The focus of Part I of this monograph has been on both the fundamental properties, graph topologies, and spectral representations of graphs. Part II embarks on these concepts to address the algorithmic and practical issues centered round data/signal processing on graphs, that is, the focus is on the analysis and estimation of both deterministic and random data on graphs. The fundamental ideas related to graph signals are introduced through a simple and intuitive, yet illustrative and general enough case study of multisensor temperature field estimation. The concept of systems on graph is defined using graph signal shift operators, which generalize the corresponding principles from traditional learning systems. At the core of the spectral domain representation of graph signals and systems is the Graph Discrete Fourier Transform (GDFT). The spectral domain representations are then used as the basis to introduce graph signal filtering concepts and address their design, including Chebyshev polynomial approximation series. Ideas related to the sampling of graph signals are presented and further linked with compressive sensing. Localized graph signal analysis in the joint vertex-spectral domain is referred to as the vertex-frequency analysis, since it can be considered as an extension of classical time-frequency analysis to the graph domain of a signal. Important topics related to the local graph Fourier transform (LGFT) are covered, together with its various forms including the graph spectral and vertex domain windows and the inversion conditions and relations. A link between the LGFT with spectral varying window and the spectral graph wavelet transform (SGWT) is also established. Realizations of the LGFT and SGWT using polynomial (Chebyshev) approximations of the spectral functions are further considered. Finally, energy versions of the vertex-frequency representations are introduced.
Human knowledge provides a formal understanding of the world. Knowledge graphs that represent structural relations between entities have become an increasingly popular research direction towards cognition and human-level intelligence. In this survey, we provide a comprehensive review on knowledge graph covering overall research topics about 1) knowledge graph representation learning, 2) knowledge acquisition and completion, 3) temporal knowledge graph, and 4) knowledge-aware applications, and summarize recent breakthroughs and perspective directions to facilitate future research. We propose a full-view categorization and new taxonomies on these topics. Knowledge graph embedding is organized from four aspects of representation space, scoring function, encoding models and auxiliary information. For knowledge acquisition, especially knowledge graph completion, embedding methods, path inference and logical rule reasoning are reviewed. We further explore several emerging topics including meta relational learning, commonsense reasoning, and temporal knowledge graphs. To facilitate future research on knowledge graphs, we also provide a curated collection of datasets and open-source libraries on different tasks. In the end, we have a thorough outlook on several promising research directions.
Real-world applications often combine learning and optimization problems on graphs. For instance, our objective may be to cluster the graph in order to detect meaningful communities (or solve other common graph optimization problems such as facility location, maxcut, and so on). However, graphs or related attributes are often only partially observed, introducing learning problems such as link prediction which must be solved prior to optimization. We propose an approach to integrate a differentiable proxy for common graph optimization problems into training of machine learning models for tasks such as link prediction. This allows the model to focus specifically on the downstream task that its predictions will be used for. Experimental results show that our end-to-end system obtains better performance on example optimization tasks than can be obtained by combining state of the art link prediction methods with expert-designed graph optimization algorithms.
Although recent neural conversation models have shown great potential, they often generate bland and generic responses. While various approaches have been explored to diversify the output of the conversation model, the improvement often comes at the cost of decreased relevance. In this paper, we propose a method to jointly optimize diversity and relevance that essentially fuses the latent space of a sequence-to-sequence model and that of an autoencoder model by leveraging novel regularization terms. As a result, our approach induces a latent space in which the distance and direction from the predicted response vector roughly match the relevance and diversity, respectively. This property also lends itself well to an intuitive visualization of the latent space. Both automatic and human evaluation results demonstrate that the proposed approach brings significant improvement compared to strong baselines in both diversity and relevance.
Embedding models for deterministic Knowledge Graphs (KG) have been extensively studied, with the purpose of capturing latent semantic relations between entities and incorporating the structured knowledge into machine learning. However, there are many KGs that model uncertain knowledge, which typically model the inherent uncertainty of relations facts with a confidence score, and embedding such uncertain knowledge represents an unresolved challenge. The capturing of uncertain knowledge will benefit many knowledge-driven applications such as question answering and semantic search by providing more natural characterization of the knowledge. In this paper, we propose a novel uncertain KG embedding model UKGE, which aims to preserve both structural and uncertainty information of relation facts in the embedding space. Unlike previous models that characterize relation facts with binary classification techniques, UKGE learns embeddings according to the confidence scores of uncertain relation facts. To further enhance the precision of UKGE, we also introduce probabilistic soft logic to infer confidence scores for unseen relation facts during training. We propose and evaluate two variants of UKGE based on different learning objectives. Experiments are conducted on three real-world uncertain KGs via three tasks, i.e. confidence prediction, relation fact ranking, and relation fact classification. UKGE shows effectiveness in capturing uncertain knowledge by achieving promising results on these tasks, and consistently outperforms baselines on these tasks.
