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Dimension reduction for large-scale text data is attracting much attention nowadays due to the rapid growth of the World Wide Web. We can categorize those popular dimension reduction algorithms into two groups: feature extraction and feature selection algorithms. In the former, new features are combined from their original features through algebraic transformation. Though many of them have been validated to be effective, these algorithms are typically associated with high computational overhead, making them difficult to be applied on real-world text data. In the latter, subsets of features are selected directly. These algorithms are widely used in real-world tasks owing to their efficiency, but are often based on greedy strategies rather than optimal solutions. An important problem remains: it has been troublesome to integrate these two types of algorithms into a single framework, making it difficult to reap the benefits from both. In this paper, we formulate the two algorithm categories through a unified optimization framework, under which we develop a novel feature selection algorithm called Trace-Oriented Feature Analysis (TOFA). In detail, we integrate the objective functions of several state-of-the-art feature extraction algorithms into a unified one under the optimization framework, and then we propose to optimize this objective function in the solution space of feature selection algorithms for dimensionality reduction. Since the proposed objective function of TOFA integrates many prominent feature extraction algorithms' objective functions, such as unsupervised Principal Component Analysis (PCA) and supervised Maximum Margin Criterion (MMC), TOFA can handle both supervised and unsupervised problems. In addition, by tuning a weight value, TOFA is also suitable to solve semisupervised learning problems. Experimental results on several real-world data sets validate the effectiveness and efficiency of TOFA in text data for dimensionality reduction purpose.