Tensorized Projection for High-Dimensional Binary Embedding

Embedding high-dimensional visual features (d-dimensional) to binary codes (b-dimensional) has shown advantages in various vision tasks such as object recognition and image retrieval. Meanwhile, recent works have demonstrated that to fully utilize the representation power of high-dimensional features, it is critical to encode them into long binary codes rather than short ones, i.e., b ∼ O(d) (Sánchez and Perronnin 2011). However, generating long binary codes involves large projection matrix and high-dimensional matrix-vector multiplication, thus is memory and computationally intensive. To tackle these problems, we propose Tensorized Projection (TP) to decompose the projection matrix using Tensor-Train (TT) format, which is a chain-like representation that allows to operate tensor in an efficient manner. As a result, TP can drastically reduce the computational complexity and memory cost. Moreover, by using the TT-format, TP can regulate the projection matrix against the risk of over-fitting, consequently, lead to better performance than using either dense projection matrix (like ITQ (Gong and Lazebnik 2011)) or sparse projection matrix (Xia et al. 2015). Experimental comparisons with state-of-the-art methods over various visual tasks demonstrate both the efficiency and performance advantages of our proposed TP, especially when generating high dimensional binary codes, e.g., when b ≥ d.