A neural networks learning algorithm for minor component analysis and its convergence analysis

The eigenvector associated with the smallest eigenvalue of the autocorrelation matrix of input signals is called minor component. Minor component analysis (MCA) is a statistical approach for extracting minor component from input signals and has been applied in many fields of signal processing and data analysis. In this letter, we propose a neural networks learning algorithm for estimating adaptively minor component from input signals. Dynamics of the proposed algorithm are analyzed via a deterministic discrete time (DDT) method. Some sufficient conditions are obtained to guarantee convergence of the proposed algorithm.

Bivariate variance-component analysis, with application to systolic blood pressure and total cholesterol levels in the Framingham Heart Study

Background :
The correlations between systolic blood pressure (SBP) and total cholesterol levels (CHOL) might result from genetic or environmental factors that determine variation in the phenotypes and are shared by family members. Based on 330 nuclear families in the Framingham Heart Study, we used a multivariate normal model, implemented in the software FISHER, to estimate genetic and shared environmental components of variation and genetic and shared environmental correlation between the phenotypes. The natural logarithm of the phenotypes measured at the last visit in both Cohort 1 and 2 was used in the analyses. The antihypertensive treatment effect was corrected before adjustment of the systolic blood pressure for age, sex, and cohort.
Results :
The univariate correlation coefficient was statistically significant for sibling pairs and parent-offspring pairs, but not significant for spouse pairs. In the bivariate analysis, the cross-trait correlation coefficients were not statistically significant for all relative pairs. The shared environmental correlation was statistically significant, but the genetic correlation was not significant.
Conclusion :
There is no significant evidence for a close genetic correlation between systolic blood pressure and total cholesterol levels. However, some shared environmental factors may determine the variation of both phenotypes.

Nonnegative blind source separation by sparse component analysis based on determinant measure

The problem of nonnegative blind source separation (NBSS) is addressed in this paper, where both the sources and the mixing matrix are nonnegative. Because many real-world signals are sparse, we deal with NBSS by sparse component analysis. First, a determinant-based sparseness measure, named D-measure, is introduced to gauge the temporal and spatial sparseness of signals. Based on this measure, a new NBSS model is derived, and an iterative sparseness maximization (ISM) approach is proposed to solve this model. In the ISM approach, the NBSS problem can be cast into row-to-row optimizations with respect to the unmixing matrix, and then the quadratic programming (QP) technique is used to optimize each row. Furthermore, we analyze the source identifiability and the computational complexity of the proposed ISM-QP method. The new method requires relatively weak conditions on the sources and the mixing matrix, has high computational efficiency, and is easy to implement. Simulation results demonstrate the effectiveness of our method.

Snapshots of complexity: using motion capture and principal component analysis to reconceptualise dance

This article brings together the disparate worlds of dance practice, motion capture and statistical analysis. Digital technologies such as motion capture offer dance artists new processes for recording and studying dance movement. Statistical analysis of these data can reveal hidden patterns in movement in ways that are semantically ‘blind’, and are hence able to challenge accepted culturo-physical ‘grammars’ of dance creation. The potential benefit to dance artists is to open up new ways of understanding choreographic movement. However, quantitative analysis does not allow for the uncertainty inherent in emergent, artistic practices such as dance. This article uses motion capture and principal component analysis (PCA), a common statistical technique in human movement recognition studies, to examine contemporary dance movement, and explores how this analysis might be interpreted in an artistic context to generate a new way of looking at the nature and role of movement patterning in dance creation.

Nonnegative Blind Source Separation by Sparse Component Analysis Based on Determinant Measure

The problem of nonnegative blind source separation (NBSS) is addressed in this paper, where both the sources and the mixing matrix are nonnegative. Because many real-world signals are sparse, we deal with NBSS by sparse component analysis. First, a determinant-based sparseness measure, named D-measure, is introduced to gauge the temporal and spatial sparseness of signals. Based on this measure, a new NBSS model is derived, and an iterative sparseness maximization (ISM) approach is proposed to solve this model. In the ISM approach, the NBSS problem can be cast into row-to-row optimizations with respect to the unmixing matrix, and then the quadratic programming (QP) technique is used to optimize each row. Furthermore, we analyze the source identifiability and the computational complexity of the proposed ISM-QP method. The new method requires relatively weak conditions on the sources and the mixing matrix, has high computational efficiency, and is easy to implement. Simulation results demonstrate the effectiveness of our method.

