of a stochastic fractal signal is estimated using the function $\sigma_{MA}^2=\frac{1}{N_{max}-n}\sum_{i=n}^{N_{max}} [y(i)-\widetilde{y}_n(i)]^2$, where $\widetilde{y}_n(i)$ is defined as $1/n \sum_{k=0}^{n-1}…

A method is proposed for generating compact fractal disordered media, by generalizing the random midpoint displacement algorithm. The obtained structures are invasive stochastic fractals, with the Hurst exponent varying as a continuous…

Spectral clustering is a fast and popular algorithm for finding clusters in networks. Recently, Chaudhuri et al. (2012) and Amini et al.(2012) proposed inspired variations on the algorithm that artificially inflate the node degrees for…

Spectral clustering is a powerful method for finding structure in a dataset through the eigenvectors of a similarity matrix. It often outperforms traditional clustering algorithms such as $k$-means when the structure of the individual…

We study the problem of applying spectral clustering to cluster multi-scale data, which is data whose clusters are of various sizes and densities. Traditional spectral clustering techniques discover clusters by processing a similarity…

The most widely used internal measure for clustering evaluation is the silhouette coefficient, whose naive computation requires a quadratic number of distance calculations, which is clearly unfeasible for massive datasets. Surprisingly,…

Spectral clustering approaches have led to well-accepted algorithms for finding accurate clusters in a given dataset. However, their application to large-scale datasets has been hindered by computational complexity of eigenvalue…

Current methods for determining whether a time series exhibits fractal structure (FS) rely on subjective assessments on estimators of the Hurst exponent (H). Here, I introduce the Bayesian Assessment of Scaling, an analytical framework for…

We evaluate the misclustering probability of a spectral clustering algorithm under a Gaussian mixture model with a general covariance structure. The algorithm partitions the data into two groups based on the sign of the first principal…

Co-clustering simultaneously clusters rows and columns, revealing more fine-grained groups. However, existing co-clustering methods suffer from poor scalability and cannot handle large-scale data. This paper presents a novel and scalable…

The characteristic feature of the discrete scale invariant (DSI) processes is the invariance of their finite dimensional distributions by dilation for certain scaling factor. DSI process with piecewise linear drift and stationary increments…

We study the clustering problem for mixtures of bounded covariance distributions, under a fine-grained separation assumption. Specifically, given samples from a $k$-component mixture distribution $D = \sum_{i =1}^k w_i P_i$, where each $w_i…

Fractal behavior and long-range dependence have been observed in an astonishing number of physical systems. Either phenomenon has been modeled by self-similar random functions, thereby implying a linear relationship between fractal…

Network clustering reveals the organization of a network or corresponding complex system with elements represented as vertices and interactions as edges in a (directed, weighted) graph. Although the notion of clustering can be somewhat…

Clustering procedures suitable for the analysis of very high-dimensional data are needed for many modern data sets. In model-based clustering, a method called high-dimensional data clustering (HDDC) uses a family of Gaussian mixture models…

We propose a simple, projection-based algorithm for clustering mixtures of discrete (Bernoulli) distributions. Unlike previous approaches that rely on coordinate-specific ``combinatorial projections,'' our algorithm is rotationally…

In this work a robust clustering algorithm for stationary time series is proposed. The algorithm is based on the use of estimated spectral densities, which are considered as functional data, as the basic characteristic of stationary time…

The discrete distribution is often used to describe complex instances in machine learning, such as images, sequences, and documents. Traditionally, clustering of discrete distributions (D2C) has been approached using Wasserstein barycenter…