Automatic feature learning algorithms are at the forefront of modern day machine learning research. We present a novel algorithm, supervised Q-walk, which applies Q-learning to generate random walks on graphs such that the walks prove to be useful for learning node features suitable for tackling with the node classification problem. We present another novel algorithm, k-hops neighborhood based confidence values learner, which learns confidence values of labels for unlabelled nodes in the network without first learning the node embedding. These confidence values aid in learning an apt reward function for Q-learning. We demonstrate the efficacy of supervised Q-walk approach over existing state-of-the-art random walk based node embedding learners in solving the single multi-label multi-class node classification problem using several real world datasets. Summarising, our approach represents a novel state-of-the-art technique to learn features, for nodes in networks, tailor-made for dealing with the node classification problem.
Factorization based techniques represent the edges in networks as matrices. These matrices are factorized to obtain the embeddings. The matrix representation and its factorization are done using various techniques @cite_0 @cite_20 @cite_17 @cite_18 @cite_6 . These methods may suffer from scalability issues for large graph datasets and sparse matrix representations need special attention.
@cite_18 @cite_6 @cite_0 @cite_20 @cite_17
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In this paper, we present GraRep , a novel model for learning vertex representations of weighted graphs. This model learns low dimensional vectors to represent vertices appearing in a graph and, unlike existing work, integrates global structural information of the graph into the learning process. We also formally analyze the connections between our work and several previous research efforts, including the DeepWalk model of as well as the skip-gram model with negative sampling of We conduct experiments on a language network, a social network as well as a citation network and show that our learned global representations can be effectively used as features in tasks such as clustering, classification and visualization. Empirical results demonstrate that our representation significantly outperforms other state-of-the-art methods in such tasks. Graph embedding algorithms embed a graph into a vector space where the structure and the inherent properties of the graph are preserved. The existing graph embedding methods cannot preserve the asymmetric transitivity well, which is a critical property of directed graphs. Asymmetric transitivity depicts the correlation among directed edges, that is, if there is a directed path from u to v, then there is likely a directed edge from u to v. Asymmetric transitivity can help in capturing structures of graphs and recovering from partially observed graphs. To tackle this challenge, we propose the idea of preserving asymmetric transitivity by approximating high-order proximity which are based on asymmetric transitivity. In particular, we develop a novel graph embedding algorithm, High-Order Proximity preserved Embedding (HOPE for short), which is scalable to preserve high-order proximities of large scale graphs and capable of capturing the asymmetric transitivity. More specifically, we first derive a general formulation that cover multiple popular high-order proximity measurements, then propose a scalable embedding algorithm to approximate the high-order proximity measurements based on their general formulation. Moreover, we provide a theoretical upper bound on the RMSE (Root Mean Squared Error) of the approximation. Our empirical experiments on a synthetic dataset and three real-world datasets demonstrate that HOPE can approximate the high-order proximities significantly better than the state-of-art algorithms and outperform the state-of-art algorithms in tasks of reconstruction, link prediction and vertex recommendation. Many areas of science depend on exploratory data analysis and visualization. The need to analyze large amounts of multivariate data raises the fundamental problem of dimensionality reduction: how to discover compact representations of high-dimensional data. Here, we introduce locally linear embedding (LLE), an unsupervised learning algorithm that computes low-dimensional, neighborhood-preserving embeddings of high-dimensional inputs. Unlike clustering methods for local dimensionality reduction, LLE maps its inputs into a single global coordinate system of lower dimensionality, and its optimizations do not involve local minima. By exploiting the local symmetries of linear reconstructions, LLE is able to learn the global structure of nonlinear manifolds, such as those generated by images of faces or documents of text. How do we judge similarity? Our mental representations of the world are formed by processing large numbers of sensory in Drawing on the correspondence between the graph Laplacian, the Laplace-Beltrami operator on a manifold, and the connections to the heat equation, we propose a geometrically motivated algorithm for constructing a representation for data sampled from a low dimensional manifold embedded in a higher dimensional space. The algorithm provides a computationally efficient approach to nonlinear dimensionality reduction that has locality preserving properties and a natural connection to clustering. Several applications are considered. Natural graphs, such as social networks, email graphs, or instant messaging patterns, have become pervasive through the internet. These graphs are massive, often containing hundreds of millions of nodes and billions of edges. While some theoretical models have been proposed to study such graphs, their analysis is still difficult due to the scale and nature of the data. We propose a framework for large-scale graph decomposition and inference. To resolve the scale, our framework is distributed so that the data are partitioned over a shared-nothing set of machines. We propose a novel factorization technique that relies on partitioning a graph so as to minimize the number of neighboring vertices rather than edges across partitions. Our decomposition is based on a streaming algorithm. It is network-aware as it adapts to the network topology of the underlying computational hardware. We use local copies of the variables and an efficient asynchronous communication protocol to synchronize the replicated values in order to perform most of the computation without having to incur the cost of network communication. On a graph of 200 million vertices and 10 billion edges, derived from an email communication network, our algorithm retains convergence properties while allowing for almost linear scalability in the number of computers.