Dynamics and spatio-temporal variability of environmental factors in Eastern Australia using functional principal component analysis

This paper introduces a new technique in ecology to analyze spatial and temporal variability in environmental variables. By using simple statistics, we explore the relations between abiotic and biotic variables that influence animal distributions. However, spatial and temporal variability in rainfall, a key variable in ecological studies, can cause difficulties to any basic model including time evolution. The study was of a landscape scale (three million square kilometers in eastern Australia), mainly over the period of 19982004. We simultaneously considered qualitative spatial (soil and habitat types) and quantitative temporal (rainfall) variables in a Geographical Information System environment. In addition to some techniques commonly used in ecology, we applied a new method, Functional Principal Component Analysis, which proved to be very suitable for this case, as it explained more than 97% of the total variance of the rainfall data, providing us with substitute variables that are easier to manage and are even able to explain rainfall patterns. The main variable came from a habitat classification that showed strong correlations with rainfall values and soil types. © 2010 World Scientific Publishing Company.

A comparison of the dietary patterns derived by principal component analysis and cluster analysis in older Australians

BACKGROUND: Despite increased use of dietary pattern methods in nutritional epidemiology, there have been few direct comparisons of methods. Older adults are a particularly understudied population in the dietary pattern literature. This study aimed to compare dietary patterns derived by principal component analysis (PCA) and cluster analysis (CA) in older adults and to examine their associations with socio-demographic and health behaviours. METHODS: Men (n = 1888) and women (n = 2071) aged 55-65 years completed a 111-item food frequency questionnaire in 2010. Food items were collapsed into 52 food groups and dietary patterns were determined by PCA and CA. Associations between dietary patterns and participant characteristics were examined using Chi-square analysis. The standardised PCA-derived dietary patterns were compared across the clusters using one-way ANOVA. RESULTS: PCA identified four dietary patterns in men and two dietary patterns in women. CA identified three dietary patterns in both men and women. Men in cluster 1 (fruit, vegetables, wholegrains, fish and poultry) scored higher on PCA factor 1 (vegetable dishes, fruit, fish and poultry) and factor 4 (vegetables) compared to factor 2 (spreads, biscuits, cakes and confectionery) and factor 3 (red meat, processed meat, white-bread and hot chips) (mean, 95 % CI; 0.92, 0.82-1.02 vs. 0.74, 0.63-0.84 vs. -0.43, -0.50- -0.35 vs. 0.60 0.46-0.74, respectively). Women in cluster 1 (fruit, vegetables and fish) scored highest on PCA factor 1 (fruit, vegetables and fish) compared to factor 2 (processed meat, hot chips cakes and confectionery) (1.05, 0.97-1.14 vs. -0.14, -0.21- -0.07, respectively). Cluster 3 (small eaters) in both men and women had negative factor scores for all the identified PCA dietary patterns. Those with dietary patterns characterised by higher consumption of red and processed meat and refined grains were more likely to be Australian-born, have a lower level of education, a higher BMI, smoke and did not meet physical activity recommendations (all P < 0.05). CONCLUSIONS: PCA and CA identified comparable dietary patterns within older Australians. However, PCA may provide some advantages compared to CA with respect to interpretability of the resulting dietary patterns. Older adults with poor dietary patterns also displayed other negative lifestyle behaviours. Food-based dietary pattern methods may inform dietary advice that is understood by the community.

Application of extended multivariate modeling for information flow analysis of event related responses

Event related potential (ERP) analysis is one of the most widely used methods in cognitive neuroscience research to study the physiological correlates of sensory, perceptual and cognitive activity associated with processing information. To this end information flow or dynamic effective connectivity analysis is a vital technique to understand the higher cognitive processing under different events. In this paper we present a Granger causality (GC)-based connectivity estimation applied to ERP data analysis. In contrast to the generally used strictly causal multivariate autoregressive model, we use an extended multivariate autoregressive model (eMVAR) which also accounts for any instantaneous interaction among variables under consideration. The experimental data used in the paper is based on a single subject data set for erroneous button press response from a two-back with feedback continuous performance task (CPT). In order to demonstrate the feasibility of application of eMVAR models in source space connectivity studies, we use cortical source time series data estimated using blind source separation or independent component analysis (ICA) for this data set.

Blind source separation dependent component analysis

This book provides readers a complete and self-contained set of knowledge about dependent source separation, including the latest development in this field. The book gives an overview on blind source separation where three promising blind separation techniques that can tackle mutually correlated sources are presented. The book further focuses on the non-negativity based methods, the time-frequency analysis based methods, and the pre-coding based methods, respectively.

