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With the abundance of data, machine learning applications engaged increased attention in the last decade. An attractive approach to robustify the statistical analysis is to preprocess the data through clustering. This paper develops a low-complexity Riemannian optimization framework for solving optimization problems on the set of positive semidefinite stochastic matrices. The low-complexity feature of the proposed algorithms stems from the factorization of the optimization variable $\mathbf {X}=\mathbf {Y}\mathbf {Y}^{\mathrm{T}}$ X = Y Y T and deriving conditions on the number of columns of $\mathbf {Y}$ Y under which the factorization yields a satisfactory solution. The paper further investigates the embedded and quotient geometries of the resulting Riemannian manifolds. In particular, the paper explicitly derives the tangent space, Riemannian gradients and Hessians, and a retraction operator allowing the design of efficient first and second-order optimization methods for the graph-based clustering applications of interest. The numerical results reveal that the resulting algorithms present a clear complexity advantage as compared with state-of-the-art euclidean and Riemannian approaches for graph clustering applications. [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]

In this paper, we propose to extend the standard Convolutional Dictionary Learning problem to a tensor representation where the activations are constrained to be “low-rank” through a Canonical Polyadic decomposition. We show that this additional constraint increases the robustness of the CDL with respect to noise and improve the interpretability of the final results. In addition, we discuss in detail the advantages of this representation and introduce two algorithms, based on ADMM or FISTA, that efficiently solve this problem. We show that by exploiting the low rank property of activations, they achieve lower complexity than the main CDL algorithms. Finally, we evaluate our approach on a wide range of experiments, highlighting the modularity and the advantages of this tensorial low-rank formulation. [ABSTRACT FROM AUTHOR]

Stochastic unit commitment is an efficient method for grid operation in the presence of significant uncertainties. An example is an operation during a predicted hurricane with uncertain line out-ages. However, the solution quality comes at the cost of substantial computational burden, which makes its adoption challenging. This paper evaluates some possible ways that machine learning can be used to reduce this computational burden. First, a set of feasibility studies is conducted. Results suggest that using machine learning as an assistant to the stochastic unit commitment solver is more advantageous than using it as a standalone solver. In particular, the machine learning model is trained to facilitate solving the problem by determining the unnecessary constraints that can be removed from the original problem without affecting the final accuracy. The variables that can be used as input features/predictors or outputs for the machine learning model are determined through feasibility studies. Then, an algorithm to train and utilize a machine learning model is proposed. The method is tested on a 500-bus synthetic South Carolina system. Various test cases show an average reduction in solution time by more than 90% by using the trained machine learning model to assist the stochastic unit commitment solver. [ABSTRACT FROM AUTHOR]

Estimating set similarity and detecting highly similar sets are fundamental problems in areas such as databases and machine learning. MinHash is a well-known technique for approximating Jaccard similarity of sets and has been successfully used for many applications. Its two compressed versions, $b$ b -bit MinHash and Odd Sketch, can significantly reduce the memory usage of the MinHash, especially for estimating high similarities (i.e., similarities around 1). Although MinHash can be applied to static sets as well as streaming sets, of which elements are given in a streaming fashion, unfortunately, $b$ b -bit MinHash and Odd Sketch fail to deal with streaming data. To solve this problem, we previously designed a memory-efficient sketch method, MaxLogHash, to accurately estimate Jaccard similarities in streaming sets. Compared with MinHash, our method uses smaller sized registers (each register consists of less than 7 bits) to build a compact sketch for each set. In this paper, we further develop a faster method, MaxLogOPH++. Compared with MaxLogHash, MaxLogOPH++ reduces the time complexity for updating each coming element from $O(k)$ O (k) to $O(1)$ O (1) with a small additional memory. We conduct experiments on a variety of datasets, and experimental results demonstrate the efficiency and effectiveness of our methods. [ABSTRACT FROM AUTHOR]

With growth in the number of smart devices and advancements in their hardware, in recent years, data-driven machine learning techniques have drawn significant attention. However, due to privacy and communication issues, it is not possible to collect this data at a centralized location. Federated learning is a machine learning setting where the centralized location trains a learning model over remote devices. Federated learning algorithms cannot be employed in the real world scenarios unless they consider unreliable and resource-constrained nature of the wireless medium. In this paper, we propose a federated learning algorithm that is suitable for cellular wireless networks. We prove its convergence, and provide a sub-optimal scheduling policy that improves the convergence rate. We also study the effect of local computation steps and communication steps on the convergence of the proposed algorithm. We prove, in practice, federated learning algorithms may solve a different problem than the one that they have been employed for if the unreliability of wireless channels is neglected. Finally, through numerous experiments on real and synthetic datasets, we demonstrate the convergence of our proposed algorithm. [ABSTRACT FROM AUTHOR]

