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Finding a consensus embedding from multiple views is the mainstream task in multiview graph-based clustering, in which the key problem is to handle the inconsistence among multiple views. In this article, we consider clustering effectiveness and practical applicability collectively, and propose a parameter-free model to alleviate the inconsistence of multiple views cleverly. To be specific, the proposed model considers the diversities of multiple views as two-layers. The first layer considers the inconsistence among different features of each view and the second layer considers linking the preembeddings of multiple views attentively. By this way, a consensus embedding can be learned via kernel method effectively and the whole learning procedure is parameter-free. To solve the optimization problem involved in the proposed model, we propose an alternative algorithm which is efficient and easy to implement in practice. In the experiments, we evaluate the proposed model on synthetic and real datasets and the experimental results demonstrate its effectiveness. [ABSTRACT FROM AUTHOR]

High-dimensional data are highly correlative and redundant, making it difficult to explore and analyze. Amount of unsupervised dimensionality reduction (DR) methods has been proposed, in which constructing a neighborhood graph is the primary step of DR methods. However, there exist two problems: 1) the construction of graph is usually separate from the selection of projection direction and 2) the original data are inevitably noisy. In this article, we propose an unsupervised adaptive embedding (UAE) method for DR to solve these challenges, which is a linear graph-embedding method. First, an adaptive allocation method of neighbors is proposed to construct the affinity graph. Second, the construction of affinity graph and calculation of projection matrix are integrated together. It considers the local relationship between samples and global characteristic of high-dimensional data, in which the cleaned data matrix is originally proposed to remove noise in subspace. The relationship between our method and local preserving projections (LPPs) is also explored. Finally, an alternative iteration optimization algorithm is derived to solve our model, the convergence and computational complexity of which are also analyzed. Comprehensive experiments on synthetic and benchmark datasets illustrate the superiority of our method. [ABSTRACT FROM AUTHOR]

Data clustering is a fundamental problem in the field of machine learning. Among the numerous clustering techniques, matrix factorization-based methods have achieved impressive performances because they are able to provide a compact and interpretable representation of the input data. However, most of the existing works assume that each class has a global centroid, which does not hold for data with complicated structures. Besides, they cannot guarantee that the sample is associated with the nearest centroid. In this work, we present a concept factorization with the local centroids (CFLCs) approach for data clustering. The proposed model has the following advantages: 1) the samples from the same class are allowed to connect with multiple local centroids such that the manifold structure is captured; 2) the pairwise relationship between the samples and centroids is modeled to produce a reasonable label assignment; and 3) the clustering problem is formulated as a bipartite graph partitioning task, and an efficient algorithm is designed for optimization. Experiments on several data sets validate the effectiveness of the CFLC model and demonstrate its superior performance over the state of the arts. [ABSTRACT FROM AUTHOR]

The conventional subspace clustering method obtains explicit data representation that captures the global structure of data and clusters via the associated subspace. However, due to the limitation of intrinsic linearity and fixed structure, the advantages of prior structure are limited. To address this problem, in this brief, we embed the structured graph learning with adaptive neighbors into the deep autoencoder networks such that an adaptive deep clustering approach, namely, autoencoder constrained clustering with adaptive neighbors (ACC_AN), is developed. The proposed method not only can adaptively investigate the nonlinear structure of data via a parameter-free graph built upon deep features but also can iteratively strengthen the correlations among the deep representations in the learning process. In addition, the local structure of raw data is preserved by minimizing the reconstruction error. Compared to the state-of-the-art works, ACC_AN is the first deep clustering method embedded with the adaptive structured graph learning to update the latent representation of data and structured deep graph simultaneously. [ABSTRACT FROM AUTHOR]

Many modern clustering models can be divided into two separated steps, i.e., constructing a similarity graph (SG) upon samples and partitioning each sample into the corresponding cluster based on SG. Therefore, learning a reasonable SG has become a hot issue in the clustering field. Many previous works that focus on constructing better SG have been proposed. However, most of them follow an ideal assumption that the importance of different features is equal, which is not adapted in practical applications. To alleviate this problem, this article proposes a self-weighted clustering with adaptive neighbors (SWCAN) model that can assign weights for different features, learn an SG, and partition samples into clusters simultaneously. In experiments, we observe that the SWCAN can assign weights for different features reasonably and outperform than comparison clustering models on synthetic and practical data sets. [ABSTRACT FROM AUTHOR]

This paper examines a matrix-regularized multiple kernel learning (MKL) technique based on a notion of $(r,~p)$ norms. For the problem of learning a linear combination in the support vector machine-based framework, model complexity is typically controlled using various regularization strategies on the combined kernel weights. Recent research has developed a generalized $\ell _{p}$ -norm MKL framework with tunable variable $p$ ($p\ge 1$) to support controlled intrinsic sparsity. Unfortunately, this “1-D” vector $\ell _{p}$ -norm hardly exploits potentially useful information on how the base kernels “interact.” To allow for higher order kernel-pair relationships, we extend the “1-D” vector $\ell _{p}$ -MKL to the “2-D” matrix $(r,~p)$ norms ($1\le r,~p<\infty $). We develop a new formulation and an efficient optimization strategy for $(r,~p)$ -MKL with guaranteed convergence. A theoretical analysis and experiments on seven UCI data sets shed light on the superiority of $(r,~p)$ -MKL over $\ell _{p}$ -MKL in various scenarios. [ABSTRACT FROM AUTHOR]

Network in network (NiN) is an effective instance and an important extension of deep convolutional neural network consisting of alternating convolutional layers and pooling layers. Instead of using a linear filter for convolution, NiN utilizes shallow multilayer perceptron (MLP), a nonlinear function, to replace the linear filter. Because of the powerfulness of MLP and $ 1\times 1 $ convolutions in spatial domain, NiN has stronger ability of feature representation and hence results in better recognition performance. However, MLP itself consists of fully connected layers that give rise to a large number of parameters. In this paper, we propose to replace dense shallow MLP with sparse shallow MLP. One or more layers of the sparse shallow MLP are sparely connected in the channel dimension or channel–spatial domain. The proposed method is implemented by applying unshared convolution across the channel dimension and applying shared convolution across the spatial dimension in some computational layers. The proposed method is called convolution in convolution (CiC). The experimental results on the CIFAR10 data set, augmented CIFAR10 data set, and CIFAR100 data set demonstrate the effectiveness of the proposed CiC method. [ABSTRACT FROM PUBLISHER]

Spatial pyramid matching is a standard architecture for categorical image retrieval. However, its performance is largely limited by the prespecified rectangular spatial regions when pooling local descriptors. In this paper, we propose to learn object-shaped and directional receptive fields for image categorization. In particular, different objects in an image are seamlessly constructed by superpixels, while the direction captures human gaze shifting path. By generating a number of superpixels in each image, we construct graphlets to describe different objects. They function as the object-shaped receptive fields for image comparison. Due to the huge number of graphlets in an image, a saliency-guided graphlet selection algorithm is proposed. A manifold embedding algorithm encodes graphlets with the semantics of training image tags. Then, we derive a manifold propagation to calculate the postembedding graphlets by leveraging visual saliency maps. The sequentially propagated graphlets constitute a path that mimics human gaze shifting. Finally, we use the learned graphlet path as receptive fields for local image descriptor pooling. The local descriptors from similar receptive fields of pairwise images more significantly contribute to the final image kernel. Thorough experiments demonstrate the advantage of our approach. [ABSTRACT FROM PUBLISHER]