Quaternion softmax classifier

• Published in: Electronics letters Vol. 50; no. 25; pp. 1929 - 1931
• Main Authors: Zeng, Rui, Wu, Jiasong, Shao, Zhuhong, Senhadji, Lotfi, Shu, Huazhong
• Format: Journal Article
• Language: English
• Published: Stevenage The Institution of Engineering and Technology 01.12.2014; John Wiley & Sons, Inc; IET
• Subjects: B channels; Bioengineering; Channels; Classifiers; Color; Colour; colour image pixel feature; colour image representation; Computer Science; Computer Vision and Pattern Recognition; Convergence; Engineering Sciences; feature extraction; feature vectors; G channels; Image and vision processing and display technology; image classification; image colour analysis; image representation; Life Sciences; Mathematical analysis; principal component analysis; QPCA feature; quaternion features; quaternion principal component analysis feature; quaternion softmax classifier; Quaternions; R channels; red‐bluegreen colour images; RGB colour images; Signal and Image processing; Vectors (mathematics); image classification; RGB colour images; R channels; B channels; colour image pixel feature; feature extraction; feature vectors; image representation; quaternion features; red-bluegreen colour images; colour image representation; quaternion principal component analysis feature; G channels; quaternion softmax classifier; image colour analysis; QPCA feature; principal component analysis; Softmax classifier; HYPERCOMPLEX; Quaternion; COLOR IMAGES; FOURIER-TRANSFORMS; Machine learning and classification methods; quaternion principle components analysis (QPCA)
• ISSN: 0013-5194; 1350-911X; 1350-911X
• DOI: 10.1049/el.2014.2526

For the feature extraction of red–blue–green (RGB) colour images, researchers usually deal with R, G and B channels separately to obtain three feature vectors, and then combine them together to obtain a long real feature vector. This approach does not exploit the relationships between the three channels of the colour images. Recently, attention has been paid to quaternion features, which take the relationships between channels into consideration and seem to be more suitable for representing colour images. However, there are only a few quaternion classifiers for dealing with quaternion features. To meet this requirement, a new quaternion classifier, namely, the quaternion softmax classifier is proposed, which is an extended version of the conventional softmax classifier generally defined in the complex (or real) domain. The proposed quaternion softmax classifier is applied to two of the most common quaternion features, that is, the quaternion principal components analysis feature and the colour image pixel feature. The experimental results show that the proposed method performs better than the quaternion back propagation neural network in terms of accuracy and convergence rate.