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The main point of the paper is to show the close relation between the nonzero principal components and the difference subspace together with the complementary close relation between the zero principal components and the common vector. A common vector representing each word-class is obtained from the eigenvectors of the covariance matrix of its own word-class; that is, the common vector is in the direction of a linear combination of the eigenvectors corresponding to the zero eigenvalues of the covariance matrix. The methods that use the nonzero principal components for recognition purposes suggest the elimination of all the features that are in the direction of the eigenvectors corresponding to the smallest eigenvalues (including the zero eigenvalues) of the covariance matrix whereas the common vector approach suggests the elimination of all the features that are in the direction of the eigenvectors corresponding to the largest, all nonzero eigenvalues of the covariance matrix.Index Terms-Common vector approach, speech recognition, subspace methods.

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In this work, the efficacy of various features on electrocardiogram (ECG) based biometric authentication process is thoroughly examined. In particular, the features acquired from temporal analysis, wavelet transformation, power spectral density estimation and QRS-complex detection over ECG signals are considered. These features are employed with two distinct classification algorithms, namely decision tree and Bayes network, specifically for gender, age and identity recognition problems. The biometric authentication framework is evaluated on a benchmark dataset that contains ECG records of 18 healthy people including 5 men, aged 26 to 45, and 13 women, aged 20 to 50. The results of the experimental analysis reveal that if all those features are used in combination rather than individually, better performance is attained for all classifiers in each recognition problem.

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