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One of the main problems in real life omics data analysis is how to extract relevant and non-redundant features from high dimensional multimodal data sets. In general, supervised regularized canonical correlation analysis (SRCCA) plays an important role in extracting new features from multimodal omics data sets. However, the existing SRCCA optimizes regularization parameters based on the quality of first pair of canonical variables only using standard feature evaluation indices. In this regard, this paper introduces a new SRCCA algorithm, integrating judiciously the merits of SRCCA and rough hypercuboid approach, to extract relevant and nonredundant features in approximation spaces from multimodal omics data sets. The proposed method optimizes regularization parameters of the SRCCA based on the quality of a set of pairs of canonical variables using rough hypercuboid approach. While the rough hypercuboid approach provides an efficient way to calculate the degree of dependency of class labels on feature set in approximation spaces, the merit of SRCCA helps in extracting non-redundant features from multimodal data sets. The effectiveness of the proposed approach, along with a comparison with related existing approaches, is demonstrated on several real life data sets.
The aim of the research was to identify the potential for the use of probability density functions (PDF) in modeling of near-surface wind speed. The approaches of Empirical Orthogonal Functions (EOF) and Canonical Correlation Analysis (CCA) are used in combination with 2-parametric Weibull distribution. The downscaling model was built using a diagnosed relationship between sea level pressure (SLP) patterns over Europe and the Northern Atlantic and estimated monthly values of Weibull parameters at 9 stations along the Polish Baltic Coast. The obtained scale (A) and shape (k) parameters make it possible to describe temporal variations of wind fields and their theoretical probability values. This may have further application in the modeling of extreme wind speeds for seasonal forecasting, climate prediction or in historical reconstructions. The model evaluation was done separately for the calibration (1971-2000) and validation periods (2001-2010). The scale parameter was reconstructed reasonably, while there were some problematic issues with the shape parameter, especially in the validation period. The quality of the developed models is generally higher for the winter season, due to larger SLP gradients, whereas the results for the spring and summer seasons were less satisfactory. Despite this, the 99th percentile of theoretical wind speeds are in most cases satisfactory, due to the lesser importance of the shape parameter for typical distributions in the analyzed region.
Celem analizy była ocena przydatności metod statystycznego downscalingu do opisu warunków anemometrycznych na polskim wybrzeżu. Za pomocą metod kanonicznych korelacji (Canonical Correlation Analysis - CCA) i analizy redundancyjnej RDA (Redundancy Analysis - RDA) skonstruowano 3 modele (z 3, 5 i 7 parami map) na podstawie okresu referencyjnego 1971-2000. Modele te opierają się na założeniu, w którym wybrany predyktor (regionalne pole baryczne) wymusza odpowiedź analizowanego elementu lokalnego (pola prędkości wiatru na polskich stacjach brzegowych). Skoncentrowano się na wybraniu spośród wymienionych modelu optymalnego, w którym warunki cyrkulacyjne determinują największą część zmienności pola prędkości wiatru. Ponadto do oceny modeli wzięto pod uwagę wartość współczynnika korelacji między serią pomiarową i zrekonstruowaną. Wyniki analizy wskazują, że modelem, który najlepiej identyfikuje relacje analizowanego elementu z regionalnym polem barycznym, jest model skonstruowany za pomocą metody CCA z 5 parami map kanonicznych. Model ten wyjaśnia największą część wariancji pola regionalnego spośród wszystkich opracowanych modeli (ok. 75%), a ilość tłumaczonej wariancji pola lokalnego jest jeszcze wyższa i wynosi 95%. Średni (ze wszystkich stacji) współczynnik korelacji między serią pomiarową a odtworzoną mówiący o wiarygodności modelu, wynosi ponad 0,30. Tak mała wartość współczynnika jest spowodowana brakiem dobrego odtwarzania przez model wysokich dobowych prędkości wiatru, co skutkuje znacznym niedoszacowaniem wariancji odtwarzanych serii. Ze względu na fakt, że w analizie spodziewanych zmian elementów meteorologicznych standardowym trybem postępowania jest integracja informacji w ogólniejszej skali czasowej, przeprowadzono agregację wartości dobowych do charakterystyk miesięcznych (średniej i kwantyla 90%). Wartości współczynników korelacji obliczone w skali miesięcznej w wartości średnich i ekstremalnych są zadowalające i na niektórych stacjach przekraczają 0,70.
