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Sparse unmixing (SU) algorithms use the existing spectral library as prior knowledge to analyze the endmembers and estimate abundance maps. The majority of SU algorithms use loss functions based on the $L_{2,1}$ -norm or $F$ -norm to minimize reconstruction error. They have different advantages and shortcomings. In short, $F$ -norm has a differentiable characteristic, and it is easy to minimize as a loss function. However, it is very sensitive to heavy noise and outliers. While the $L_{2,1}$ -norm emphasizes the reconstruction error on each band and is robust to noise with different intensities in different bands. But the $L_{2,1}$ -norm is nondifferentiable at zero-point. This article introduces an adaptive loss function based on the $\sigma $ -norm for SU, which combines the advantages of the $L_{2,1}$ -norm and $F$ -norm. The adaptive loss function is related to a nonnegative parameter $\sigma $. By adjusting the parameter $\sigma $ , the adaptive loss function can approach the $F$ -norm or $L_{2,1}$ -norm. To the best of our knowledge, it is the first time to apply an adaptive loss function to SU. Moreover, the adaptive loss function is globally differentiable, and we propose an optimization algorithm for the adaptive loss function and verify its convergence. Experiments on real-world and synthetic HSIs show that the adaptive loss function effectively enhances the performance of the SU algorithms. [ABSTRACT FROM AUTHOR]

Binarized neural networks (BNNs) have drawn significant attention in recent years, owing to great potential in reducing computation and storage consumption. While it is attractive, traditional BNNs usually suffer from slow convergence speed and dramatical accuracy-degradation on large-scale classification datasets. To minimize the gap between BNNs and deep neural networks (DNNs), we propose a new framework of designing BNNs, dubbed Hyper-BinaryNet, from the aspect of enhanced information-flow. Our contributions are threefold: 1) Considering the capacity-limitation in the backward pass, we propose an 1-bit convolution module named HyperConv. By exploiting the capacity of auxiliary neural networks, BNNs gain better performance on large-scale image classification task. 2) Considering the slow convergence speed in BNNs, we rethink the gradient accumulation mechanism and propose a hyper accumulation technique. By accumulating gradients in multiple variables rather than one as before, the gradient paths for each weight increase, which escapes BNNs from the gradient bottleneck problem during training. 3) Considering the ill-posed optimization problem, a novel gradient estimation warmup strategy, dubbed STE-Warmup, is developed. This strategy prevents BNNs from the unstable optimization process by progressively transferring neural networks from 32-bit to 1-bit. We conduct evaluations with variant architectures on three public datasets: CIFAR-10/100 and ImageNet. Compared with state-of-the-art BNNs, Hyper-BinaryNet shows faster convergence speed and outperforms existing BNNs by a large margin. [ABSTRACT FROM AUTHOR]

The multiple kernel $k$ -means (MKKM) and its variants utilize complementary information from different sources, achieving better performance than kernel $k$ -means (KKM). However, the optimization procedures of most previous works comprise two stages, learning the continuous relaxation matrix and obtaining the discrete one by extra discretization procedures. Such a two-stage strategy gives rise to a mismatched problem and severe information loss. Even worse, most existing MKKM methods overlook the correlation among prespecified kernels, which leads to the fusion of mutually redundant kernels and bad effects on the diversity of information sources, finally resulting in unsatisfying results. To address these issues, we elaborate a novel Discrete and Parameter-free Multiple Kernel $k$ -means (DPMKKM) model solved by an alternative optimization method, which can directly obtain the cluster assignment results without subsequent discretization procedure. Moreover, DPMKKM can measure the correlation among kernels by implicitly introducing a regularization term, which is able to enhance kernel fusion by reducing redundancy and improving diversity. Noteworthily, the time complexity of optimization algorithm is successfully reduced, through masterly utilizing of coordinate descent technique, which contributes to higher algorithm efficiency and broader applications. What’s more, our proposed model is parameter-free avoiding intractable hyperparameter tuning, which makes it feasible in practical applications. Lastly, extensive experiments conducted on a number of real-world datasets illustrated the effectiveness and superiority of the proposed DPMKKM model. [ABSTRACT FROM AUTHOR]

$k$ k -means method using Lloyd heuristic is a traditional clustering method which has played a key role in multiple downstream tasks of machine learning because of its simplicity. However, Lloyd heuristic always finds a bad local minimum, i.e., the bad local minimum makes objective function value not small enough, which limits the performance of $k$ k -means. In this paper, we use coordinate descent (CD) method to solve the problem. First, we show that the $k$ k -means minimization problem can be reformulated as a trace maximization problem, then a simple and efficient coordinate descent scheme is proposed to solve the maximization problem. Two interesting findings through theory are that Lloyd cannot decrease the objective function value of $k$ k -means produced by our CD further, and our proposed method CD to solve $k$ k -means problem can avoid produce empty clusters. In addition, according to the computational complexity analysis, it is verified CD has the same time complexity with original $k$ k -means method. Extensive experiments including statistical hypothesis testing, on several real-world datasets with varying number of clusters, varying number of samples and varying number of dimensions show that CD performs better compared to Lloyd, i.e., lower objective value, better local minimum and fewer iterations. And CD is more robust to initialization than Lloyd whether the initialization strategy is random or initialization of $k$ k -means++. [ABSTRACT FROM AUTHOR]

