Canonical Correlation Analysis Technique Research Articles

Color image canonical correlation analysis for face feature extraction and recognition

Canonical correlation analysis (CCA) is a powerful statistical analysis technique, which can extract canonical correlated features from two data sets. However, it cannot be directly used for color images that are usually represented by three data sets, i.e., red, green and blue components. Current multi-set CCA (mCCA) methods, on the other hand, can only provide the iterative solutions, not the analytical solutions, when processing multiple data sets. In this paper, we develop the CCA technique and propose a color image CCA (CICCA) approach, which can extract canonical correlated features from three color components and provide the analytical solution. We show the mathematical model of CICCA, prove that CICCA can be cast as solving three eigen-equations, and present the realization algorithm of CICCA. Experimental results on the AR and FRGC-2 public color face image databases demonstrate that CICCA outperforms several representative color face recognition methods.

Exploring a canonical correlation analysis technique for the study of articulatory coordination.

Canonical correlation analysis provides an effective way to visualize the patterns of association or inter-relations between two sets of variables. When observations or measurements are curves such as time series or serial data in general, a canonical correlation analysis technique provided by the functional data analysis (FDA) methodology [Ramsay and Silverman (2005)] is an ideal choice. Although the FDA canonical correlation analysis has a potential usefulness in the study of articulatory coordination, it has been rarely utilized for that purpose. In this study, the FDA canonical correlation analysis technique is applied to midsagittal vocal tract contour data produced in four different emotions (neutral, anger, happiness, and sadness) obtained by a real-time magnetic resonance imaging technique. The purpose is to examine overall differences in the coordination of x and y components of vocal tract contours as a function of emotion. Results indicate that differences in the variance-covariance matrices of x and y components as well as differences in the first three canonical variates among the four emotions are clearly observable, which indicates different weighting patterns of x and y components along the vocal tract for emotional contrast. Those results and other possible applications of the technique will be discussed. [Work supported by NIH.]

Properness and Widely Linear Processing of Quaternion Random Vectors

In this paper, the second-order circularity of quaternion random vectors is analyzed. Unlike the case of complex vectors, there exist three different kinds of quaternion properness, which are based on the vanishing of three different complementary covariance matrices. The different kinds of properness have direct implications on the Cayley-Dickson representation of the quaternion vector, and also on several well-known multivariate statistical analysis methods. In particular, the quaternion extensions of the partial least squares (PLS), multiple linear regression (MLR) and canonical correlation analysis (CCA) techniques are analyzed, showing that, in general, the optimal linear processing is full-widely linear. However, in the case of jointly Q-proper or C <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">η</sup> -proper vectors, the optimal processing reduces, respectively, to the conventional or semi-widely linear processing. Finally, a measure for the degree of improperness of a quaternion random vector is proposed, which is based on the Kullback-Leibler divergence between two zero-mean Gaussian distributions, one of them with the actual augmented covariance matrix, and the other with its closest proper version. This measure quantifies the entropy loss due to the improperness of the quaternion vector, and it admits an intuitive geometrical interpretation based on Kullback-Leibler projections onto sets of proper augmented covariance matrices.

Statistical Downscaling Forecasts for Winter Monsoon Precipitation in Malaysia Using Multimodel Output Variables

Abstract This paper compares the skills of four different forecasting approaches in predicting the 1-month lead time of the Malaysian winter season precipitation. Two of the approaches are based on statistical downscaling techniques of multimodel ensembles (MME). The third one is the ensemble of raw GCM forecast without any downscaling, whereas the fourth approach, which provides a baseline comparison, is a purely statistical forecast based solely on the preceding sea surface temperature anomaly. The first multimodel statistical downscaling method was developed by the Asia-Pacific Economic Cooperation (APEC) Climate Center (APCC) team, whereas the second is based on the canonical correlation analysis (CCA) technique using the same predictor variables. For the multimodel downscaling ensemble, eight variables from seven operational GCMs are used as predictors with the hindcast forecast data spanning a period of 21 yr from 1983/84 to 2003/04. The raw GCM forecast ensemble tends to have higher skills than the baseline skills of the purely statistical forecast that relates the dominant modes of observed sea surface temperature variability to precipitation. However, the downscaled MME forecasts have higher skills than the raw GCM products. In particular, the model developed by APCC showed significant improvement over the peninsular Malaysia region. This is attributed to the model’s ability to capture regional and large-scale predictor signatures from which the additional skills originated. Overall, the results showed that the appropriate downscaling technique and ensemble of various GCM forecasts could result in some skill enhancement, particularly over peninsular Malaysia, where other models tend to have lower or no skills.