Sparse unmixing has become a popular tool for hyperspectral imagery interpretation. It refers to finding the optimal subset of a spectral library to reconstruct the image data and further estimate the proportions of different materials. Recently, multi-objective based sparse unmixing methods have presented promising performance because of their advantages in addressing combinatorial problems. A spectral and multi-objective based sparse unmixing (SMoSU) algorithm was proposed in our previous work, which solves the decision-making problem well. However, it does not show outstanding advantages in strong noise cases. To solve the problem, in this paper, SMoSU is improved based on the estimation of distribution algorithms (EDAs). The machine learning based EDAs have been a reliable approach in solving multi-objective problems. However, most of them are for special problems and relatively weak in theoretical foundations. Thus, it is unreliable to extend it directly to sparse unmixing. Here, we improve EDA on the basis of classification and propose a classification-based model for individual generating under the framework of SMoSU (CM-MoSU). In CM-MoSU, the whole population is divided to be positive and negative. Then, the macroinformation of positive individuals is used to guide the generation of new individuals. Therefore, the optimization task could pay more attention to the feasible space with high quality. Moreover, some theoretical analyses are presented to prove the reliability of CM-MoSU. In experiments, several state-of-the-art sparse unmixing algorithms are compared. Both synthetic and real-world experiments demonstrate the effectiveness of CM-MoSU. [ABSTRACT FROM AUTHOR]

Evolutionary algorithms (EAs) have become the standards and paradigms for solving inverse problems. However, their two inherited operations, namely, the crossover and mutation operations, are complicated and difficult, both in theory and in numerical implementations. In this regard, increasing efforts have been devoted to EAs which are based on probabilistic models (EAPMs) to overcome the shortcomings of available EAs. The population-based incremental learning (PBIL) is an EAPM; moreover, it can bridge the gap between machine learning and the EAs, hence enjoying several merits compared with other EAs. However, lukewarm efforts have been devoted to PBILs, especially the real coded PBILs, in the study of inverse problems in electromagnetics. In this regard, a novel real coded PBIL is being proposed in this paper. In the proposed real coded PBIL, a probability matrix is proposed to randomly generate a population, and the updating formulas for this probability matrix using the so far searched best solution and the best solution of the current population are introduced to strike a balance between convergence performance and solution quality. The proposed real coded PBIL algorithm is numerically experimented on several case studies and promising results are reported in this paper. [ABSTRACT FROM PUBLISHER]

In this paper, we propose a Hierarchical Sampling-based Multi-Instance ensemble LEarning (HSMILE) method. Due to the unique multi-instance learning nature, a positive bag contains at least one positive instance whereas samples (instance and sample are interchangeable terms in this paper) in a negative bag are all negative, simply applying bootstrap sampling to individual bags may severely damage a positive bag because a sampled positive bag may not contain any positive sample at all. To solve the problem, we propose to calculate probable positive sample distributions in each positive bag and use the distributions to preserve at least one positive instance in a sampled bag. The hierarchical sampling involves inter- and intrabag sampling to adequately perturb bootstrap sample sets for multi-instance ensemble learning. Theoretical analysis and experiments confirm that HSMILE outperforms existing multi-instance ensemble learning methods. [ABSTRACT FROM PUBLISHER]

In multiple instance learning problems, patterns are often given as bags and each bag consists of some instances. Most of existing research in the area focuses on multiple instance classification and multiple instance regression, while very limited work has been conducted for multiple instance clustering (MIC). This paper formulates a novel framework, maximum margin multiple instance clustering (M^3IC), for MIC. However, it is impractical to directly solve the optimization problem of M^3IC. Therefore, M^3IC is relaxed in this paper to enable an efficient optimization solution with a combination of the constrained concave-convex procedure and the cutting plane method. Furthermore, this paper presents some important properties of the proposed method and discusses the relationship between the proposed method and some other related ones. An extensive set of empirical results are shown to demonstrate the advantages of the proposed method against existing research for both effectiveness and efficiency. [ABSTRACT FROM AUTHOR]

