Binary Multi-View Clustering.

How to economically cluster large-scale multi-view images is a long-standing problem in computer vision. To tackle this challenge, we introduce a novel approach named Highly-economized Scalable Image Clustering (HSIC) that radically surpasses conventional image clustering methods via binary compression. We intuitively unify the binary representation learning and efficient binary cluster structure learning into a joint framework. In particular, common binary representations are learned by exploiting both sharable and individual information across multiple views to capture their underlying correlations. Meanwhile, cluster assignment with robust binary centroids is also performed via effective discrete optimization under \(\ell _{21}\)-norm constraint. By this means, heavy continuous-valued Euclidean distance computations can be successfully reduced by efficient binary XOR operations during the clustering procedure. To our best knowledge, HSIC is the first binary clustering work specifically designed for scalable multi-view image clustering. Extensive experimental results on four large-scale image datasets show that HSIC consistently outperforms the state-of-the-art approaches, whilst significantly reducing computational time and memory footprint.

In many online web services, precisely recommending relevant items from massive candidates is a crucial yet computationally expensive task. To confront with the scalability issue, discrete latent factors learning is advocated since it permits exact top-K item recommendation with sub-linear time complexity. However, the performance of existing discrete methods is limited due to they only consider the cross-view user-item relations. In this paper, we propose a new method called Discrete Manifold-Regularized Collaborative Filtering (DMRCF), which jointly exploits cross-view user-item relations and intra-view user-user/item-item affinities in the hamming space. On one hand, inspired by the observation that similar users are more likely to prefer similar items, manifold regularization terms are introduced to enforce similar users/items have similar binary codes in the hamming space. Accordingly, our method is able to learn more about the preference of user and then recommend items based on user’s attributes. On the other hand, for cross-view relations, we cast the reconstruction errors of user-item rating matrix and ranking loss for relative preferences of users into a joint learning framework. Due to latent factors are restricted to be binary values, the optimization is generally a challenging NP-hard problem. To reduce the quantization error, we develop an efficient algorithm to solve the overall discrete optimization problem. Experiments on two real-world datasets demonstrate that DMRCF outperforms the state-of-the-art methods significantly.

The objective of cluster structure ensemble is to find a unified cluster structure from multiple cluster structures obtained from different datasets. Unfortunately, not all the cluster structures contribute to the unified cluster structure. This paper investigates the problem of how to select the suitable cluster structures in the ensemble which will be summarized to a more representative cluster structure. Specifically, the cluster structure is first represented by a mixture of Gaussian distributions, the parameters of which are estimated using the expectation-maximization algorithm. Then, several distribution-based distance functions are designed to evaluate the similarity between two cluster structures. Based on the similarity comparison results, we propose a new approach, which is referred to as the distribution-based cluster structure ensemble (DCSE) framework, to find the most representative unified cluster structure. We then design a new technique, the distribution-based cluster structure selection strategy (DCSSS), to select a subset of cluster structures. Finally, we propose using a distribution-based normalized hypergraph cut algorithm to generate the final result. In our experiments, a nonparametric test is adopted to evaluate the difference between DCSE and its competitors. We adopt 20 real-world datasets obtained from the University of California, Irvine and knowledge extraction based on evolutionary learning repositories, and a number of cancer gene expression profiles to evaluate the performance of the proposed methods. The experimental results show that: 1) DCSE works well on the real-world datasets and 2) DCSE based on DCSSS can further improve the performance of the algorithm.

Learning based hashing has become increasingly popular because of its high efficiency in handling the large scale image retrieval. Preserving the pairwise similarities of data points in the Hamming space is critical in state-of-the-art hashing techniques. However, most previous methods ignore to capture the local geometric structure residing on original data, which is essential for similarity search. In this paper, we propose a novel hashing framework, which simultaneously optimizes similarity preserving hash codes and reconstructs the locally linear structures of data in the Hamming space. In specific, we learn two hash functions such that the resulting two sets of binary codes can well preserve the pairwise similarity and sparse neighborhood in the original feature space. By taking advantage of the flexibility of asymmetric hash functions, we devise an efficient alternating algorithm to optimize the hash coding function and high-quality binary codes jointly. We evaluate the proposed method on several large-scale image datasets, and the results demonstrate it significantly outperforms recent state-of-the-art hashing methods on large-scale image retrieval problems.