Local region structured noise reduction for cortical optical imaging

In this paper, we proposed a local region structured noise reduction method for cortical optical imaging (OI). In our method, block-designed task paradigm was employed. Canonical correlation analysis (CCA) technique was used to extract the underlying structured sources voxel by voxel. The response signals were detected among structured sources by surrogate test based on the reduced autoregression model (ST-RARM) technique. The power of structured noise was eliminated from original time series and then the data were reconstructed. Monte-Carlo simulation was applied to demonstrate the validity of our method. The results showed that our method was more efficient in activated voxel detection compared to the generally used methods PCA, DCT. Further, by using our method the phase knowledge of response signals was well preserved in the reconstructed data and hence a more accurate estimate was obtained. The final activity mapping was generated by utilizing the knowledge of both response amplitude and phase. The vein artifacts were efficiently reduced. Six sets of true OI data collected from the hind-paw (HP) area of rat's cortex were processed and improved activity mappings were obtained.

Removal of the ballistocardiographic artifact from EEG–fMRI data: a canonical correlation approach

The simultaneous recording of electroencephalogram (EEG) and functional magnetic resonance imaging (fMRI) can give new insights into how the brain functions. However, the strong electromagnetic field of the MR scanner generates artifacts that obscure the EEG and diminish its readability. Among them, the ballistocardiographic artifact (BCGa) that appears on the EEG is believed to be related to blood flow in scalp arteries leading to electrode movements. Average artifact subtraction (AAS) techniques, used to remove the BCGa, assume a deterministic nature of the artifact. This assumption may be too strong, considering the blood flow related nature of the phenomenon. In this work we propose a new method, based on canonical correlation analysis (CCA) and blind source separation (BSS) techniques, to reduce the BCGa from simultaneously recorded EEG–fMRI. We optimized the method to reduce the user's interaction to a minimum. When tested on six subjects, recorded in 1.5 T or 3 T, the average artifact extracted with BSS–CCA and AAS did not show significant differences, proving the absence of systematic errors. On the other hand, when compared on the basis of intra-subject variability, we found significant differences and better performance of the proposed method with respect to AAS. We demonstrated that our method deals with the intrinsic subject variability specific to the artifact that may cause averaging techniques to fail.

Quantifying environmental adaptation of metabolic pathways in metagenomics

Recently, approaches have been developed to sample the genetic content of heterogeneous environments (metagenomics). However, by what means these sequences link distinct environmental conditions with specific biological processes is not well understood. Thus, a major challenge is how the usage of particular pathways and subnetworks reflects the adaptation of microbial communities across environments and habitats-i.e., how network dynamics relates to environmental features. Previous research has treated environments as discrete, somewhat simplified classes (e.g., terrestrial vs. marine), and searched for obvious metabolic differences among them (i.e., treating the analysis as a typical classification problem). However, environmental differences result from combinations of many factors, which often vary only slightly. Therefore, we introduce an approach that employs correlation and regression to relate multiple, continuously varying factors defining an environment to the extent of particular microbial pathways present in a geographic site. Moreover, rather than looking only at individual correlations (one-to-one), we adapted canonical correlation analysis and related techniques to define an ensemble of weighted pathways that maximally covaries with a combination of environmental variables (many-to-many), which we term a metabolic footprint. Applied to available aquatic datasets, we identified footprints predictive of their environment that can potentially be used as biosensors. For example, we show a strong multivariate correlation between the energy-conversion strategies of a community and multiple environmental gradients (e.g., temperature). Moreover, we identified covariation in amino acid transport and cofactor synthesis, suggesting that limiting amounts of cofactor can (partially) explain increased import of amino acids in nutrient-limited conditions.

A stochastic process formulation of learning in cooperative agents

We investigate the problem of agent communication when such agents are cooperating rather than competing. We do this using the statistical technique of canonical correlation analysis. We consider two stochastic process methods for performing canonica

Seasonal cycles and long-term trends of plankton in shelf and oceanic habitats of the Norwegian Sea in relation to environmental variables

The plankton abundance data of the Continuous Plankton Recorder (CPR) route from Bergen or Rotterdam to Weather Station Mike (64°44'N, 2°E) from 1949 to 1981 were analysed for long-term trends and seasonal production cycles, and were related to environmental data. The data were explored using the canonical correlation analysis and nonparametric techniques like the Nadaraya-Watson regression. While large copepods such as Calanus spp. and Metridia lucens did not show any temporal trends, a sharp decrease in the abundances of smaller copepods and phytoplankton was observed after 1960. The temporal trends were not related to the NAO, but did show a correlation with the wind direction. Seasonal abundance curves showed that production of both phytoplankton and zooplankton taxa started earlier in coastal water compared to Atlantic water. From the 1950s to the 1970s most taxa showed a delay in the start of the seasonal production cycles, indicating a reduction in the length of the productive cycle. This may to some extent explain the reduced abundance of smaller copepods, phytoplankton and other species during the 1960s and 1970s.