The aim of the analysis was the assessment of the applicability of the statistical-empirical down-scaling methods in the analysis of the anemometric conditions on the Polish coast. With the usage of Canonical Correlation Analysis (CCA) and Redundancy Analysis (RDA) three models were constructed (with 3, 5 and 7 pairs of maps) for 1971-2000 period. The models base on the assumption that chosen predictor (regional pressure field - SLP) triggers an answer of the analyzed variable (wind speed at Polish coastal stations). From those 3 models the focus was placed on the selection of the optimal one in which the circulation conditions determine most of the local field variability and also the correlation between the observed and reconstructed time series of analyzed elements are at reasonable level. The results confirm that the optimal model which identifies the relations between the regional and local variables was the model constructed with CCA method (5 canonical correlation maps used). This model explains most of the regional field (75%) and the amount of wind speed's explained variance exceeds 95%. The average (for all the stations) correlation coefficient exceeds Q.3Q. Such low values of coefficients is the result of weak ability to reconstruct high speed wind values. However the standard time scale in the future climate change scenarios is the integration of information on longer timescales. Such analysis was added and it seems that the correlation between averages and extremes of wind speed in monthly scale are much better and for some stations exceed Q.7Q.
Content available remote Analysis of correlation based dimension reduction methods
Dimension reduction is an important topic in data mining and machine learning. Especially dimension reduction combined with feature fusion is an effective preprocessing step when the data are described by multiple feature sets. Canonical Correlation Analysis (CCA) and Discriminative Canonical Correlation Analysis (DCCA) are feature fusion methods based on correlation. However, they are different in that DCCA is a supervised method utilizing class label information, while CCA is an unsupervised method. It has been shown that the classification performance of DCCA is superior to that of CCA due to the discriminative power using class label information. On the other hand, Linear Discriminant Analysis (LDA) is a supervised dimension reduction method and it is known as a special case of CCA. In this paper, we analyze the relationship between DCCA and LDA, showing that the projective directions by DCCA are equal to the ones obtained from LDA with respect to an orthogonal transformation. Using the relation with LDA, we propose a new method that can enhance the performance of DCCA. The experimental results show that the proposed method exhibits better classification performance than the original DCCA.
The paper presents a novel approach to Canonical Correlation Analysis (CCA) applied to visible and thermal infrared spectrum facial images. In the typical CCA framework biometrical information is transformed from original feature space into the space of canonical variates, and further processing takes place in this space. Extracted features are maximally correlated in canonical variates space, making it possible to expose, investigate and model latent relationships between measured variables. In the paper the CCA is implemented along two directions (along rows and columns of pixel matrix of dimension M x N) using a cascade scheme. The first stage of transformation proceeds along rows of data matrices. Its results are reorganized by transposition. These reorganized matrices are inputs to the second processing stage, namely basic CCA procedure performed along the rows of reorganized matrices, resulting in fact in proceeding along the columns of input data matrix. The so called cascading 2DCCA method also solves the Small Sample Size problem, because instead of the images of size MxN pixels in fact we are using N images of size M x 1 pixels and M images of size 1 x N pixels. In the paper several numerical experiments performed on FERET and Equinox databases are presented.
Nearshore bed variations of the southem Baltic shore were investigated with the aim of detecting co-variability among bed forms of a multi-bar system. The studied area is located at IBW PAN Coastal Research Station at Lubiatowo. The beach consists of fine sand of median grain equal to 0.22 mm, is mildly sloping and boasts multiple (usually 4) bars, which is typical for the coast in the southem Baltic. Data on bed topography were collected along 27 lines, equally spanned every 100 m, since 1987 to 1999, usually twice a year. Fairly high alongshore bed homogeneity made it possible to choose one representative profile for which the CCA method was employed. The method demonstrated considerable potential for detecting co-variability of bed features in the nearshore zone. The results show that some 80% of variability in the region of the offshore slope of the outermost bar can be attributed to variations of Dean equilibrium profiles. The portion of variability of the two innermost bars due to variations of equilibrium profiles equals 40%. Horizontal counter-movements of outer and inner bars can be responsible for same 20%. The remaining 40% should be related to highly variable short time scale phenomena like breakers and wave driven currents in the vicinity of inner bars.
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