This paper introduces a framework of experienced-based decision making as an extension of case-based decision making, a recently proposed alternative to expected utility theory. In experienced-based decision making, an agent faced with a new decision problem acts on the basis of experience gathered from previous problems in the past, either through predicting the utility of potential actions or through establishing a direct relationship between decision problems and appropriate actions. In the paper, a realization of the latter approach in the form of "satisficing" decision trees is proposed. [ABSTRACT FROM AUTHOR]

Texts in natural scenes carry critical semantic clues for understanding images. When capturing natural scene images, especially by handheld cameras, a common artifact, i.e., blur, frequently happens. To improve the visual quality of such images, deblurring techniques are desired, which also play an important role in character recognition and image understanding. In this paper, we study the problem of recovering the clear scene text by exploiting the text field characteristics. A series of text-specific multiscale dictionaries (TMD) and a natural scene dictionary is learned for separately modeling the priors on the text and nontext fields. The TMD-based text field reconstruction helps to deal with the different scales of strings in a blurry image effectively. Furthermore, an adaptive version of nonuniform deblurring method is proposed to efficiently solve the real-world spatially varying problem. Dictionary learning allows more flexible modeling with respect to the text field property, and the combination with the nonuniform method is more appropriate in real situations where blur kernel sizes are depth dependent. Experimental results show that the proposed method achieves the deblurring results with better visual quality than the state-of-the-art methods. [ABSTRACT FROM PUBLISHER]

Both cost-sensitive classification and online learning have been extensively studied in data mining and machine learning communities, respectively. However, very limited study addresses an important intersecting problem, that is, “Cost-Sensitive Online Classification”. In this paper, we formally study this problem, and propose a new framework for Cost-Sensitive Online Classification by directly optimizing cost-sensitive measures using online gradient descent techniques. Specifically, we propose two novel cost-sensitive online classification algorithms, which are designed to directly optimize two well-known cost-sensitive measures: (i) maximization of weighted sum of sensitivity and specificity, and (ii) minimization of weighted misclassification cost. We analyze the theoretical bounds of the cost-sensitive measures made by the proposed algorithms, and extensively examine their empirical performance on a variety of cost-sensitive online classification tasks. Finally, we demonstrate the application of the proposed technique for solving several online anomaly detection tasks, showing that the proposed technique could be a highly efficient and effective tool to tackle cost-sensitive online classification tasks in various application domains. [ABSTRACT FROM AUTHOR]

Process discovery is the learning task that entails the construction of process models from event logs of information systems. Typically, these event logs are large data sets that contain the process executions by registering what activity has taken place at a certain moment in time. By far the most arduous challenge for process discovery algorithms consists of tackling the problem of accurate and comprehensible knowledge discovery from highly flexible environments. Event logs from such flexible systems often contain a large variety of process executions which makes the application of process mining most interesting. However, simply applying existing process discovery techniques will often yield highly incomprehensible process models because of their inaccuracy and complexity. With respect to resolving this problem, trace clustering is one very interesting approach since it allows to split up an existing event log so as to facilitate the knowledge discovery process. In this paper, we propose a novel trace clustering technique that significantly differs from previous approaches. Above all, it starts from the observation that currently available techniques suffer from a large divergence between the clustering bias and the evaluation bias. By employing an active learning inspired approach, this bias divergence is solved. In an assessment using four complex, real-life event logs, it is shown that our technique significantly outperforms currently available trace clustering techniques. [ABSTRACT FROM PUBLISHER]

In this paper, we use shape grammars (SGs) for facade parsing, which amounts to segmenting 2D building facades into balconies, walls, windows, and doors in an architecturally meaningful manner. The main thrust of our work is the introduction of reinforcement learning (RL) techniques to deal with the computational complexity of the problem. RL provides us with techniques such as Q-learning and state aggregation which we exploit to efficiently solve facade parsing. We initially phrase the 1D parsing problem in terms of a Markov Decision Process, paving the way for the application of RL-based tools. We then develop novel techniques for the 2D shape parsing problem that take into account the specificities of the facade parsing problem. Specifically, we use state aggregation to enforce the symmetry of facade floors and demonstrate how to use RL to exploit bottom-up, image-based guidance during optimization. We provide systematic results on the Paris building dataset and obtain state-of-the-art results in a fraction of the time required by previous methods. We validate our method under diverse imaging conditions and make our software and results available online. [ABSTRACT FROM AUTHOR]