We study natural cluster structures in the rings of regular func- tions on simple complex Lie groups and Poisson-Lie structures compatible with these cluster structures. According to our main conjecture, each class in the Belavin-Drinfeld classification of Poisson-Lie structures on G corresponds to a cluster structure in O(G). We prove a reduction theorem explaining how different parts of the conjecture are related to each other. The conjecture is established for SLn, n < 5, and for any G in the case of the standard Poisson- Lie structure. Since the invention of cluster algebras in 2001, a large part of research in the field has been devoted to uncovering cluster structures in rings of regular functions on various algebraic varieties arising in algebraic geometry, representation theory, and mathematical physics. Once the existence of such a structure was established, abstract features of cluster algebras were used to study geometric properties of underlying objects. Research in this direction led to many exciting results (SSVZ, FoGo1, FoGo2). It also created an impression that, given an algebraic variety, there is a unique (if at all) natural cluster structure associated with it. The main goal of the current paper is to establish the following phenomenon: in certain situations, the same ring may have multiple natural cluster structures. More exactly, we engage into a systematic study of multiple cluster structures in the rings of regular functions on simple Lie groups (in what follows we will shorten that to cluster structures on simple Lie groups). Consistent with the philosophy advocated in (GSV1, GSV2, GSV3, GSV4, GSV5, GSV6), we will focus on compatible Poisson structures on the Lie groups, that is, on compatible Poisson-Lie structures. The notion of a Poisson bracket compatible with a cluster structure was intro- duced in (GSV1). It was used there to interpret cluster transformations and matrix mutations from a viewpoint of Poisson geometry. In addition, it was shown that if a Poisson algebraic variety (M,f�,ŧ ) possesses a coordinate chart that consists of regular functions whose logarithms have pairwise constant Poisson brackets, then one can use this chart to define a cluster structure CM compatible with f�,ŧ . Al- gebraic structures corresponding to CM (the cluster algebra and the upper cluster algebra) are closely related to the ring O(M) of regular functions on M. More pre- cisely, under certain rather mild conditions, O(M) can be obtained by tensoring one of these algebras by C.

Training on the Edge enables neural networks to learn continuously from new data after deployment on memory-constrained edge devices. Previous work is mostly concerned with reducing the number of model parameters which is only beneficial for inference. However, memory footprint from activations is the main bottleneck for training on the edge. Existing incremental training methods fine-tune the last few layers sacrificing accuracy gains from re-training the whole model. In this work, we investigate the memory footprint of training deep learning models, and use our observations to propose BitTrain. In BitTrain, we exploit activation sparsity and propose a novel bitmap compression technique that reduces the memory footprint during training. We save the activations in our proposed bitmap compression format during the forward pass of the training, and restore them during the backward pass for the optimizer computations. The proposed method can be integrated seamlessly in the computation graph of modern deep learning frameworks. Our implementation is safe by construction, and has no negative impact on the accuracy of model training. Experimental results show up to 34% reduction in the memory footprint at a sparsity level of 50%. Further pruning during training results in more than 70% sparsity, which can lead to up to 56% reduction in memory footprint. BitTrain advances the efforts towards bringing more machine learning capabilities to edge devices. Our source code is available at https://github.com/scale-lab/BitTrain.

Global color consistency correction for multiview images in three-dimensional (3-D) reconstruction is an important problem. The color differences between the images will affect the result of dense matching, thereby reducing the geometric accuracy of the mesh model. Moreover, it will also affect the result of texture mapping, causing color differences in the textured model. The color correction method based on global optimization is mainly used to solve this problem. And existing methods usually use sparse matching points as the color correspondences, but the correction results are not accurate enough as a result of the sparsity of the points. Besides, their efficiency of solving large-scale images globally is low. This article proposes a novel color correction method to eliminate the color differences between large-scale multiview images effectively. The core idea of our method is to group images by graph partition algorithm, and then perform intragroup correction and intergroup correction in sequence. First, for each pair of images, we calculate the reliable matching regions around the sparse points as the color correspondences according to the local homography principle. Compared with sparse matching points, our strategy can achieve more accurate color correction results. Next, for large-scale images, we partition them into many groups. For each group of images, the correction parameters are solved to eliminate the color differences of the images included in the group. Finally, we eliminate the color differences between groups by intergroup correction to achieve overall color consistency. Experimental results on typical datasets demonstrate that the proposed method is better than the current representative methods. The proposed method shows better color consistency in the extreme cases, and also exhibits higher computational efficiency on large-scale image sets.

