Identification of indoor multi-component pollution gas aliasing peak based on JADE

Monitoring indoor harmful gas can obtain the infrared spectra of mixed harmful gases.Since the absorption bands of mixed gases overlap and their qualitative and quantitative analyses are not easy,feature extraction method based on joint approximative diagonalization of eigenmatrix（JADE）is proposed.By fully mining the hidden information of original data and analyzing higher-order statistics information of the data,each substance spectrum in the mixed gas can be accurately distinguished.In addition,a multi-dimensional data quantitative analysis model of the extracted independent source is established by using support vector machine（SVM）based on regular theory.The experimental results show that the correlation coefficients of the components of mixed gases is above 0.999 1by quantitative analysis,which verifies the accuracy of this feature extraction method.

Gradient Search Non-Orthogonal Approximate Joint Diagonalization Algorithm

The problem of approximate joint diagonalization of a set of matrices is instrumental in numerous statistical signal processing applications. This paper describes a relative gradient non-orthogonal approximate joint diagonalization （AJD） algorithm based on a non-least squares AJD criterion and a special AJD using a non-square diagonalizing matrix and an AJD method for ill-conditioned matrices. Simulation results demonstrate the better performance of the relative gradient AJD algorithm compared with the conventional least squares （LS） criteria based gradient-type AJD algorithms. The algorithm is attractive for practical applications since it is simple and efficient.

Descriptors for DNA Sequences Based on Joint Diagonalization of Their Feature Matrices from Dinucleotide Physicochemical Properties

Numerical characterizations of DNA sequence can facilitate analysis of similar sequences. To visualize and compare different DNA sequences in less space, a novel descriptors extraction approach was proposed for numerical characterizations and similarity analysis of sequences. Initially, a transformation method was introduced to represent each DNA sequence with dinucleotide physicochemical property matrix. Then, based on the approximate joint diagonalization theory, an eigenvalue vector was extracted from each DNA sequence,which could be considered as descriptor of the DNA sequence. Moreover, similarity analyses were performed by calculating the pair-wise distances among the obtained eigenvalue vectors. The results show that the proposed approach can capture more sequence information, and can jointly analyze the information contained in all involved multiple sequences, rather than separately, whose effectiveness was demonstrated intuitively by constructing a dendrogram for the 15 beta-globin gene sequences.