Epilepsy is one of the most common neurological disorders that can be diagnosed through electroencephalogram (EEG), in which the following epileptic events can be observed: pre-ictal, ictal, post-ictal, and interictal. In this paper, we present a novel method for epilepsy detection into two differentiation contexts: binary and multiclass classification. For feature extraction, a total of 105 measures were extracted from power spectrum, spectrogram, and bispectrogram. For classifier building, eight different machine learning algorithms were used. Our method was applied in a widely used EEG database. As a result, random forest and backpropagation based on multilayer perceptron algorithms reached the highest accuracy for binary (98.75%) and multiclass (96.25%) classification problems, respectively. Subsequently, the statistical tests did not find a model that would achieve a better performance than the other classifiers. In the evaluation based on confusion matrices, it was also not possible to identify a classifier that stands out in relation to other models for EEG classification. Even so, our results are promising and competitive with the findings in the literature.

Because GBDT inherits the good performance from its ensemble essence, much attention has been drawn to the optimization of this model. With its popularization, an increasing need for model interpretation arises. Besides the commonly used feature importance as a global interpretation, feature contribution is a local measure that reveals the relationship between a specific instance and the related output. This work focuses on the local interpretation and proposes an unified computation mechanism to get the instance-level feature contributions for GBDT in any version. Practicality of this mechanism is validated by the listed experiments as well as applications in real industry scenarios.

Clustering is an essential technique for network analysis, with applications in a diverse range of fields. Although spectral clustering is a popular and effective method, it fails to consider higher-order structure and can perform poorly on directed networks. One approach is to capture and cluster higher-order structures using motif adjacency matrices. However, current formulations fail to take edge weights into account, and thus are somewhat limited when weight is a key component of the network under study. We address these shortcomings by exploring motif-based weighted spectral clustering methods. We present new and computationally useful matrix formulae for motif adjacency matrices on weighted networks, which can be used to construct efficient algorithms for any anchored or non-anchored motif on three nodes. In a very sparse regime, our proposed method can handle graphs with five million nodes and tens of millions of edges in under ten minutes. We further use our framework to construct a motif-based approach for clustering bipartite networks. We provide comprehensive experimental results, demonstrating (i) the scalability of our approach, (ii) advantages of higher-order clustering on synthetic examples, and (iii) the effectiveness of our techniques on a variety of real world data sets. We conclude that motif-based spectral clustering is a valuable tool for analysis of directed and bipartite weighted networks, which is also scalable and easy to implement.

In many artificial intelligence and computer vision systems, the same object can be observed at distinct viewpoints or by diverse sensors, which raises the challenges for recognizing objects from different, even heterogeneous views. Multi-view discriminant analysis (MvDA) is an effective multi-view subspace learning method, which finds a discriminant common subspace by jointly learning multiple view-specific linear projections for object recognition from multiple views, in a non-pairwise way. In this paper, we propose the kernel version of multi-view discriminant analysis, called kernel multi-view discriminant analysis (KMvDA). To overcome the well-known computational bottleneck of kernel methods, we also study the performance of using random Fourier features (RFF) to approximate Gaussian kernels in KMvDA, for large scale learning. Theoretical analysis on stability of this approximation is developed. We also conduct experiments on several popular multi-view datasets to illustrate the effectiveness of our proposed strategy.

The paper proposes an approach for surrogate-assisted tuning of knowledge discovery algorithms. The approach is based on the prediction of both the quality and performance of the target algorithm. The prediction is furtherly used as objectives for the optimization and tuning of the algorithm. The approach is investigated using clinical pathways (CP) discovery problem resolved using the evolutionary-based clustering of electronic health records (EHR). Target algorithm and the proposed approach were applied to the discovery of CPs for Acute Coronary Syndrome patients in 3434 EHRs of patients treated in Almazov National Medical Research Center (Saint Petersburg, Russia). The study investigates the possible acquisition of interpretable clusters of typical CPs within a single disease. It shows how the approach could be used to improve complex data-driven analytical knowledge discovery algorithms. The study of the results includes the feature importance of the best surrogate model and discover how the parameters of input data influence the predictions.

We present a direct (primal only) derivation of Mirror Descent as a "partial" discretization of gradient flow on a Riemannian manifold where the metric tensor is the Hessian of the Mirror Descent potential function. We argue that this discretization is more faithful to the geometry than Natural Gradient Descent, which is obtained by a "full" forward Euler discretization. This view helps shed light on the relationship between the methods and allows generalizing Mirror Descent to any Riemannian geometry, even when the metric tensor is not a Hessian, and thus there is no "dual".

Image classification has been studied extensively but there has been limited work in the direction of using non-conventional, external guidance other than traditional image-label pairs to train such models. In this thesis we present a set of methods to leverage information about the semantic hierarchy induced by class labels. In the first part of the thesis, we inject label-hierarchy knowledge to an arbitrary classifier and empirically show that availability of such external semantic information in conjunction with the visual semantics from images boosts overall performance. Taking a step further in this direction, we model more explicitly the label-label and label-image interactions by using order-preserving embedding-based models, prevalent in natural language, and tailor them to the domain of computer vision to perform image classification. Although, contrasting in nature, both the CNN-classifiers injected with hierarchical information, and the embedding-based models outperform a hierarchy-agnostic model on the newly presented, real-world ETH Entomological Collection image dataset.

We consider autocovariance operators of a stationary stochastic process on a Polish space that is embedded into a reproducing kernel Hilbert space. We investigate how empirical estimates of these operators converge along realizations of the process under various conditions. In particular, we examine ergodic and strongly mixing processes and prove several asymptotic results as well as finite sample error bounds with a detailed analysis for the Gaussian kernel. We provide applications of our theory in terms of consistency results for kernel PCA with dependent data and the conditional mean embedding of transition probabilities. Finally, we use our approach to examine the nonparametric estimation of Markov transition operators and highlight how our theory can give a consistency analysis for a large family of spectral analysis methods including kernel-based dynamic mode decomposition.

Graph representation learning based on graph neural networks (GNNs) can greatly improve the performance of downstream tasks, such as node and graph classification. However, the general GNN models do not aggregate node information in a hierarchical manner, and can miss key higher-order structural features of many graphs. The hierarchical aggregation also enables the graph representations to be explainable. In addition, supervised graph representation learning requires labeled data, which is expensive and error-prone. To address these issues, we present an unsupervised graph representation learning method, Unsupervised Hierarchical Graph Representation (UHGR), which can generate hierarchical representations of graphs. Our method focuses on maximizing mutual information between "local" and high-level "global" representations, which enables us to learn the node embeddings and graph embeddings without any labeled data. To demonstrate the effectiveness of the proposed method, we perform the node and graph classification using the learned node and graph embeddings. The results show that the proposed method achieves comparable results to state-of-the-art supervised methods on several benchmarks. In addition, our visualization of hierarchical representations indicates that our method can capture meaningful and interpretable clusters.

A sum-product network (SPN) is a probabilistic model, based on a rooted acyclic directed graph, in which terminal nodes represent univariate probability distributions and non-terminal nodes represent convex combinations (weighted sums) and products of probability functions. They are closely related to probabilistic graphical models, in particular to Bayesian networks with multiple context-specific independencies. Their main advantage is the possibility of building tractable models from data, i.e., models that can perform several inference tasks in time proportional to the number of links in the graph. They are somewhat similar to neural networks and can address the same kinds of problems, such as image processing and natural language understanding. This paper offers a survey of SPNs, including their definition, the main algorithms for inference and learning from data, the main applications, a brief review of software libraries, and a comparison with related models