9 research outputs found
On the Efficacy and High-Performance Implementation of Quaternion Matrix Multiplication
Quaternion symmetry is ubiquitous in the physical sciences. As such, much
work has been afforded over the years to the development of efficient schemes
to exploit this symmetry using real and complex linear algebra. Recent years
have also seen many advances in the formal theoretical development of
explicitly quaternion linear algebra with promising applications in image
processing and machine learning. Despite these advances, there do not currently
exist optimized software implementations of quaternion linear algebra. The
leverage of optimized linear algebra software is crucial in the achievement of
high levels of performance on modern computing architectures, and thus provides
a central tool in the development of high-performance scientific software. In
this work, a case will be made for the efficacy of high-performance quaternion
linear algebra software for appropriate problems. In this pursuit, an optimized
software implementation of quaternion matrix multiplication will be presented
and will be shown to outperform a vendor tuned implementation for the analogous
complex matrix operation. The results of this work pave the path for further
development of high-performance quaternion linear algebra software which will
improve the performance of the next generation of applicable scientific
applications
Color image classification via quaternion principal component analysis network
International audienceThe principal component analysis network (PCANet), which is one of the recently proposed deep learning architectures, achieves the state-of-the-art classification accuracy in various datasets and reveals a simple baseline for deep learning networks. However, the performance of PCANet may be degraded when dealing with color images due to the fact that the architecture of PCANet cannot properly utilize the spatial relationship between each color channel in three dimensional color image. In this paper, a quaternion principal component analysis network (QPCANet), which extends PCANet by using quaternion theory, is proposed for color image classification. Compared to PCANet, the proposed QPCANet takes into account the spatial distribution information of RGB channels in color images and ensures larger amount of intra-class invariance by using quaternion domain representation for color images. Experiments conducted on different color image datasets such as UC Merced Land Use, Georgia Tech face, CURet and Caltech-101 have revealed that the proposed QPCANet generally achieves higher classification accuracy than PCANet in color image classification task. The experimental results also verify that QPCANet has much better rotation invariance than PCANet when color image dataset contains lots of rotation information and demonstrate even a simple one-layer QPCANet may obtain satisfactory accuracy when compared with two-layer PCANet