Modeling data from visual and linguistic modalities together creates opportunities for better understanding of both, and supports many useful applications. Examples of dual visual-linguistic data includes images with keywords, video with narrative, and figures in documents. We consider two key task-driven themes: translating from one modality to another (e.g., inferring annotations for images) and understanding the data using all modalities, where one modality can help disambiguate information in another. The multiple modalities can either be essentially semantically redundant (e.g., keywords...

Linear algebra is one of the most basic foundations of a wide range of scientific domains, and most textbooks of linear algebra are written by mathematicians. However, this book is specifically intended to students and researchers of pattern information processing, analyzing signals such as images and exploring computer vision and computer graphics applications. The author himself is a researcher of this domain. Such pattern information processing deals with a large amount of data, which are represented by high-dimensional vectors and matrices. There, the role of linear algebra is not...