Sentiment classification aims to automatically predict sentiment polarity (e.g., positive or negative) of user-generated sentiment data (e.g., reviews, blogs). To obtain sentiment classification with high accuracy, supervised techniques require a large amount of manually labeled data. The labeling work can be time-consuming and expensive, which makes unsupervised (or semi-supervised) sentiment analysis essential for this application. In this paper, we propose a novel algorithm, called graph co-regularized non-negative matrix tri-factorization (GNMTF), from the geometric perspective. GNMTF assumes that if two words (or documents) are sufficiently close to each other, they tend to share the same sentiment polarity. To achieve this, we encode the geometric information by constructing the nearest neighbor graphs, in conjunction with a non-negative matrix tri-factorization framework. We derive an efficient algorithm for learning the factorization, analyze its complexity, and provide proof of convergence. Our empirical study on two open data sets validates that GNMTF can consistently improve the sentiment classification accuracy in comparison to the state-of-the-art methods.
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