Most exact methods for k-nearest neighbour search suffer from the curse of dimensionality; that is, their query times exhibit exponential dependence on either the ambient or the intrinsic dimensionality. Dynamic Continuous Indexing (DCI) offers a promising way of circumventing the curse and successfully reduces the dependence of query time on intrinsic dimensionality from exponential to sublinear. In this paper, we propose a variant of DCI, which we call Prioritized DCI, and show a remarkable improvement in the dependence of query time on intrinsic dimensionality. In particular, a linear increase in intrinsic dimensionality, or equivalently, an exponential increase in the number of points near a query, can be mostly counteracted with just a linear increase in space. We also demonstrate empirically that Prioritized DCI significantly outperforms prior methods. In particular, relative to Locality-Sensitive Hashing (LSH), Prioritized DCI reduces the number of distance evaluations by a factor of 14 to 116 and the memory consumption by a factor of 21.
Our work is most closely related to Dynamic Continuous Indexing (DCI) @cite_14 , which is an exact randomized algorithm for Euclidean space whose query time is linear in ambient dimensionality, sublinear in dataset size and sublinear in intrinsic dimensionality and uses space linear in the dataset size. Rather than partitioning the vector space, it uses multiple global one-dimensional indices, each of which orders data points along a certain random direction and combines these indices to find points that are near the query along multiple random directions. The proposed algorithm builds on the ideas introduced by DCI and achieves a significant improvement in the dependence on intrinsic dimensionality.
@cite_14
2887556118 2798834175 2557641257 2287612586
Abstract Visual tracking algorithms based on structured output support vector machine (SOSVM) have demonstrated excellent performance. However, sampling methods and optimization strategies of SOSVM undesirably increase the computational overloads, which hinder real-time application of these algorithms. Moreover, due to the lack of high-dimensional features and dense training samples, SOSVM-based algorithms are unstable to deal with various challenging scenarios, such as occlusions and scale variations. Recently, visual tracking algorithms based on discriminative correlation filters (DCF), especially the combination of DCF and features from deep convolutional neural networks (CNN), have been successfully applied to visual tracking, and attains surprisingly good performance on recent benchmarks. The success is mainly attributed to two aspects: the circular correlation properties of DCF and the powerful representation capabilities of CNN features. Nevertheless, compared with SOSVM, DCF-based algorithms are restricted to simple ridge regression which has a weaker discriminative ability. In this paper, a novel circular and structural operator tracker (CSOT) is proposed for high performance visual tracking, it not only possesses the powerful discriminative capability of SOSVM but also efficiently inherits the superior computational efficiency of DCF. Based on the proposed circular and structural operators, a set of primal confidence score maps can be obtained by circular correlating feature maps with their corresponding structural correlation filters. Furthermore, an implicit interpolation is applied to convert the multi-resolution feature maps to the continuous domain and make all primal confidence score maps have the same spatial resolution. Then, we exploit an efficient ensemble post-processor based on relative entropy, which can coalesce primal confidence score maps and create an optimal confidence score map for more accurate localization. The target is localized on the peak of the optimal confidence score map. Besides, we introduce a collaborative optimization strategy to update circular and structural operators by iteratively training structural correlation filters, which significantly reduces computational complexity and improves robustness. Experimental results demonstrate that our approach achieves state-of-the-art performance in mean AUC scores of 71.5 and 69.4 on the OTB2013 and OTB2015 benchmarks respectively, and obtains a third-best expected average overlap (EAO) score of 29.8 on the VOT2017 benchmark. Due to its computation efficiency and retrieval quality, hashing has been widely applied to approximate nearest neighbor search for large-scale image retrieval, while deep hashing further improves the retrieval quality by end-to-end representation learning and hash coding. With compact hash codes, Hamming space retrieval enables the most efficient constant-time search that returns data points within a given Hamming radius to each query, by hash table lookups instead of linear scan. However, subject to the weak capability of concentrating relevant images to be within a small Hamming ball due to mis-specified loss functions, existing deep hashing methods may underperform for Hamming space retrieval. This work presents Deep Cauchy Hashing (DCH), a novel deep hashing model that generates compact and concentrated binary hash codes to enable efficient and effective Hamming space retrieval. The main idea is to design a pairwise cross-entropy loss based on Cauchy distribution, which penalizes significantly on similar image pairs with Hamming distance larger than the given Hamming radius threshold. Comprehensive experiments demonstrate that DCH can generate highly concentrated hash codes and yield state-of-the-art Hamming space retrieval performance on three datasets, NUS-WIDE, CIFAR-10, and MS-COCO. In recent years, Discriminative Correlation Filter (DCF) based methods have significantly advanced the state-of-the-art in tracking. However, in the pursuit of ever increasing tracking performance, their characteristic speed and real-time capability have gradually faded. Further, the increasingly complex models, with massive number of trainable parameters, have introduced the risk of severe over-fitting. In this work, we tackle the key causes behind the problems of computational complexity and over-fitting, with the aim of simultaneously improving both speed and performance. We revisit the core DCF formulation and introduce: (i) a factorized convolution operator, which drastically reduces the number of parameters in the model, (ii) a compact generative model of the training sample distribution, that significantly reduces memory and time complexity, while providing better diversity of samples, (iii) a conservative model update strategy with improved robustness and reduced complexity. We perform comprehensive experiments on four benchmarks: VOT2016, UAV123, OTB-2015, and TempleColor. When using expensive deep features, our tracker provides a 20-fold speedup and achieves a 13.0 relative gain in Expected Average Overlap compared to the top ranked method [12] in the VOT2016 challenge. Moreover, our fast variant, using hand-crafted features, operates at 60 Hz on a single CPU, while obtaining 65.0 AUC on OTB-2015. Domain Adaptation (DA) techniques aim at enabling machine learning methods learn effective classifiers for a "target" domain when the only available training data belongs to a different "source" domain. In this paper we present the Distributional Correspondence Indexing (DCI) method for domain adaptation in sentiment classification. DCI derives term representations in a vector space common to both domains where each dimension re ects its distributional correspondence to a pivot, i.e., to a highly predictive term that behaves similarly across domains. Term correspondence is quantified by means of a distributional correspondence function (DCF). We propose a number of efficient DCFs that are motivated by the distributional hypothesis, i.e., the hypothesis according to which terms with similar meaning tend to have similar distributions in text. Experiments show that DCI obtains better performance than current state-of-the-art techniques for cross-lingual and cross-domain sentiment classification. DCI also brings about a significantly reduced computational cost, and requires a smaller amount of human intervention. As a final contribution, we discuss a more challenging formulation of the domain adaptation problem, in which both the cross-domain and cross-lingual dimensions are tackled simultaneously.