We present Deep Graph Infomax (DGI), a general approach for learning node representations within graph-structured data in an unsupervised manner. DGI relies on maximizing mutual information between patch representations and corresponding high-level summaries of graphs---both derived using established graph convolutional network architectures. The learnt patch representations summarize subgraphs centered around nodes of interest, and can thus be reused for downstream node-wise learning tasks. In contrast to most prior approaches to unsupervised learning with GCNs, DGI does not rely on random walk objectives, and is readily applicable to both transductive and inductive learning setups. We demonstrate competitive performance on a variety of node classification benchmarks, which at times even exceeds the performance of supervised learning.
Clustering and classification critically rely on distance metrics that provide meaningful comparisons between data points. We present mixed-integer optimization approaches to find optimal distance metrics that generalize the Mahalanobis metric extensively studied in the literature. Additionally, we generalize and improve upon leading methods by removing reliance on pre-designated "target neighbors," "triplets," and "similarity pairs." Another salient feature of our method is its ability to enable active learning by recommending precise regions to sample after an optimal metric is computed to improve classification performance. This targeted acquisition can significantly reduce computational burden by ensuring training data completeness, representativeness, and economy. We demonstrate classification and computational performance of the algorithms through several simple and intuitive examples, followed by results on real image and medical datasets.
Many problems on signal processing reduce to nonparametric function estimation. We propose a new methodology, piecewise convex fitting (PCF), and give a two-stage adaptive estimate. In the first stage, the number and location of the change points is estimated using strong smoothing. In the second stage, a constrained smoothing spline fit is performed with the smoothing level chosen to minimize the MSE. The imposed constraint is that a single change point occurs in a region about each empirical change point of the first-stage estimate. This constraint is equivalent to requiring that the third derivative of the second-stage estimate has a single sign in a small neighborhood about each first-stage change point. We sketch how PCF may be applied to signal recovery, instantaneous frequency estimation, surface reconstruction, image segmentation, spectral estimation and multivariate adaptive regression.
Machine Learning has been the quintessential solution for many AI problems, but learning is still heavily dependent on the specific training data. Some learning models can be incorporated with a prior knowledge in the Bayesian set up, but these learning models do not have the ability to access any organised world knowledge on demand. In this work, we propose to enhance learning models with world knowledge in the form of Knowledge Graph (KG) fact triples for Natural Language Processing (NLP) tasks. Our aim is to develop a deep learning model that can extract relevant prior support facts from knowledge graphs depending on the task using attention mechanism. We introduce a convolution-based model for learning representations of knowledge graph entity and relation clusters in order to reduce the attention space. We show that the proposed method is highly scalable to the amount of prior information that has to be processed and can be applied to any generic NLP task. Using this method we show significant improvement in performance for text classification with News20, DBPedia datasets and natural language inference with Stanford Natural Language Inference (SNLI) dataset. We also demonstrate that a deep learning model can be trained well with substantially less amount of labeled training data, when it has access to organised world knowledge in the form of knowledge graph.
Neural word embeddings have been widely used in biomedical Natural Language Processing (NLP) applications since they provide vector representations of words that capture the semantic properties of words and the linguistic relationship between words. Many biomedical applications use different textual sources to train word embeddings and apply these word embeddings to downstream biomedical applications. However, there has been little work on comprehensively evaluating the word embeddings trained from these resources. In this study, we provide a comprehensive empirical evaluation of word embeddings trained from four different resources, namely clinical notes, biomedical publications, Wikepedia, and news. We perform the evaluation qualitatively and quantitatively. In qualitative evaluation, we manually inspect five most similar medical words to a given set of target medical words, and then analyze word embeddings through the visualization of those word embeddings. Quantitative evaluation falls into two categories: extrinsic and intrinsic evaluation. Based on the evaluation results, we can draw the following conclusions. First, EHR and PubMed can capture the semantics of medical terms better than GloVe and Google News and find more relevant similar medical terms. Second, the medical semantic similarity captured by the word embeddings trained on EHR and PubMed are closer to human experts' judgments, compared to these trained on GloVe and Google News. Third, there does not exist a consistent global ranking of word embedding quality for downstream biomedical NLP applications. However, adding word embeddings as extra features will improve results on most downstream tasks. Finally, word embeddings trained from a similar domain corpus do not necessarily have better performance than other word embeddings for any downstream biomedical tasks.
Querying graph structured data is a fundamental operation that enables important applications including knowledge graph search, social network analysis, and cyber-network security. However, the growing size of real-world data graphs poses severe challenges for graph databases to meet the response-time requirements of the applications. Planning the computational steps of query processing - Query Planning - is central to address these challenges. In this paper, we study the problem of learning to speedup query planning in graph databases towards the goal of improving the computational-efficiency of query processing via training queries.We present a Learning to Plan (L2P) framework that is applicable to a large class of query reasoners that follow the Threshold Algorithm (TA) approach. First, we define a generic search space over candidate query plans, and identify target search trajectories (query plans) corresponding to the training queries by performing an expensive search. Subsequently, we learn greedy search control knowledge to imitate the search behavior of the target query plans. We provide a concrete instantiation of our L2P framework for STAR, a state-of-the-art graph query reasoner. Our experiments on benchmark knowledge graphs including DBpedia, YAGO, and Freebase show that using the query plans generated by the learned search control knowledge, we can significantly improve the speed of STAR with negligible loss in accuracy.