Due to the exponential growth of multimedia data, multi-modal hashing as a promising technique to make cross-view retrieval scalable is attracting more and more attention. However, most of the existing multi-modal hashing methods either divide the learning process unnaturally into two separate stages or treat the discrete optimization problem simplistically as a continuous one, which leads to suboptimal results. Recently, a few discrete multi-modal hashing methods that try to address such issues have emerged, but they still ignore several important discrete constraints (such as the balance and decorrelation of hash bits). In this paper, we overcome those limitations by proposing a novel method named “Enhanced Discrete Multi-modal Hashing (EDMH)” which learns binary codes and hashing functions simultaneously from the pairwise similarity matrix of data, under the aforementioned discrete constraints. Although the model of EDMH looks a lot more complex than the other models for multi-modal hashing, we are actually able to develop a fast iterative learning algorithm for it, since the subproblems of its optimization all have closed-form solutions after introducing a couple of auxiliary variables. Our experimental results on three real-world datasets have revealed the usefulness of those previously ignored discrete constraints and demonstrated that EDMH not only performs much better than state-of-the-art competitors according to several retrieval metrics but also runs much faster than most of them. [ABSTRACT FROM AUTHOR]

Recently, several robust principle component analysis (RPCA) models have been proposed to improve the robustness of principle component analysis (PCA). But an important problem that the robustness to outliers affects the discrimination of correct samples has not been solved yet. To solve this problem, we propose a truncated robust principle component analysis (T-RPCA) model which treats correct samples and outliers separately. In fact, the proposed model performs an implicitly truncated weighted learning scheme which is more reasonable for robustness learning respective to previous works. Moreover, we propose a re-weighted (RW) optimization framework to solve a general problem and generalize two sub-frameworks upon it. To be specific, the first sub-framework orients a general truncated loss optimization problem which contains the objective problem of T-RPCA, and the second one focuses on a general singular-value based optimization problem. Besides, we provide rigorously theoretical guarantees for the proposed model, RW framework and sub-frameworks. Empirical studies demonstrate that the proposed T-RPCA model outperforms previous RPCA models on reconstruction and classification tasks. [ABSTRACT FROM AUTHOR]

Semisupervised band selection (BS) technique plays an important role in processing hyperspectral images (HSIs) because of its superiority of using the limited labeled data and plentiful unlabeled data to select the discriminative and informative feature, which copes with the problem of high-dimensional and scare labeled samples of HSIs. Among semisupervised BS models, graph-based methods are superior to others in many situations and have received more and more attention. However, traditional graph-based models construct a similarity matrix and select valuable bands independently. The similarity matrix remains constant, which will damage the local manifold structure and lead to a suboptimal result. To solve this problem, we propose a semisupervised band selection with an optimal graph (BSOG) approach, which performs BS and local structure learning simultaneously. Instead of fixing the input similarity matrix, the similarity matrix is updated constantly to learn a better local structure. Besides, the learned similarity matrix is adaptive. Then, the optimal band subset can be selected by analyzing the obtained projection matrix $\boldsymbol W$. An efficient and simple optimization algorithm is proposed to solve this model. Experiments on four real HSIs data validate the effectiveness of the proposed model. [ABSTRACT FROM AUTHOR]

Spectral clustering methods are gaining more and more interests and successfully applied in many fields because of their superior performance. However, there still exist two main problems to be solved: 1) spectral clustering methods consist of two successive optimization stages—spectral embedding and spectral rotation, which may not lead to globally optimal solutions, 2) and it is known that spectral methods are time-consuming with very high computational complexity. There are methods proposed to reduce the complexity for data vectors but not for graphs that only have information about similarity matrices. In this paper, we propose a new method to solve these two challenging problems for graph clustering. In the new method, a new framework is established to perform spectral embedding and spectral rotation simultaneously. The newly designed objective function consists of both terms of embedding and rotation, and we use an improved spectral rotation method to make it mathematically rigorous for the optimization. To further accelerate the algorithm, we derive a low-dimensional representation matrix from a graph by using label propagation, with which, in return, we can reconstruct a double-stochastic and positive semidefinite similarity matrix. Experimental results demonstrate that our method has excellent performance in time cost and accuracy. [ABSTRACT FROM AUTHOR]

• ε -dragging technique was introduced into BLS to improve the discriminative ability. • Regularization is adopted to optimize network structure. • Theoretical analysis verifies the convergence of the algorithm. • Numerical simulations are conducted to verify the performance of the algorithm. This paper presents the framework of the smoothing group L 1 / 2 regularized discriminative broad learning system for pattern classification and regression. The core idea is to improve the sparseness of the standard broad learning system and improve performance on recognition and generalization. First, the ε -dragging technique is introduced into the standard broad learning system to relax regression targets and enlarge distances between categories. Then, we integrate the group L 1 / 2 regularization to optimize the network architecture to achieve sparsity. For the original group L 1 / 2 regularization, the objective function is non-convex and non-smooth, which is hard for theoretical analysis. Therefore, we propose a simple and effective smoothing technique, i.e.,smoothing group L 1 / 2 regularization, which can effectively eliminate the deficiency of the original group L 1 / 2 regularization. As a result, the final weights projection matrix has a compact form and shows discriminative power capability. In addition, the alternating direction method of multipliers was adopted to optimize the algorithm. The simulation results show that the proposed algorithm has redundancy control capability and improved performance on recognition and generalization. The simulation results proves the efficiency of the theoretical analysis. [ABSTRACT FROM AUTHOR]