To achieve a good trade-off between recognition accuracy and computational efficiency, it is often needed to reduce high-dimensional visual data to medium-dimensional ones. For this task, even applying a simple full-matrix-based linear projection causes significant computation and memory use. When the number of visual data is large, how to efficiently learn such a projection could even become a problem. The recent feature merging approach offers an efficient way to reduce the dimensionality, which only requires a single scan of features to perform reduction. However, existing merging algorithms do not scale well with high-dimensional data, especially in the unsupervised case. To address this problem, we formulate unsupervised feature merging as a PCA problem imposed with a special structure constraint. By exploiting its connection with k-means, we transform this constrained PCA problem into a feature clustering problem. Moreover, we employ the hashing technique to improve its scalability. These produce a scalable feature merging algorithm for our dimensionality reduction task. In addition, we develop an extension of this method by leveraging the neighborhood structure in the data to further improve dimensionality reduction performance. In further, we explore the incorporation of bipolar merging - a variant of merging function which allows the subtraction operation - into our algorithms. Through three applications in visual recognition, we demonstrate that our methods can not only achieve good dimensionality reduction performance with little computational cost but also help to create more powerful representation at both image level and local feature level.
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