Probabilistic cluster structure ensemble

The memory footprint is considered an important constraint for embedded systems. This is especially important in the context of increasing sophistication of embedded software, and the increasing use of modern software engineering techniques like component-based design. Since reusability is the major motivation for using components, most components are not optimized for the (limited) functionality they have to realize in an embedded system. All this leads to an increasing amount of code and data that might not be needed for a given functionality.The memory footprint of an embedded system consists of 2 parts: the footprint of the application and the footprint of the operating system. In this keynote talk, I will focus on the memory footprint reduction of application as well as the Linux kernel. I will report memory footprint reductions that have been obtained by the Diablo binary rewriter, which has been used to substantially reduce the memory footprint of both applications and of the system software.For the applications, the optimizer is capable of reducing the code size of programs compiled with two proprietary ARM tool chains (ADS 1.1 and RVCT 2.1) with on average 16% for statically linked ARM programs, while making them 12.8% faster. Execution of the rewritten programs also consumes on average 10.7% less energy.For the system software, we specialize the kernel both for the system calls that are actually occurring in the application program, and for the boot parameters of the kernel. We also assume that the hardware is fixed so that part of the bootstrap process is completely deterministic and can be optimized based on actual trace information.Finally, we compress frozen code, and we swap cold code to flash memory. All combined, these compaction techniques on the kernel can reduce the kernel's RAM footprint with up to 48% for the Linux kernel. The slowdown was limited to 1--2%.This proves that binary rewriting can help in substantially reducing the memory footprint of both the application and the system software. The nice thing is that it can be done automatically, and that it also reduces the execution time and the power consumption.

Multiview clustering via binary representation has attracted intensive attention due to its effectiveness in handling large-scale multiple view data. However, these kind of clustering approaches usually ignore a very important potential high-order correlation in discrete representation learning. In this article, we propose a novel all-in collaborative multiview binary representation for clustering (AC-MVBC) framework, where multiview collaborative binary representation and clustering structure are learned in a joint manner. Specifically, using a new type of tensor low-rank constraint, the high-order collaborations, i.e., cross-view and inner view collaborations, can be effectively captured in our model. Moreover, by incorporating the Bregman discrepancy, the projective consistency among different views can be guaranteed to achieve a more powerful binary representation. An efficient optimization algorithm is also proposed to solve the objective function with fast convergence empirically. Experimental results on several challenge datasets demonstrate that the proposed method has achieved highly competent performance compared with the state-of-the-art multiview clustering (MVC) methods while maintaining low computational and memory requirements.

CHIMERA: Top-down model for hierarchical, overlapping and directed cluster structures in directed and weighted complex networks

Dynamics of cluster structures in a financial market network

The interplay of cluster structures in light nuclei: The model and the application to 7Li

Coupling of cluster and deformed structures are important for dynamics of nuclear structure. Threshold energy has been discussed to explain cluster structures coupling to deformed states but relation between threshold energy and excitation energy has open problems. Negative-parity superdeformed (SD) states were observed by a $\gamma$-spectroscopy experiment in $^{35}$Cl but its detailed structure is unclear. By analyzing coupling of cluster structures in deformed states and high-lying cluster states in $^{35}$Cl, cluster structures coupling to deformed states and excitation energy of high-lying cluster states are investigated. The antisymmetrized molecular dynamics (AMD) and the generator coordinate method (GCM) are used. An AMD wave function is a Slater determinant of Gaussian wave packets. By energy variational calculations with constraints on deformation and clustering, wave functions of deformed structures and $\alpha$- and $t$-cluster structures are obtained. Adopting those wave functions as GCM basis, wave functions of ground and excited states are calculated. Various deformed bands are obtained and predicted. A $K^\pi = \frac{1}{2}^-$ deformed band, which corresponds to the observed SD band, dominates deformed structure and compact $\alpha$- and $t$-cluster structure components. Particle-hole configurations of the dominant components with deformed and cluster structures are similar. In high-lying states, almost pure $\alpha$- and $t$-cluster states are obtained in negative-parity states, and excitation energies of the $t$-cluster states are higher than those of $\alpha$-cluster states. In conclusions, particle-hole configurations of cluster structure with small intercluster distance are important for coupling to low-energy deformed states. Threshold energies reflect to excitation energies of high-lying almost pure cluster states.

Clustering and deformation are important for dynamics of nuclear structure, and cluster structures couple to deformed states. However, its mechanism is unclear. Cluster structures that couple to each deformed state and the mechanism are investigated in $^{35}$Cl. The antisymmetrized molecular dynamics (AMD) and the generator coordinate method (GCM) are used. An AMD function is a Slater determinant of Gaussian wave packets. By energy variational calculations with constraints for deformation and clustering, wave functions that have deformed and $\alpha$-$^{31}$P and $t$-$^{32}$S cluster structures are obtained. Adopting those wave functions as GCM basis, wave functions of ground and excited states are calculated. Various cluster deformed bands are obtained and predicted. The $K^\pi = \frac{1}{2}^-$ deformed bands contains large amount of $\alpha$-$^{31}$P and $t$-$^{32}$S cluster structure components. Particle-hole configurations of both cluster structures are same as dominant components of the $K^\pi = \frac{1}{2}^-$ bands in small intercluster distance. Particle-hole configurations of cluster structure in small intercluster distance are important for coupling of cluster structure to deformed states.