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Register a new userPairwise Rotation Hashing for High-dimensional Features
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Binary Hashing is widely used for effective approximate nearest neighbors search. Even though various binary hashing methods have been proposed, very few methods are feasible for extremely high-dimensional features often used in visual tasks today. We propose a novel highly sparse linear hashing method based on pairwise rotations. The encoding cost of the proposed algorithm is $mathrm{O}(n log n)$ for n-dimensional features, whereas that of the existing state-of-the-art method is typically $mathrm{O}(n^2)$. The proposed method is also remarkably faster in the learning phase. Along with the efficiency, the retrieval accuracy is comparable to or slightly outperforming the state-of-the-art. Pairwise rotations used in our method are formulated from an analytical study of the trade-off relationship between quantization error and entropy of binary codes. Although these hashing criteria are widely used in previous researches, its analytical behavior is rarely studied. All building blocks of our algorithm are based on the analytical solution, and it thus provides a fairly simple and efficient procedure.
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Recommendation efficiency and data sparsity problems have been regarded as two challenges of improving performance for online recommendation. Most of the previous related work focus on improving recommendation accuracy instead of efficiency. In this paper, we propose a Deep Pairwise Hashing (DPH) to map users and items to binary vectors in Hamming space, where a users preference for an item can be efficiently calculated by Hamming distance, which significantly improves the efficiency of online recommendation. To alleviate data sparsity and cold-start problems, the user-item interactive information and item content information are unified to learn effective representations of items and users. Specifically, we first pre-train robust item representation from item content data by a Denoising Auto-encoder instead of other deterministic deep learning frameworks; then we finetune the entire framework by adding a pairwise loss objective with discrete constraints; moreover, DPH aims to minimize a pairwise ranking loss that is consistent with the ultimate goal of recommendation. Finally, we adopt the alternating optimization method to optimize the proposed model with discrete constraints. Extensive experiments on three different datasets show that DPH can significantly advance the state-of-the-art frameworks regarding data sparsity and item cold-start recommendation.
Hashing has been recognized as an efficient representation learning method to effectively handle big data due to its low computational complexity and memory cost. Most of the existing hashing methods focus on learning the low-dimensional vectorized binary features based on the high-dimensional raw vectorized features. However, studies on how to obtain preferable binary codes from the original 2D image features for retrieval is very limited. This paper proposes a bilinear supervised discrete hashing (BSDH) method based on 2D image features which utilizes bilinear projections to binarize the image matrix features such that the intrinsic characteristics in the 2D image space are preserved in the learned binary codes. Meanwhile, the bilinear projection approximation and vectorization binary codes regression are seamlessly integrated together to formulate the final robust learning framework. Furthermore, a discrete optimization strategy is developed to alternatively update each variable for obtaining the high-quality binary codes. In addition, two 2D image features, traditional SURF-based FVLAD feature and CNN-based AlexConv5 feature are designed for further improving the performance of the proposed BSDH method. Results of extensive experiments conducted on four benchmark datasets show that the proposed BSDH method almost outperforms all competing hashing methods with different input features by different evaluation protocols.
Semantic Hashing is a popular family of methods for efficient similarity search in large-scale datasets. In Semantic Hashing, documents are encoded as short binary vectors (i.e., hash codes), such that semantic similarity can be efficiently computed using the Hamming distance. Recent state-of-the-art approaches have utilized weak supervision to train better performing hashing models. Inspired by this, we present Semantic Hashing with Pairwise Reconstruction (PairRec), which is a discrete variational autoencoder based hashing model. PairRec first encodes weakly supervised training pairs (a query document and a semantically similar document) into two hash codes, and then learns to reconstruct the same query document from both of these hash codes (i.e., pairwise reconstruction). This pairwise reconstruction enables our model to encode local neighbourhood structures within the hash code directly through the decoder. We experimentally compare PairRec to traditional and state-of-the-art approaches, and obtain significant performance improvements in the task of document similarity search.
For high-dimensional small sample size data, Hotellings T2 test is not applicable for testing mean vectors due to the singularity problem in the sample covariance matrix. To overcome the problem, there are three main approaches in the literature. Note, however, that each of the existing approaches may have serious limitations and only works well in certain situations. Inspired by this, we propose a pairwise Hotelling method for testing high-dimensional mean vectors, which, in essence, provides a good balance between the existing approaches. To effectively utilize the correlation information, we construct the new test statistics as the summation of Hotellings test statistics for the covariate pairs with strong correlations and the squared $t$ statistics for the individual covariates that have little correlation with others. We further derive the asymptotic null distributions and power functions for the proposed Hotelling tests under some regularity conditions. Numerical results show that our new tests are able to control the type I error rates, and can achieve a higher statistical power compared to existing methods, especially when the covariates are highly correlated. Two real data examples are also analyzed and they both demonstrate the efficacy of our pairwise Hotelling tests.
Many applications use sequences of n consecutive symbols (n-grams). Hashing these n-grams can be a performance bottleneck. For more speed, recursive hash families compute hash values by updating previous values. We prove that recursive hash families cannot be more than pairwise independent. While hashing by irreducible polynomials is pairwise independent, our implementations either run in time O(n) or use an exponential amount of memory. As a more scalable alternative, we make hashing by cyclic polynomials pairwise independent by ignoring n-1 bits. Experimentally, we show that hashing by cyclic polynomials is is twice as fast as hashing by irreducible polynomials. We also show that randomized Karp-Rabin hash families are not pairwise independent.
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