A stochastic process formulation of learning in cooperative agents

We investigate the problem of agent communication when such agents are cooperating rather than competing. We do this using the statistical technique of canonical correlation analysis. We consider t...

Canonical correlation and quantitative phase analysis of microdiffraction patterns in bone-tissue engineering

A novel method is described that combines high-resolution scanning microdiffraction techniques, Rietveld quantitative phase analysis and a statistical method known as canonical correlation analysis (CCA). The method has been applied to a sample taken from a bone-tissue-engineered bioceramic porous scaffold implanted in a mouse for six months. The CCA technique allows the detection of those pixels throughout the investigated sample that best correlate with signal models. Besides the standard usage of this approach, which requires theoretical profiles as signal models, a novel application is presented here, which consists of picking the model spectra out of the experimental data set. Patterns representative of a reasonable range of phase compositions were selected among the huge number of two-dimensional patterns (folded in one-dimensional profiles) to extract quantitative phase fractions. At this stage, the CCA approach was also used to overcome the low Poisson statistic of signal models, so making Rietveld quantitative analysis more reliable. These patterns have been used as profile models for CCA. The final classification map, obtained by assigning the considered pixel to the model spectrum with the highest canonical coefficient, provides the spatial variation of phase concentration.

Level and source of predictability of seasonal rainfall anomalies in Malaysia using canonical correlation analysis

AbstractThis study examines the level and origin of seasonal forecast skills of rainfall anomalies in Malaysia. The forecast models are based on an empirical technique known as the canonical correlation analysis (CCA). The CCA technique searches for maximally correlated coupled patterns between sets of predictor and predictand matrices. The predictive skills of five predictor fields, namely station rainfall in preceding seasons (i.e. the predictand itself), local sea surface temperature (SST) over the western Pacific sector, quasi‐global SST, sea level pressure, and northern hemisphere 700 hPa geopotential height, are investigated. The sequence of four consecutive 3‐month predictor periods is used to capture evolutionary features in the predictor fields. The predictor‐predictand setup is designed such that the predictor fields are followed by a lead‐time ranging from 0 to 9 months and then by a single predictand period of 3 months' duration. The skills are estimated in hindcast mode using the one‐year‐out version of the cross‐validation technique. Skill estimates are expressed as temporal correlation coefficients between forecasts and observed values.A series of experiments with different predictor combinations reveal that the model with quasi‐global SST alone produces most favourable forecast skills. The forecast skills of this model generally outperform the persistence forecast. Moreover, the model also has higher forecast skills in the East Malaysian region compared to those in Peninsular Malaysia. The forecast skill peaks during the late Northern Hemisphere winter season (January–February–March (JFM)) with a secondary maximum during the early summer season (May–June–July, (MJJ)). The average forecast skills are between 0.3–0.5 for up to 5 months' lead‐time in the East Malaysian region and this can be considered very useful for the appropriate users. In the Peninsular Malaysia region, the forecast skills are generally weak, although some stations registered modest skills even at a 5‐month lead‐time. For both prediction periods, the source of predictability originates from anomalous SST conditions associated with the El Niño‐Southern Oscillation (ENSO) phenomenon. Generally, during a La Niña (an El Niño) event, regions in northern Borneo experience excess (deficit) rainfall during the JFM period. Similar conditions are experienced during the MJJ period except that the impact tends to be more widespread throughout the country. Interestingly, the origin of predictability during the JFM period can be traced to typical ENSO events, while ENSO events of longer duration are responsible for the MJJ period. Copyright © 2007 Royal Meteorological Society

Análise Envoltória de Dados na avaliação de hospitais públicos nas capitais brasileiras

