Subset selection in dimension reduction methods

Dimension reduction methods play an important role in multivariate statistical analysis, in particular with high-dimensional data. Linear methods can be seen as a linear mapping from the original feature space to a dimension reduction subspace. The aim is to transform the data so that the essential structure is more easily understood. However, highly correlated variables provide redundant information, whereas some other feature may be irrelevant, and we would like to identify and then discard both of them while pursuing dimension reduction. Here we propose a greedy search algorithm, which avoids the search over all possible subsets, for ranking subsets of variables based on their ability to explain variation in the dimension reduction variates.Dimension reduction methods, Linear mapping, Subset selection, Greedy search

Matching pursuit-based compressive sensing in a wearable biomedical accelerometer fall diagnosis device

There is a significant high fall risk population, where individuals are susceptible to frequent falls and obtaining significant injury, where quick medical response and fall information are critical to providing efficient aid. This article presents an evaluation of compressive sensing techniques in an accelerometer-based intelligent fall detection system modelled on a wearable Shimmer biomedical embedded computing device with Matlab. The presented fall detection system utilises a database of fall and activities of daily living signals evaluated with discrete wavelet transforms and principal component analysis to obtain binary tree classifiers for fall evaluation. 14 test subjects undertook various fall and activities of daily living experiments with a Shimmer device to generate data for principal component analysis-based fall classifiers and evaluate the proposed fall analysis system. The presented system obtains highly accurate fall detection results, demonstrating significant advantages in comparison with the thresholding method presented. Additionally, the presented approach offers advantageous fall diagnostic information. Furthermore, transmitted data accounts for over 80% battery current usage of the Shimmer device, hence it is critical the acceleration data is reduced to increase transmission efficiency and in-turn improve battery usage performance. Various Matching pursuit-based compressive sensing techniques have been utilised to significantly reduce acceleration information required for transmission.Scopu

In-network Sparsity-regularized Rank Minimization: Algorithms and Applications

Given a limited number of entries from the superposition of a low-rank matrix plus the product of a known fat compression matrix times a sparse matrix, recovery of the low-rank and sparse components is a fundamental task subsuming compressed sensing, matrix completion, and principal components pursuit. This paper develops algorithms for distributed sparsity-regularized rank minimization over networks, when the nuclear- and $\ell_1$-norm are used as surrogates to the rank and nonzero entry counts of the sought matrices, respectively. While nuclear-norm minimization has well-documented merits when centralized processing is viable, non-separability of the singular-value sum challenges its distributed minimization. To overcome this limitation, an alternative characterization of the nuclear norm is adopted which leads to a separable, yet non-convex cost minimized via the alternating-direction method of multipliers. The novel distributed iterations entail reduced-complexity per-node tasks, and affordable message passing among single-hop neighbors. Interestingly, upon convergence the distributed (non-convex) estimator provably attains the global optimum of its centralized counterpart, regardless of initialization. Several application domains are outlined to highlight the generality and impact of the proposed framework. These include unveiling traffic anomalies in backbone networks, predicting networkwide path latencies, and mapping the RF ambiance using wireless cognitive radios. Simulations with synthetic and real network data corroborate the convergence of the novel distributed algorithm, and its centralized performance guarantees.Comment: 30 pages, submitted for publication on the IEEE Trans. Signal Proces

Statistical Compressed Sensing of Gaussian Mixture Models

A novel framework of compressed sensing, namely statistical compressed sensing (SCS), that aims at efficiently sampling a collection of signals that follow a statistical distribution, and achieving accurate reconstruction on average, is introduced. SCS based on Gaussian models is investigated in depth. For signals that follow a single Gaussian model, with Gaussian or Bernoulli sensing matrices of O(k) measurements, considerably smaller than the O(k log(N/k)) required by conventional CS based on sparse models, where N is the signal dimension, and with an optimal decoder implemented via linear filtering, significantly faster than the pursuit decoders applied in conventional CS, the error of SCS is shown tightly upper bounded by a constant times the best k-term approximation error, with overwhelming probability. The failure probability is also significantly smaller than that of conventional sparsity-oriented CS. Stronger yet simpler results further show that for any sensing matrix, the error of Gaussian SCS is upper bounded by a constant times the best k-term approximation with probability one, and the bound constant can be efficiently calculated. For Gaussian mixture models (GMMs), that assume multiple Gaussian distributions and that each signal follows one of them with an unknown index, a piecewise linear estimator is introduced to decode SCS. The accuracy of model selection, at the heart of the piecewise linear decoder, is analyzed in terms of the properties of the Gaussian distributions and the number of sensing measurements. A maximum a posteriori expectation-maximization algorithm that iteratively estimates the Gaussian models parameters, the signals model selection, and decodes the signals, is presented for GMM-based SCS. In real image sensing applications, GMM-based SCS is shown to lead to improved results compared to conventional CS, at a considerably lower computational cost