240,351 research outputs found
Sequential Logistic Principal Component Analysis (SLPCA): Dimensional Reduction in Streaming Multivariate Binary-State System
Sequential or online dimensional reduction is of interests due to the
explosion of streaming data based applications and the requirement of adaptive
statistical modeling, in many emerging fields, such as the modeling of energy
end-use profile. Principal Component Analysis (PCA), is the classical way of
dimensional reduction. However, traditional Singular Value Decomposition (SVD)
based PCA fails to model data which largely deviates from Gaussian
distribution. The Bregman Divergence was recently introduced to achieve a
generalized PCA framework. If the random variable under dimensional reduction
follows Bernoulli distribution, which occurs in many emerging fields, the
generalized PCA is called Logistic PCA (LPCA). In this paper, we extend the
batch LPCA to a sequential version (i.e. SLPCA), based on the sequential convex
optimization theory. The convergence property of this algorithm is discussed
compared to the batch version of LPCA (i.e. BLPCA), as well as its performance
in reducing the dimension for multivariate binary-state systems. Its
application in building energy end-use profile modeling is also investigated.Comment: 6 pages, 4 figures, conference submissio
Sparse logistic principal components analysis for binary data
We develop a new principal components analysis (PCA) type dimension reduction
method for binary data. Different from the standard PCA which is defined on the
observed data, the proposed PCA is defined on the logit transform of the
success probabilities of the binary observations. Sparsity is introduced to the
principal component (PC) loading vectors for enhanced interpretability and more
stable extraction of the principal components. Our sparse PCA is formulated as
solving an optimization problem with a criterion function motivated from a
penalized Bernoulli likelihood. A Majorization--Minimization algorithm is
developed to efficiently solve the optimization problem. The effectiveness of
the proposed sparse logistic PCA method is illustrated by application to a
single nucleotide polymorphism data set and a simulation study.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS327 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Dynamic gesture recognition using PCA with multi-scale theory and HMM
In this paper, a dynamic gesture recognition system is presented which requires no special hardware other than a Webcam. The system is based on a novel method combining Principal Component Analysis (PCA) with hierarchical multi-scale theory and Discrete Hidden Markov Models (DHMM). We use a hierarchical decision tree based on multiscale theory. Firstly we convolve all members of the training data with a Gaussian kernel, which blurs differences between images and reduces their separation in feature space. This reduces the number of eigenvectors needed to describe the data. A principal component space is computed from the convolved data. We divide the data in this space into two clusters using the k-means algorithm. Then the level of blurring is reduced and PCA is applied to each of the clusters separately. A new principal component space is formed from each cluster. Each of these spaces is then divided into two and the process is repeated. We thus produce a binary tree of principal component spaces where each level of the tree represents a different degree of blurring. The search time is then proportional to the depth of the tree, which makes it possible to search hundreds of gestures in real time. The output of the decision tree is then input into DHMM to recognize temporal information
Unsupervised spectral decomposition of X-ray binaries with application to GX 339-4
In this paper we explore unsupervised spectral decomposition methods for
distinguishing the effect of different spectral components for a set of
consecutive spectra from an X-ray binary. We use well-established linear
methods for the decomposition, namely principal component analysis, independent
component analysis and non-negative matrix factorisation (NMF). Applying these
methods to a simulated dataset consisting of a variable multicolour disc black
body and a cutoff power law, we find that NMF outperforms the other two methods
in distinguishing the spectral components. In addition, due the non-negative
nature of NMF, the resulting components may be fitted separately, revealing the
evolution of individual parameters. To test the NMF method on a real source, we
analyse data from the low-mass X-ray binary GX 339-4 and found the results to
match those of previous studies. In addition, we found the inner radius of the
accretion disc to be located at the innermost stable circular orbit in the
intermediate state right after the outburst peak. This study shows that using
unsupervised spectral decomposition methods results in detecting the separate
component fluxes down to low flux levels. Also, these methods provide an
alternative way of detecting the spectral components without performing actual
spectral fitting, which may prove to be practical when dealing with large
datasets.Comment: 12 pages, 13 figure
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
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