Recognising faces in unseen modes : a tensor based approach

This paper addresses the limitation of current multilinear techniques (multilinear PCA, multilinear ICA) when applied to face recognition for handling faces in unseen illumination and viewpoints. We propose a new recognition method, exploiting the interaction of all the subspaces resulting from multilinear decomposition (for both multilinear PCA and ICA), to produce a new basis called multilinear-eigenmodes. This basis offers the flexibility to handle face images at unseen illumination or viewpoints. Experiments on benchmarked datasets yield superior performance in terms of both accuracy and computational cost.

Separation of Doppler radar-based respiratory signatures

Respiration detection using microwave Doppler radar has attracted significant interest primarily due to its unobtrusive form of measurement. With less preparation in comparison with attaching physical sensors on the body or wearing special clothing, Doppler radar for respiration detection and monitoring is particularly useful for long-term monitoring applications such as sleep studies (i.e. sleep apnoea, SIDS). However, motion artefacts and interference from multiple sources limit the widespread use and the scope of potential applications of this technique. Utilising the recent advances in independent component analysis (ICA) and multiple antenna configuration schemes, this work investigates the feasibility of decomposing respiratory signatures into each subject from the Doppler-based measurements. Experimental results demonstrated that FastICA is capable of separating two distinct respiratory signatures from two subjects adjacent to each other even in the presence of apnoea. In each test scenario, the separated respiratory patterns correlate closely to the reference respiration strap readings. The effectiveness of FastICA in dealing with the mixed Doppler radar respiration signals confirms its applicability in healthcare applications, especially in long-term home-based monitoring as it usually involves at least two people in the same environment (i.e. two people sleeping next to each other). Further, the use of FastICA to separate involuntary movements such as the arm swing from the respiratory signatures of a single subject was explored in a multiple antenna environment. The separated respiratory signal indeed demonstrated a high correlation with the measurements made by a respiratory strap used currently in clinical settings.

A convex geometry-based blind source separation method for separating nonnegative sources

This paper presents a convex geometry (CG)-based method for blind separation of nonnegative sources. First, the unaccessible source matrix is normalized to be column-sum-to-one by mapping the available observation matrix. Then, its zero-samples are found by searching the facets of the convex hull spanned by the mapped observations. Considering these zero-samples, a quadratic cost function with respect to each row of the unmixing matrix, together with a linear constraint in relation to the involved variables, is proposed. Upon which, an algorithm is presented to estimate the unmixing matrix by solving a classical convex optimization problem. Unlike the traditional blind source separation (BSS) methods, the CG-based method does not require the independence assumption, nor the uncorrelation assumption. Compared with the BSS methods that are specifically designed to distinguish between nonnegative sources, the proposed method requires a weaker sparsity condition. Provided simulation results illustrate the performance of our method.

Rapid discrimination and determination of polyunsaturated fatty acid composition in marine oils by FTIR Spectroscopy and Multivariate Data Analysis

A rapid analytical approach for discrimination and quantitative determination of polyunsaturated fatty acid (PUFA) contents, particularly eicosapentaenoic acid (EPA) and docosahexaenoic acid (DHA), in a range of oils extracted from marine resources has been developed by using attenuated total reflection Fourier transform infrared spectroscopy and multivariate data analysis. The spectral data were collected without any sample preparation; thus, no chemical preparation was involved, but data were rather processed directly using the developed spectral analysis platform, making it fast, very cost effective, and suitable for routine use in various biotechnological and food research and related industries. Unsupervised pattern recognition techniques, including principal component analysis and unsupervised hierarchical cluster analysis, discriminated the marine oils into groups by correlating similarities and differences in their fatty acid (FA) compositions that corresponded well to the FA profiles obtained from traditional lipid analysis based on gas chromatography (GC). Furthermore, quantitative determination of unsaturated fatty acids, PUFAs, EPA and DHA, by partial least square regression analysis through which calibration models were optimized specifically for each targeted FA, was performed in both known marine oils and totally independent unknown n - 3 oil samples obtained from an actual commercial product in order to provide prospective testing of the developed models towards actual applications. The resultant predicted FAs were achieved at a good accuracy compared to their reference GC values as evidenced through (1) low root mean square error of prediction, (2) good coefficient of determination close to 1 (i.e., R 2≥ 0.96), and (3) the residual predictive deviation values that indicated the predictive power at good and higher levels for all the target FAs. © 2014 Springer Science+Business Media New York.