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In this paper, we extend the notion of similarity matrix, which has been used to define similarity between nodes of two graphs, to the case of colored graphs, where the coloring is either on the nodes or on the edges of both graphs. The proposed method tries to find the optimal matching between the nodes or edges of both graphs but only performs the comparison when their colors are the same. The proposed cost function nevertheless uses the connectivity between all nodes and edges of both graphs. We then also show how to extend this to the notion of low rank similarity matrix, by defining it as a constrained optimization problem. [ABSTRACT FROM AUTHOR]

Modern information retrieval systems use keywords within documents as indexing terms for search of relevant documents. As Chinese is an ideographic character-based language, the words in the texts are not delimited by white spaces. Indexing of Chinese documents is impossible without a proper segmentation algorithm. Many Chinese segmentation algorithms have been proposed in the past. Traditional segmentation algorithms cannot operate without a large dictionary or a large corpus of training data. Nowadays, the Web has become the largest corpus that is ideal for Chinese segmentation. Although most search engines have problems in segmenting texts into proper words, they maintain huge databases of documents and frequencies of character sequences in the documents. Their databases are important potential resources for segmentation. In this paper, we propose a segmentation algorithm by mining Web data with the help of search engines. On the other hand, the Romanized pinyin of Chinese language indicates boundaries of words in the text. Our algorithm is the first to utilize the Romanized pinyin to segmentation. It is the first unified segmentation algorithm for the Chinese language from different geographical areas, and it is also domain independent because of the nature of the Web. Experiments have been conducted on the datasets of a recent Chinese segmentation competition. The results show that our algorithm outperforms the traditional algorithms in terms of precision and recall. Moreover, our algorithm can effectively deal with the problems of segmentation ambiguity, new word (unknown word) detection, and stop words. [ABSTRACT FROM AUTHOR]