Discovering communities in complex networks means grouping nodes similar to each other, to uncover latent information about them. There are hundreds of different algorithms to solve the community detection task, each with its own understanding and definition of what a "community" is. Dozens of review works attempt to order such a diverse landscape -- classifying community discovery algorithms by the process they employ to detect communities, by their explicitly stated definition of community, or by their performance on a standardized task. In this paper, we classify community discovery algorithms according to a fourth criterion: the similarity of their results. We create an Algorithm Similarity Network (ASN), whose nodes are the community detection approaches, connected if they return similar groupings. We then perform community detection on this network, grouping algorithms that consistently return the same partitions or overlapping coverage over a span of more than one thousand synthetic and real world networks. This paper is an attempt to create a similarity-based classification of community detection algorithms based on empirical data. It improves over the state of the art by comparing more than seventy approaches, discovering that the ASN contains well-separated groups, making it a sensible tool for practitioners, aiding their choice of algorithms fitting their analytic needs.
The first -- most popular -- category includes works classifying algorithms by the techniques they employ to divide the graph into groups of nodes, i.e. by their . Examples in this category are @cite_21 , @cite_24 , @cite_33 , @cite_9 , @cite_8 , @cite_26 ; @cite_12 -- focusing on multilayer networks; and @cite_10 -- whose attention narrows down to genetic algorithms. Here, we are agnostic about how an algorithm works, as we are focused on figuring out which algorithm returns similar partitions to which other. This is influenced by how they work, but even algorithms based on the philosophy of modularity maximization might end up in different categories.
@cite_26 @cite_33 @cite_8 @cite_9 @cite_21 @cite_24 @cite_10 @cite_12
2169847772 2757338536 2013172302 2143774383 1714704734 2513804397 2112993448 2764172504
This work addresses graph-based semi-supervised classification and betweenness computation in large, sparse, networks (several millions of nodes). The objective of semi-supervised classification is to assign a label to unlabeled nodes using the whole topology of the graph and the labeling at our disposal. Two approaches are developed to avoid explicit computation of pairwise proximity between the nodes of the graph, which would be impractical for graphs containing millions of nodes. The first approach directly computes, for each class, the sum of the similarities between the nodes to classify and the labeled nodes of the class, as suggested initially in [1,2]. Along this approach, two algorithms exploiting different state-of-the-art kernels on a graph are developed. The same strategy can also be used in order to compute a betweenness measure. The second approach works on a trellis structure built from biased random walks on the graph, extending an idea introduced in [3]. These random walks allow to define a biased bounded betweenness for the nodes of interest, defined separately for each class. All the proposed algorithms have a linear computing time in the number of edges while providing good results, and hence are applicable to large sparse networks. They are empirically validated on medium-size standard data sets and are shown to be competitive with state-of-the-art techniques. Finally, we processed a novel data set, which is made available for benchmarking, for multi-class classification in a large network: the U.S. patents citation network containing 3M nodes (of six different classes) and 38M edges. The three proposed algorithms achieve competitive results (around 85 classification rate) on this large network-they classify the unlabeled nodes within a few minutes on a standard workstation. While much of the work in the design of convolutional networks over the last five years has revolved around the empirical investigation of the importance of depth, filter sizes, and number of feature channels, recent studies have shown that branching, i.e., splitting the computation along parallel but distinct threads and then aggregating their outputs, represents a new promising dimension for significant improvements in performance. To combat the complexity of design choices in multi-branch architectures, prior work has adopted simple strategies, such as a fixed branching factor, the same input being fed to all parallel branches, and an additive combination of the outputs produced by all branches at aggregation points. In this work we remove these predefined choices and propose an algorithm to learn the connections between branches in the network. Instead of being chosen a priori by the human designer, the multi-branch connectivity is learned simultaneously with the weights of the network by optimizing a single loss function defined with respect to the end task. We demonstrate our approach on the problem of multi-class image classification using four different datasets where it yields consistently higher accuracy compared to the state-of-the-art ResNeXt'' multi-branch network given the same learning capacity. Classifying a set of objects into clusters can be done in numerous ways, producing different results. They can be visually compared using contingency tables [27], mosaicplots [13], fluctuation diagrams [15], tableplots [20] , (modified) parallel coordinates plots [28], Parallel Sets plots [18] or circos diagrams [19]. Unfortunately the interpretability of all these graphical displays decreases rapidly with the numbers of categories and clusterings. In his famous book A Semiology of Graphics [5] Bertin writes “the discovery of an ordered concept appears as the ultimate point in logical simplification since it permits reducing to a single instant the assimilation of series which previously required many instants of study”. Or in more everyday language, if you use good orderings you can see results immediately that with other orderings might take a lot of effort. This is also related to the idea of effect ordering [12], that data should be organised to reflect the effect you want to observe. This paper presents an efficient algorithm based on Bertin's idea and concepts related to Kendall's t [17], which finds informative joint orders for two or more nominal classification variables. We also show how these orderings improve the various displays and how groups of corresponding categories can be detected using a top-down partitioning algorithm. Different clusterings based on data on the environmental performance of cars sold in Germany are used for illustration. All presented methods are available in the R package extracat which is used to compute the optimized orderings