To apply the Data Envelopment Analysis (DEA) methodology for evaluating the performance of public hospitals, in terms of clinical medical admissions. The efficiency of the hospitals was measured according to the performance of decision-making units in relation to the variables studied for each hospital, in the year 2000. Data relating to clinical medical admissions in hospitals within the public system in Brazilian state capitals and Federal District (mortality rate, mean length of stay, mean cost of stay and disease profile) were analyzed. The canonical correlation analysis technique was introduced to restrict the variation range of the variables used. The constant returns to scale model was used to generate scores that would enable assessment of the efficiency of the units. From the scores obtained, these cities were classified according to their relative performance in the variables analyzed. It was sought to correlate between the classification scores and the exogenous variables of the expenditure on primary care programs per inhabitant and the human development index for each state capital. In the hospitals studied, circulatory diseases were the most prevalent (23.6% of admissions), and the mortality rate was 10.3% of admissions. Among the 27 state capitals, four reached 100% efficiency (Palmas, Macapá, Teresina and Goiânia), seven were between 85 and 100%, ten were between 70 and 85% and ten had efficiency of less than 70%. The tool utilized was shown to be applicable for evaluating the performance of public hospitals. It revealed large variations among the Brazilian state capitals in relation to clinical medical admissions.

The characteristics of the semi-diurnal tides in mesosphere/low-thermosphere (MLT) during 2002 at Wuhan (30.6°N, 114.4°E) – using canonical correlation analysis technique

In this paper, we use canonical correlation analysis (CCA) method to investigate the semi-diurnal tidal winds in mesosphere and low thermosphere (MLT) region, observed by a newly installed meteor radar at Wuhan (30.6°N, 114.4°E), during the year 2002. In general, 4(3) effective semi-diurnal tidal pairs of patterns are obtained, which represent ∼2/3 total variances of the origin data set. These patterns are expected to be corresponding to the atmospheric oscillations within the semi-diurnal frequency band excited or modulated by different sources, i.e., the seasonal variations, the modulations by the planetary wave oscillations or the solar 27-day activity. Among all the patterns, the 1st pattern, which represents ∼1/3 of total variances, is the most notable. Its amplitudes show maximum values in spring and autumn, and the vertical wavelengths are longer in summer and shorter in winter, which is in line with the results obtained from traditional harmonic analysis. The vertical wavelengths of the higher order patterns (∼50 km) suggest the classic semi-tidal mode S(2, 4)/S(2, 5) is dominant.

The Regularized Iteratively Reweighted MAD Method for Change Detection in Multi- and Hyperspectral Data

This paper describes new extensions to the previously published multivariate alteration detection (MAD) method for change detection in bi-temporal, multi- and hypervariate data such as remote sensing imagery. Much like boosting methods often applied in data mining work, the iteratively reweighted (IR) MAD method in a series of iterations places increasing focus on "difficult" observations, here observations whose change status over time is uncertain. The MAD method is based on the established technique of canonical correlation analysis: for the multivariate data acquired at two points in time and covering the same geographical region, we calculate the canonical variates and subtract them from each other. These orthogonal differences contain maximum information on joint change in all variables (spectral bands). The change detected in this fashion is invariant to separate linear (affine) transformations in the originally measured variables at the two points in time, such as 1) changes in gain and offset in the measuring device used to acquire the data, 2) data normalization or calibration schemes that are linear (affine) in the gray values of the original variables, or 3) orthogonal or other affine transformations, such as principal component (PC) or maximum autocorrelation factor (MAF) transformations. The IR-MAD method first calculates ordinary canonical and original MAD variates. In the following iterations we apply different weights to the observations, large weights being assigned to observations that show little change, i.e., for which the sum of squared, standardized MAD variates is small, and small weights being assigned to observations for which the sum is large. Like the original MAD method, the iterative extension is invariant to linear (affine) transformations of the original variables. To stabilize solutions to the (IR-)MAD problem, some form of regularization may be needed. This is especially useful for work on hyperspectral data. This paper describes ordinary two-set canonical correlation analysis, the MAD transformation, the iterative extension, and three regularization schemes. A simple case with real Landsat Thematic Mapper (TM) data at one point in time and (partly) constructed data at the other point in time that demonstrates the superiority of the iterative scheme over the original MAD method is shown. Also, examples with SPOT High Resolution Visible data from an agricultural region in Kenya, and hyperspectral airborne HyMap data from a small rural area in southeastern Germany are given. The latter case demonstrates the need for regularization.

