We outline a new approach for solving optimization problems which enforce triangle inequalities on output variables. We refer to this as metric-constrained optimization, and give several examples where problems of this form arise in machine learning applications and theoretical approximation algorithms for graph clustering. Although these problem are interesting from a theoretical perspective, they are challenging to solve in practice due to the high memory requirement of black-box solvers. In order to address this challenge we first prove that the metric-constrained linear program relaxation of correlation clustering is equivalent to a special case of the metric nearness problem. We then developed a general solver for metric-constrained linear and quadratic programs by generalizing and improving a simple projection algorithm originally developed for metric nearness. We give several novel approximation guarantees for using our framework to find lower bounds for optimal solutions to several challenging graph clustering problems. We also demonstrate the power of our framework by solving optimizing problems involving up to 10^{8} variables and 10^{11} constraints.

Deep Gaussian processes (DGPs) provide a Bayesian non-parametric alternative to standard parametric deep learning models. A DGP is formed by stacking multiple GPs resulting in a well-regularized composition of functions. The Bayesian framework that equips the model with attractive properties, such as implicit capacity control and predictive uncertainty, makes it at the same time challenging to combine with a convolutional structure. This has hindered the application of DGPs in computer vision tasks, an area where deep parametric models (i.e. CNNs) have made breakthroughs. Standard kernels used in DGPs such as radial basis functions (RBFs) are insufficient for handling pixel variability in raw images. In this paper, we build on the recent convolutional GP to develop Convolutional DGP (CDGP) models which effectively capture image level features through the use of convolution kernels, therefore opening up the way for applying DGPs to computer vision tasks. Our model learns local spatial influence and outperforms strong GP based baselines on multi-class image classification. We also consider various constructions of convolution kernel over the image patches, analyze the computational trade-offs and provide an efficient framework for convolutional DGP models. The experimental results on image data such as MNIST, rectangles-image, CIFAR10 and Caltech101 demonstrate the effectiveness of the proposed approaches.

Cluster analysis is widely used in the areas of machine learning and data mining. Fuzzy clustering is a particular method that considers that a data point can belong to more than one cluster. Fuzzy clustering helps obtain flexible clusters, as needed in such applications as text categorization. The performance of a clustering algorithm critically depends on the number of clusters, and estimating the optimal number of clusters is a challenging task. Quality indices help estimate the optimal number of clusters. However, there is no quality index that can obtain an accurate number of clusters for different datasets. Thence, in this paper, we propose a new cluster quality index associated with a visual, graph-based solution that helps choose the optimal number of clusters in fuzzy partitions.

We present a personalized and reliable prediction model for healthcare, which can provide individually tailored medical services such as diagnosis, disease treatment and prevention. Our proposed framework targets to making reliable predictions from time-series data, such as Electronic Health Records (EHR), by modeling two complementary components: i) shared component that captures global trend across diverse patients and ii) patient-specific component that models idiosyncratic variability for each patient. To this end, we propose a composite model of a deep recurrent neural network (RNN) to exploit expressive power of the RNN in estimating global trends from large number of patients, and Gaussian Processes (GP) to probabilistically model individual time-series given relatively small number of time points. We evaluate the strength of our model on diverse and heterogeneous tasks in EHR datasets. The results show that our model significantly outperforms baselines such as RNN, demonstrating clear advantage over existing models when working with noisy medical data.

Clustering using neural networks has recently demon- strated promising performance in machine learning and computer vision applications. However, the performance of current approaches is limited either by unsupervised learn- ing or their dependence on large set of labeled data sam- ples. In this paper, we propose ClusterNet that uses pair- wise semantic constraints from very few labeled data sam- ples (< 5% of total data) and exploits the abundant un- labeled data to drive the clustering approach. We define a new loss function that uses pairwise semantic similarity between objects combined with constrained k-means clus- tering to efficiently utilize both labeled and unlabeled data in the same framework. The proposed network uses con- volution autoencoder to learn a latent representation that groups data into k specified clusters, while also learning the cluster centers simultaneously. We evaluate and com- pare the performance of ClusterNet on several datasets and state of the art deep clustering approaches.

