The clustering methods have absorbed even-increasing attention in machine learning and computer vision communities in recent years. Exploring manifold information in multi-way graph cut clustering, such as ratio cut clustering, has shown its promising performance. However, traditional multi-way ratio cut clustering method is NP-hard and thus the spectral solution may deviate from the optimal one. In this paper, we propose a new relaxed multi-way graph cut clustering method, where l 2,1 -norm distance instead of squared distance is utilized to preserve the solution having much more clearer cluster structures. Furthermore, the resulting solution is constrained with normalization to obtain more sparse representation, which can encourage the solution to contain more discrete values with many zeros. For the objective function, it is very difficult to optimize due to minimizing the ratio of two non-smooth items. To address this problem, we transform the objective function into a quadratic problem on the Stiefel manifold (QPSM), and introduce a novel yet efficient iterative algorithm to solve it. Experimental results on several benchmark datasets show that our method significantly outperforms several state-of-the-art clustering approaches.

Orthogonal matrix has shown advantages in training Recurrent Neural Networks (RNNs), but such matrix is limited to be square for the hidden-to-hidden transformation in RNNs. In this paper, we generalize such square orthogonal matrix to orthogonal rectangular matrix and formulating this problem in feed-forward Neural Networks (FNNs) as Optimization over Multiple Dependent Stiefel Manifolds (OMDSM). We show that the orthogonal rectangular matrix can stabilize the distribution of network activations and regularize FNNs. We propose a novel orthogonal weight normalization method to solve OMDSM. Particularly, it constructs orthogonal transformation over proxy parameters to ensure the weight matrix is orthogonal. To guarantee stability, we minimize the distortions between proxy parameters and canonical weights over all tractable orthogonal transformations. In addition, we design orthogonal linear module (OLM) to learn orthogonal filter banks in practice, which can be used as an alternative to standard linear module. Extensive experiments demonstrate that by simply substituting OLM for standard linear module without revising any experimental protocols, our method improves the performance of the state-of-the-art networks, including Inception and residual networks on CIFAR and ImageNet datasets.

Hashing has been proven a promising technique for fast nearest neighbor search over massive databases. In many practical tasks it usually builds multiple hash tables for a desired level of recall performance. However, existing multi-table hashing methods suffer from the heavy table redundancy, without strong table complementarity and effective hash code learning. To address the problem, this paper proposes a multi-table learning method which pursues a specified number of complementary and informative hash tables from a perspective of ensemble learning. By regarding each hash table as a neighbor prediction model, the multi-table search procedure boils down to a linear assembly of predictions stemming from multiple tables. Therefore, a sequential updating and learning framework is naturally established in a boosting mechanism, theoretically guaranteeing the table complementarity and algorithmic convergence. Furthermore, each boosting round pursues the discriminative hash functions for each table by a discrete optimization in the binary code space. Extensive experiments carried out on two popular tasks including Euclidean and semantic nearest neighbor search demonstrate that the proposed boosted complementary hash-tables method enjoys the strong table complementarity and significantly outperforms the state-of-the-arts.

With benefits of low storage cost and fast query speed, cross-modal hashing has received considerable attention recently. However, almost all existing methods on cross-modal hashing cannot obtain powerful hash codes due to directly utilizing hand-crafted features or ignoring heterogeneous correlations across different modalities, which will greatly degrade the retrieval performance. In this paper, we propose a novel deep cross-modal hashing method to generate compact hash codes through an end-to-end deep learning architecture, which can effectively capture the intrinsic relationships between various modalities. Our architecture integrates different types of pairwise constraints to encourage the similarities of the hash codes from an intra-modal view and an inter-modal view, respectively. Moreover, additional decorrelation constraints are introduced to this architecture, thus enhancing the discriminative ability of each hash bit. Extensive experiments show that our proposed method yields state-of-the-art results on two cross-modal retrieval datasets.

Recent years have witnessed the success of hashingtechniques in approximate nearest neighbor search. Inpractice, multiple hash tables are usually employed toretrieve more desired results from all hit buckets ofeach table. However, there are rare works studying theunified approach to constructing multiple informativehash tables except the widely used random way. In thispaper, we regard the table construction as a selectionproblem over a set of candidate hash functions. Withthe graph representation of the function set, we proposean efficient solution that sequentially applies normal-ized dominant set to finding the most informative andindependent hash functions for each table. To furtherreduce the redundancy between tables, we explore thereciprocal hash tables in a boosting manner, where thehash function graph is updated with high weights em-phasized on the misclassified neighbor pairs of previoushash tables. The construction method is general andcompatible with different types of hashing algorithmsusing different feature spaces and/or parameter settings.Extensive experiments on two large-scale benchmarksdemonstrate that the proposed method outperforms bothnaive construction method and state-of-the-art hashingalgorithms, with up to 65.93% accuracy gains.