SO2 emission characteristics and BP neural networks prediction in MSW/coal co-fired fluidized beds

The HCl emission characteristics of typical municipal solid waste (MSW) components and their mixtures have been investigated in a phi 150 mm fluidized bed. Some influencing factors of HCl emission in MSW fluidized bed incinerator was found in this study. The HCl emission is increasing with the growth of bed temperature, while it is decreasing with the increment of oxygen concentration at furnace exit. When the weight percentage of auxiliary coal is increased, the conversion rate of Cl to HCl is increasing. The HCl emission is decreased, if the sorbent (CaO) is added during the incineration process. Based on these experimental results, a 14 x 6 x 1 three-layer BP neural networks prediction model of HCl emission in MSW/coal co-fired fluidized bed incinerator was built. The numbers of input nodes and hidden nodes were fixed on by canonical correlation analysis technique and dynamic construction method respectively. The prediction results of this model gave good agreement with the experimental results, which indicates that the model has relatively high accuracy and good generalization ability. It was found that BP neural network is an effectual method used to predict the HCl emission of MSW/coal co-fired fluidized bed incinerator.

Interannual Tropical Pacific Sea Surface Temperatures and Their Relation to Preceding Sea Level Pressures in the NCAR CCSM2

Abstract This paper describes aspects of tropical interannual ocean/atmosphere variability in the NCAR Community Climate System Model Version 2.0 (CCSM2). The CCSM2 tropical Pacific Ocean/atmosphere system exhibits much stronger biennial variability than is observed. However, a canonical correlation analysis technique decomposes the simulated boreal winter tropical Pacific sea surface temperature (SST) variability into two modes, both of which are related to atmospheric variability during the preceding boreal winter. The first mode of ocean/atmosphere variability is related to the strong biennial oscillation in which La Niña–related sea level pressure (SLP) conditions precede El Niño–like SST conditions the following winter. The second mode of variability indicates that boreal winter tropical Pacific SST anomalies can also be initiated by SLP anomalies over the subtropical central and eastern North Pacific 12 months earlier. The evolution of both modes is characterized by recharge/discharge within the equatorial subsurface temperature field. For the first mode of variability, this recharge/discharge produces a lag between the basin-average equatorial Pacific isotherm depth anomalies and the isotherm–slope anomalies, equatorial SSTs, and wind stress fields. Significant anomalies are present up to a year before the boreal winter SLP variations and two years prior to the boreal winter ENSO-like events. For the second canonical factor pattern, the recharge/discharge mechanism is induced concurrent with the boreal winter SLP pattern approximately one year prior to the ENSO-like events, when isotherms initially deepen and change their slope across the basin. A rapid deepening of the isotherms in the eastern equatorial Pacific and a warming of the overlying SST anomalies then occurs during the subsequent 12 months.

The Impact of IT Personnel Skills on IS Infrastructure and Competitive IS

The knowledge and skills of information technology (IT) personnel have become of critical importance as the strategic value of IT in modern organizations has become apparent. In addition to technical skills traditionally expected of IT personnel, organizational, functional, and managerial skills have been increasingly cited as mandatory for these employees. This paper used a well-accepted typology of IT personnel knowledge and skills, and investigated its relationship to desirable technological traits in organizations and to technological variables that have been closely aligned to competitive advantage in organizations. This exploratory examination used the statistical technique of canonical correlation analysis to investigate the relationship between IT personnel knowledge and skills and the flexibility of information systems (IS) infrastructure. Additionally, the same technique was used to test the relationship between the knowledge and skills of these personnel and measures of IT contribution to competitive advantage. In both cases, the relationships were significant and positive. Implications of these findings and a call for further research into the strategic value of IT personnel knowledge and skills are discussed.

Influence of Fatty acids on foaming properties of cider.

Seventy-seven ciders from four consecutive harvests, which were produced at industrial scale by cider-makers from the region of Asturias (northern Spain), were analyzed to evaluate their foam capacity. The Bikerman method for the evaluation of foaming characteristics was adapted to ciders. In foaming, there are two parameters, foam formation and foam stability, which are found to be related to each other. To determine the relationship between fatty acid content and foaming properties of cider, the multivariate analysis technique of canonical correlation analysis was applied. Foam stability is positively related to the content of caprylic acid. Foam height is positively related to linolenic, pentadecanoic, and palmitic acid and negatively related to stearic and linoleic acid.

Kernel and nonlinear canonical correlation analysis.

We review a neural implementation of the statistical technique of Canonical Correlation Analysis (CCA) and extend it to nonlinear CCA. We then derive the method of kernel-based CCA and compare these two methods on real and artificial data sets before using both on the Blind Separation of Sources.