Classifier ensembles are pattern recognition structures composed of a set of classification algorithms (members), organized in a parallel way, and a combination method with the aim of increasing the classification accuracy of a classification system. In this study, we investigate the application of a generalized mixture (GM) functions as a new approach for providing an efficient combination procedure for these systems through the use of dynamic weights in the combination process. Therefore, we present three GM functions to be applied as a combination method. The main advantage of these functions is that they can define dynamic weights at the member outputs, making the combination process more efficient. In order to evaluate the feasibility of the proposed approach, an empirical analysis is conducted, applying classifier ensembles to 25 different classification data sets. In this analysis, we compare the use of the proposed approaches to ensembles using traditional combination methods as well as the state-of-the-art ensemble methods. Our findings indicated gains in terms of performance when comparing the proposed approaches to the traditional ones as well as comparable results with the state-of-the-art methods.

Graph embedding is a central problem in social network analysis and many other applications, aiming to learn the vector representation for each node. While most existing approaches need to specify the neighborhood and the dependence form to the neighborhood, which may significantly degrades the flexibility of representation, we propose a novel graph node embedding method (namely GESF) via the set function technique. Our method can 1) learn an arbitrary form of representation function from neighborhood, 2) automatically decide the significance of neighbors at different distances, and 3) be applied to heterogeneous graph embedding, which may contain multiple types of nodes. Theoretical guarantee for the representation capability of our method has been proved for general homogeneous and heterogeneous graphs and evaluation results on benchmark data sets show that the proposed GESF outperforms the state-of-the-art approaches on producing node vectors for classification tasks.

Due to the advantage of achieving a better performance under weak regularization, elastic net has attracted wide attention in statistics, machine learning, bioinformatics, and other fields. In particular, a variation of the elastic net, adaptive elastic net (AEN), integrates the adaptive grouping effect. In this paper, we aim to develop a new algorithm: Adaptive Elastic Net with Conditional Mutual Information (AEN-CMI) that further improves AEN by incorporating conditional mutual information into the gene selection process. We apply this new algorithm to screen significant genes for two kinds of cancers: colon cancer and leukemia. Compared with other algorithms including Support Vector Machine, Classic Elastic Net and Adaptive Elastic Net, the proposed algorithm, AEN-CMI, obtains the best classification performance using the least number of genes.

Model-based clustering is a popular approach for clustering multivariate data which has seen applications in numerous fields. Nowadays, high-dimensional data are more and more common and the model-based clustering approach has adapted to deal with the increasing dimensionality. In particular, the development of variable selection techniques has received a lot of attention and research effort in recent years. Even for small size problems, variable selection has been advocated to facilitate the interpretation of the clustering results. This review provides a summary of the methods developed for variable selection in model-based clustering. Existing R packages implementing the different methods are indicated and illustrated in application to two data analysis examples.

Fitness landscape analysis investigates features with a high influence on the performance of optimization algorithms, aiming to take advantage of the addressed problem characteristics. In this work, a fitness landscape analysis using problem features is performed for a Multi-objective Bayesian Optimization Algorithm (mBOA) on instances of MNK-landscape problem for 2, 3, 5 and 8 objectives. We also compare the results of mBOA with those provided by NSGA-III through the analysis of their estimated runtime necessary to identify an approximation of the Pareto front. Moreover, in order to scrutinize the probabilistic graphic model obtained by mBOA, the Pareto front is examined according to a probabilistic view. The fitness landscape study shows that mBOA is moderately or loosely influenced by some problem features, according to a simple and a multiple linear regression model, which is being proposed to predict the algorithms performance in terms of the estimated runtime. Besides, we conclude that the analysis of the probabilistic graphic model produced at the end of evolution can be useful to understand the convergence and diversity performances of the proposed approach.