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In this paper, a fully Bayesian algorithm for endmember extraction and abundance estimation for hyperspectral imagery is introduced. Following the linear mixing model, each pixel spectrum of the hyperspectral image is decomposed as a linear combination of pure endmember spectra. The estimation of the unknown endmember spectra and the corresponding abundances is conducted in a unified manner by generating...
This paper focusses on a new clustering method called evidence accumulation clustering with dual rooted prim tree cuts (EAC-DC), based on the principle of cluster ensembles also known as ldquocombining multiple clustering methodsrdquo. A simple weak clustering algorithm is introduced based upon the properties of dual rooted minimal spanning trees and it is extended to multiple rooted trees. Co-association...
Adaptively monitoring the states of nodes in a large complex network is of interest in domains such as national security, public health, and energy grid management. Here, we present an information theoretic adaptive tracking and sampling framework that recursively selects measurements using the feedback from performing inference on a dynamic Bayesian Network. We also present conditions for the existence...
There have been several recently presented works on finding information-geometric embeddings using the properties of statistical manifolds. These methods have generally focused on embedding probability density functions into an open Euclidean space. In this paper we propose adding an additional constraint by embedding onto the surface of the sphere in an unsupervised manner. This additional constraint...
The scalar shrinkage-thresholding operator (SSTO) is a key ingredient of many modern statistical signal processing algorithms including: sparse inverse problem solutions, wavelet denoising, and JPEG2000 image compression. In these applications, it is customary to select the threshold of the operator by solving a scalar sparsity penalized quadratic optimization. In this work, we present a natural multidimensional...
Divergence measures find application in many areas of statistics, signal processing and machine learning, thus necessitating the need for good estimators of divergence measures. While several estimators of divergence measures have been proposed in literature, the performance of these estimators is not known. We propose a simple kNN density estimation based plug-in estimator for estimation of divergence...
To date, most studies on spam have focused only on the spamming phase of the spam cycle and have ignored the harvesting phase, which consists of the mass acquisition of email addresses. It has been observed that spammers conceal their identity to a lesser degree in the harvesting phase, so it may be possible to gain new insights into spammers' behavior by studying the behavior of harvesters, which...
We propose a new approach to adaptive system identification when the system model is sparse. The approach applies lscr1 relaxation, common in compressive sensing, to improve the performance of LMS-type adaptive methods. This results in two new algorithms, the zero-attracting LMS (ZA-LMS) and the reweighted zero-attracting LMS (RZA-LMS). The ZA-LMS is derived via combining a lscr1 norm penalty on the...
We consider principal component analysis (PCA) in decomposable Gaussian graphical models. We exploit the prior information in these models in order to distribute its computation. For this purpose, we reformulate the problem in the sparse inverse covariance (concentration) domain and solve the global eigenvalue problem using a sequence of local eigenvalue problems in each of the cliques of the decomposable...
Due to the curse of dimensionality, high-dimensional data is often pre-processed with some form of dimensionality reduction for the classification task. Many common methods of supervised dimensionality reduction have focused on separating and collapsing the data near the class centroids. These methods often make assumptions on the distributions of the data classes - namely Gaussianity - which can...
We address covariance estimation under mean-squared loss in the Gaussian setting. Specifically, we consider shrinkage methods which are suitable for high dimensional problems with small number of samples (large p small n). First, we improve on the Ledoit-Wolf (LW) method by conditioning on a sufficient statistic via the Rao-Blackwell theorem, obtaining a new estimator RBLW whose mean-squared error...
In this paper, we propose a Bayesian model and a Monte Carlo Markov chain (MCMC) algorithm for reconstructing images that consist of only few non-zero pixels. An appropriate distribution that promotes sparsity is proposed as prior distribution for the pixel values. The hyperparameters involved in the modeling are also assigned prior distributions, resulting in a hierarchical model. A Gibbs sampler...
Dimensionality reduction is required for "human in the loop" analysis of high dimensional data. We present a method for dimensionality reduction that is tailored to tasks of data set discrimination. As contrasted with Euclidean dimensionality reduction, which preserves Euclidean distance or Euler angles in the lower dimensional space, our method seeks to preserve information as measured...
Much of modern machine learning and statistics research consists of extracting information from high-dimensional patterns. Often times, the large number of features that comprise this high-dimensional pattern are themselves vector valued, corresponding to sampled values in a time-series. Here, we present a classification methodology to accommodate multiple time-series using boosting. This method constructs...
Like many biomedical applications, flow cytometry is a field in which dimensionality reduction is important for analysis and diagnosis. Through expression patterns of various fluorescent biomarkers, flow cytometry is often used to characterize the malignant cells in cancer patients, traced to the level of the individual cell. Typically, diagnosticians analyze cytometric data through a series of 2-dimensional...
Adaptive sensing involves actively managing sensor resources to achieve a sensing task, such as object detection, classification, and tracking, and represents a promising direction for new applications of discrete event system methods. We describe an approach to adaptive sensing based on approximately solving a partially observable Markov decision process (POMDP) formulation of the problem. Such approximations...
Local intrinsic dimension estimation has been shown to be useful for many tasks such as image segmentation, anomaly detection, and de-biasing global dimension estimates. Of particular concern with local dimension estimation algorithms is the high variance for high dimensions, leading to points which lie on the same manifold estimating at different dimensions. We propose adding adaptive 'neighborhood...
This paper considers the image reconstruction problem when the original image is assumed to be sparse and when limited information of the point spread function (PSF) is available. In particular, we are interested in reconstructing the magnetization density given magnetic resonance force microscopy (MRFM) image data, and an alternating iterative algorithm is presented to solve this problem. Simulations...
We consider the problem of emitter tracking using received signal strengths (RSS) measured at a number of in-range access points (AP) when some of the AP locations are unknown. This can be formulated as a Euclidean distance matrix completion problem (EDMCP) to which an iterative distributed weighted multidimensional scaling (dwMDS) algorithm can be applied to simultaneously track emitters and localize...
The problem of document classification considers categorizing or grouping of various document types. Each document can be represented as a bag of words, which has no straightforward Euclidean representation. Relative word counts form the basis for similarity metrics among documents. Endowing the vector of term frequencies with a Euclidean metric has no obvious straightforward justification. A more...
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