Exhaustive and Efficient Constraint Propagation: A Semi-Supervised Learning Perspective and Its Applications

This paper presents a novel pairwise constraint propagation approach by decomposing the challenging constraint propagation problem into a set of independent semi-supervised learning subproblems which can be solved in quadratic time using label propagation based on k-nearest neighbor graphs. Considering that this time cost is proportional to the number of all possible pairwise constraints, our approach actually provides an efficient solution for exhaustively propagating pairwise constraints throughout the entire dataset. The resulting exhaustive set of propagated pairwise constraints are further used to adjust the similarity matrix for constrained spectral clustering. Other than the traditional constraint propagation on single-source data, our approach is also extended to more challenging constraint propagation on multi-source data where each pairwise constraint is defined over a pair of data points from different sources. This multi-source constraint propagation has an important application to cross-modal multimedia retrieval. Extensive results have shown the superior performance of our approach.Comment: The short version of this paper appears as oral paper in ECCV 201

Transforming Graph Representations for Statistical Relational Learning

Relational data representations have become an increasingly important topic due to the recent proliferation of network datasets (e.g., social, biological, information networks) and a corresponding increase in the application of statistical relational learning (SRL) algorithms to these domains. In this article, we examine a range of representation issues for graph-based relational data. Since the choice of relational data representation for the nodes, links, and features can dramatically affect the capabilities of SRL algorithms, we survey approaches and opportunities for relational representation transformation designed to improve the performance of these algorithms. This leads us to introduce an intuitive taxonomy for data representation transformations in relational domains that incorporates link transformation and node transformation as symmetric representation tasks. In particular, the transformation tasks for both nodes and links include (i) predicting their existence, (ii) predicting their label or type, (iii) estimating their weight or importance, and (iv) systematically constructing their relevant features. We motivate our taxonomy through detailed examples and use it to survey and compare competing approaches for each of these tasks. We also discuss general conditions for transforming links, nodes, and features. Finally, we highlight challenges that remain to be addressed

Nonparametric Feature Extraction from Dendrograms

We propose feature extraction from dendrograms in a nonparametric way. The Minimax distance measures correspond to building a dendrogram with single linkage criterion, with defining specific forms of a level function and a distance function over that. Therefore, we extend this method to arbitrary dendrograms. We develop a generalized framework wherein different distance measures can be inferred from different types of dendrograms, level functions and distance functions. Via an appropriate embedding, we compute a vector-based representation of the inferred distances, in order to enable many numerical machine learning algorithms to employ such distances. Then, to address the model selection problem, we study the aggregation of different dendrogram-based distances respectively in solution space and in representation space in the spirit of deep representations. In the first approach, for example for the clustering problem, we build a graph with positive and negative edge weights according to the consistency of the clustering labels of different objects among different solutions, in the context of ensemble methods. Then, we use an efficient variant of correlation clustering to produce the final clusters. In the second approach, we investigate the sequential combination of different distances and features sequentially in the spirit of multi-layered architectures to obtain the final features. Finally, we demonstrate the effectiveness of our approach via several numerical studies

Methods of Hierarchical Clustering

We survey agglomerative hierarchical clustering algorithms and discuss efficient implementations that are available in R and other software environments. We look at hierarchical self-organizing maps, and mixture models. We review grid-based clustering, focusing on hierarchical density-based approaches. Finally we describe a recently developed very efficient (linear time) hierarchical clustering algorithm, which can also be viewed as a hierarchical grid-based algorithm.Comment: 21 pages, 2 figures, 1 table, 69 reference

Attributed Network Embedding for Learning in a Dynamic Environment

Network embedding leverages the node proximity manifested to learn a low-dimensional node vector representation for each node in the network. The learned embeddings could advance various learning tasks such as node classification, network clustering, and link prediction. Most, if not all, of the existing works, are overwhelmingly performed in the context of plain and static networks. Nonetheless, in reality, network structure often evolves over time with addition/deletion of links and nodes. Also, a vast majority of real-world networks are associated with a rich set of node attributes, and their attribute values are also naturally changing, with the emerging of new content patterns and the fading of old content patterns. These changing characteristics motivate us to seek an effective embedding representation to capture network and attribute evolving patterns, which is of fundamental importance for learning in a dynamic environment. To our best knowledge, we are the first to tackle this problem with the following two challenges: (1) the inherently correlated network and node attributes could be noisy and incomplete, it necessitates a robust consensus representation to capture their individual properties and correlations; (2) the embedding learning needs to be performed in an online fashion to adapt to the changes accordingly. In this paper, we tackle this problem by proposing a novel dynamic attributed network embedding framework - DANE. In particular, DANE first provides an offline method for a consensus embedding and then leverages matrix perturbation theory to maintain the freshness of the end embedding results in an online manner. We perform extensive experiments on both synthetic and real attributed networks to corroborate the effectiveness and efficiency of the proposed framework.Comment: 10 page