Feature extraction and dimensionality reduction are important tasks in many fields of science dealing with signal processing and analysis. The relevance of these techniques is increasing as current sensory devices are developed with ever higher resolution, and problems involving multimodal data sources become more common. A plethora of feature extraction methods are available in the literature collectively grouped under the field of Multivariate Analysis (MVA). This paper provides a uniform treatment of several methods: Principal Component Analysis (PCA), Partial Least Squares (PLS), Canonical Correlation Analysis (CCA) and Orthonormalized PLS (OPLS), as well as their non-linear extensions derived by means of the theory of reproducing kernel Hilbert spaces. We also review their connections to other methods for classification and statistical dependence estimation, and introduce some recent developments to deal with the extreme cases of large-scale and low-sized problems. To illustrate the wide applicability of these methods in both classification and regression problems, we analyze their performance in a benchmark of publicly available data sets, and pay special attention to specific real applications involving audio processing for music genre prediction and hyperspectral satellite images for Earth and climate monitoring.

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Slow convergence is observed in the EM algorithm for linear state-space models. We propose to circumvent the problem by applying any off-the-shelf quasi-Newton-type optimizer, which operates on the gradient of the log-likelihood function. Such an algorithm is a practical alternative due to the fact that the exact gradient of the log-likelihood function can be computed by recycling components of the expectation-maximization (EM) algorithm. We demonstrate the efficiency of the proposed method in three relevant instances of the linear state-space model. In high signal-to-noise ratios, where EM is particularly prone to converge slowly, we show that gradient-based learning results in a sizable reduction of computation time.

A solid-phase conjugation method utilizing carrier protein bound to an ion exchange matrix was developed. Ovalbumin was adsorbed to an anion exchange matrix using a batch procedure, and the immobilized protein was then derivatized with iodoacetic acid N-hydroxysuccinimid ester. The activated protein was conjugated with glutathione, the conjugation ratio determined by acid hydrolysis, and amino acid analysis performed with quantification of carboxymethyl cysteine. Elution of conjugates from the resin by a salt gradient revealed considerable heterogeneity in the degree of derivatization, and immunization experiments with the eluted conjugates showed that the more substituted conjugates gave rise to the highest titers of glutathione antibodies. Direct immunization with the conjugates adsorbed to the ion exchange matrix was possible and gave rise to high titers of glutathione antibodies. Conjugates of ovalbumin and various peptides were prepared in a similar manner and used for production of peptide antisera by direct immunization with the conjugates bound to the ion exchanger. Advantages of the method are its solid-phase nature, allowing fast and efficient reactions and intermediate washings, and the ability to release conjugates from the solid phase under mild conditions.