for the example dataset. This paper studies the problem of leveraging computationally intensive classification algorithms for large scale text categorization problems. We propose a hierarchical approach which decomposes the classification problem into a coarse level task and a fine level task. A simple yet scalable classifier is applied to perform the coarse level classification while a more sophisticated model is used to separate classes at the fine level. However, instead of relying on a human-defined hierarchy to decompose the problem, we we use a graph algorithm to discover automatically groups of highly similar classes. As an illustrative example, we apply our approach to real-world industrial data from eBay, a major e-commerce site where the goal is to classify live items into a large taxonomy of categories. In such industrial setting, classification is very challenging due to the number of classes, the amount of training data, the size of the feature space and the real-world requirements on the response time. We demonstrate through extensive experimental evaluation that (1) the proposed hierarchical approach is superior to flat models, and (2) the data-driven extraction of latent groups works significantly better than the existing human-defined hierarchy. In this paper we study a paradigm to generalize online classification algorithms for binary classification problems to multiclass problems. The particular hypotheses we investigate maintain one prototype vector per class. Given an input instance, a multiclass hypothesis computes a similarity-score between each prototype and the input instance and sets the predicted label to be the index of the prototype achieving the highest similarity. To design and analyze the learning algorithms in this paper we introduce the notion of ultraconservativeness. Ultraconservative algorithms are algorithms that update only the prototypes attaining similarity-scores which are higher than the score of the correct label's prototype. We start by describing a family of additive ultraconservative algorithms where each algorithm in the family updates its prototypes by finding a feasible solution for a set of linear constraints that depend on the instantaneous similarity-scores. We then discuss a specific online algorithm that seeks a set of prototypes which have a small norm. The resulting algorithm, which we term MIRA (for Margin Infused Relaxed Algorithm) is ultraconservative as well. We derive mistake bounds for all the algorithms and provide further analysis of MIRA using a generalized notion of the margin for multiclass problems. We discuss the form the algorithms take in the binary case and show that all the algorithms from the first family reduce to the Perceptron algorithm while MIRA provides a new Perceptron-like algorithm with a margin-dependent learning rate. We then return to multiclass problems and describe an analogous multiplicative family of algorithms with corresponding mistake bounds. We end the formal part by deriving and analyzing a multiclass version of Li and Long's ROMMA algorithm. We conclude with a discussion of experimental results that demonstrate the merits of our algorithms. Analyzing massive social networks challenges both high-performance computers and human understanding. These massive networks cannot be visualized easily, and their scale makes applying complex analysis methods computationally expensive. We present a region-growing method for finding a smaller, more tractable subgraph, a community, given a few example seed vertices. Unlike existing work, we focus on a small number of seed vertices, from two to a few dozen. We also present the first comparison between five algorithms for expanding a small seed set into a community. Our comparison applies these algorithms to an R-MAT generated graph component with 240 thousand vertices and 32 million edges and evaluates the community size, modularity, Kullback-Leibler divergence, conductance, and clustering coefficient. We find that our new algorithm with a local modularity maximizing heuristic based on Clauset, Newman, and Moore performs very well when the output is limited to 100 or 1 000 vertices. When run without a vertex size limit, a heuristic from McCloskey and Bader generates communities containing around 60 of the graph’s vertices and having a small conductance and modularity appropriate to the result size. A personalized PageRank algorithm based on Andersen, Lang, and Chung also performs well with respect to our metrics. Many methods have been proposed to solve the image classification problem for a large number of categories. Among them, methods based on tree-based representations achieve good trade-off between accuracy and test time efficiency. While focusing on learning a tree-shaped hierarchy and the corresponding set of classifiers, most of them [11, 2, 14] use a greedy prediction algorithm for test time efficiency. We argue that the dramatic decrease in accuracy at high efficiency is caused by the specific design choice of the learning and greedy prediction algorithms. In this work, we propose a classifier which achieves a better trade-off between efficiency and accuracy with a given tree-shaped hierarchy. First, we convert the classification problem as finding the best path in the hierarchy, and a novel branch-and-bound-like algorithm is introduced to efficiently search for the best path. Second, we jointly train the classifiers using a novel Structured SVM (SSVM) formulation with additional bound constraints. As a result, our method achieves a significant 4.65 , 5.43 , and 4.07 (relative 24.82 , 41.64 , and 109.79 ) improvement in accuracy at high efficiency compared to state-of-the-art greedy "tree-based" methods [14] on Caltech-256 [15], SUN [32] and Image Net 1K [9] dataset, respectively. Finally, we show that our branch-and-bound-like algorithm naturally ranks the paths in the hierarchy (Fig. 8) so that users can further process them. We consider the enumeration of maximal bipartite cliques (bicliques) from a large graph, a task central to many practical data mining problems in social network analysis and bioinformatics. We present novel parallel algorithms for the MapReduce platform, and an experimental evaluation using Hadoop MapReduce. Our algorithm is based on clustering the input graph into smaller sized subgraphs, followed by processing different subgraphs in parallel. Our algorithm uses two ideas that enable it to scale to large graphs: (1) the redundancy in work between different subgraph explorations is minimized through a careful pruning of the search space, and (2) the load on different reducers is balanced through the use of an appropriate total order among the vertices. Our evaluation shows that the algorithm scales to large graphs with millions of edges and tens of millions of maximal bicliques. To our knowledge, this is the first work on maximal biclique enumeration for graphs of this scale.