Bottom-up saliency detection aims to detect salient areas within natural images usually without learning from labeled images. Typically, the saliency map of an image is inferred by only using the information within this image (referred to as the “current image”). While efficient, such single-image-based methods may fail to obtain reliable results, because the information within a single image may be insufficient for defining saliency. In this paper, we investigate how saliency detection can benefit from the nearest neighbor structure in the image space. First, we show that existing methods can be improved by extending them to include the visual neighborhood information. This verifies the significance of the neighbors. Next, a solution of multitask sparsity pursuit is proposed to integrate the current image and its neighbors to collaboratively detect saliency. The integration is done by first representing each image as a feature matrix, and then seeking the consistently sparse elements from the joint decompositions of multiple matrices into pairs of low-rank and sparse matrices. The computational procedure is formulated as a constrained nuclear norm and \ell2,1-norm minimization problem, which is convex and can be solved efficiently with the augmented Lagrange multiplier method. Besides the nearest neighbor structure in the visual feature space, the proposed model can also be generalized to handle multiple visual features. Extensive experiments have clearly validated its superiority over other state-of-the-art methods. [ABSTRACT FROM PUBLISHER]

Level set methods are a popular way to solve the image segmentation problem. The solution contour is found by solving an optimization problem where a cost functional is minimized. Gradient descent methods are often used to solve this optimization problem since they are very easy to implement and applicable to general nonconvex functionals. They are, however, sensitive to local minima and often display slow convergence. Traditionally, cost functionals have been modified to avoid these problems. In this paper, we instead propose using two modified gradient descent methods, one using a momentum term and one based on resilient propagation. These methods are commonly used in the machine learning community. In a series of 2-D/3-D-experiments using real and synthetic data with ground truth, the modifications are shown to reduce the sensitivity for local optima and to increase the convergence rate. The parameter sensitivity is also investigated. The proposed methods are very simple modifications of the basic method, and are directly compatible with any type of level set implementation. Downloadable reference code with examples is available online. [ABSTRACT FROM PUBLISHER]

Assessing the similarity between cases is a key aspect of the retrieval phase in case-based reasoning (CBR). In most CBR work, similarity is assessed based on feature value descriptions of cases using similarity metrics, which use these feature values. In fact, it might be said that this notion of a feature value representation is a defining part of the CBR worldview—it underpins the idea of a problem space with cases located relative to each other in this space. Recently, a variety of similarity mechanisms have emerged that are not founded on this feature space idea. Some of these new similarity mechanisms have emerged in CBR research and some have arisen in other areas of data analysis. In fact, research on kernel-based learning is a rich source of novel similarity representations because of the emphasis on encoding domain knowledge in the kernel function. In this paper, we present a taxonomy that organizes these new similarity mechanisms and more established similarity mechanisms in a coherent framework. [ABSTRACT FROM AUTHOR]

In this paper, we propose two cooperative ensemble learning algorithms, i.e., NegBagg and NegBoost, for designing neural network (NN) ensembles. The proposed algorithms incrementally train different individual NNs in an ensemble using the negative correlation learning algorithm. Bagging and boosting algorithms are used in NegBagg and NegBoost, respectively, to create different training sets for different NNs in the ensemble. The idea behind using negative correlation learning in conjunction with the bagging/boosting algorithm is to facilitate interaction and cooperation among NNs during their training. Both NegBagg and NegBoost use a constructive approach to automatically determine the number of hidden neurons for NNs. NegBoost also uses the constructive approach to automatically determine the number of NNs for the ensemble. The two algorithms have been tested on a number of benchmark problems in machine learning and NNs, including Australian credit card assessment, breast cancer, diabetes, glass, heart disease, letter recognition, satellite, soybean, and waveform problems. The experimental results show that NegBagg and NegBoost require a small number of training epochs to produce compact NN ensembles with good generalization. [ABSTRACT FROM AUTHOR]

Support vector machines (SVMs) have been extensively used. However, it is known that SVMs face difficulty in solving large complex problems due to the intensive computation involved in their training algorithms, which are at least quadratic with respect to the number of training examples. This paper proposes a new, simple, and efficient network architecture which consists of several SVMs each trained on a small subregion of the whole data sampling space and the same number of simple neural quantizer modules which inhibit the outputs of all the remote SVMs and only allow a single local SVM to fire (produce actual output) at any time. In principle, this region-computing based modular network method can significantly reduce the learning time of SYM algorithms without sacrificing much generalization performance. The experiments on a few real large complex bench- mark problems demonstrate that our method can be significantly faster than single SVMs without losing much generalization performance. [ABSTRACT FROM AUTHOR]