Evaluating Overfit and Underfit in Models of Network Community Structure

A common data mining task on networks is community detection, which seeks an unsupervised decomposition of a network into structural groups based on statistical regularities in the network's connectivity. Although many methods exist, the No Free Lunch theorem for community detection implies that each makes some kind of tradeoff, and no algorithm can be optimal on all inputs. Thus, different algorithms will over or underfit on different inputs, finding more, fewer, or just different communities than is optimal, and evaluation methods that use a metadata partition as a ground truth will produce misleading conclusions about general accuracy. Here, we present a broad evaluation of over and underfitting in community detection, comparing the behavior of 16 state-of-the-art community detection algorithms on a novel and structurally diverse corpus of 406 real-world networks. We find that (i) algorithms vary widely both in the number of communities they find and in their corresponding composition, given the same input, (ii) algorithms can be clustered into distinct high-level groups based on similarities of their outputs on real-world networks, and (iii) these differences induce wide variation in accuracy on link prediction and link description tasks. We introduce a new diagnostic for evaluating overfitting and underfitting in practice, and use it to roughly divide community detection methods into general and specialized learning algorithms. Across methods and inputs, Bayesian techniques based on the stochastic block model and a minimum description length approach to regularization represent the best general learning approach, but can be outperformed under specific circumstances. These results introduce both a theoretically principled approach to evaluate over and underfitting in models of network community structure and a realistic benchmark by which new methods may be evaluated and compared.Comment: 22 pages, 13 figures, 3 table

A Clustering System for Dynamic Data Streams Based on Metaheuristic Optimisation

open access articleThis article presents the Optimised Stream clustering algorithm (OpStream), a novel approach to cluster dynamic data streams. The proposed system displays desirable features, such as a low number of parameters and good scalability capabilities to both high-dimensional data and numbers of clusters in the dataset, and it is based on a hybrid structure using deterministic clustering methods and stochastic optimisation approaches to optimally centre the clusters. Similar to other state-of-the-art methods available in the literature, it uses “microclusters” and other established techniques, such as density based clustering. Unlike other methods, it makes use of metaheuristic optimisation to maximise performances during the initialisation phase, which precedes the classic online phase. Experimental results show that OpStream outperforms the state-of-the-art methods in several cases, and it is always competitive against other comparison algorithms regardless of the chosen optimisation method. Three variants of OpStream, each coming with a different optimisation algorithm, are presented in this study. A thorough sensitive analysis is performed by using the best variant to point out OpStream’s robustness to noise and resiliency to parameter changes

Finding and tracking multi-density clusters in an online dynamic data stream

The file attached to this record is the author's final peer reviewed version.Change is one of the biggest challenges in dynamic stream mining. From a data-mining perspective, adapting and tracking change is desirable in order to understand how and why change has occurred. Clustering, a form of unsupervised learning, can be used to identify the underlying patterns in a stream. Density-based clustering identifies clusters as areas of high density separated by areas of low density. This paper proposes a Multi-Density Stream Clustering (MDSC) algorithm to address these two problems; the multi-density problem and the problem of discovering and tracking changes in a dynamic stream. MDSC consists of two on-line components; discovered, labelled clusters and an outlier buffer. Incoming points are assigned to a live cluster or passed to the outlier buffer. New clusters are discovered in the buffer using an ant-inspired swarm intelligence approach. The newly discovered cluster is uniquely labelled and added to the set of live clusters. Processed data is subject to an ageing function and will disappear when it is no longer relevant. MDSC is shown to perform favourably to state-of-the-art peer stream-clustering algorithms on a range of real and synthetic data-streams. Experimental results suggest that MDSC can discover qualitatively useful patterns while being scalable and robust to noise

Time series classification based on fractal properties

The article considers classification task of fractal time series by the meta algorithms based on decision trees. Binomial multiplicative stochastic cascades are used as input time series. Comparative analysis of the classification approaches based on different features is carried out. The results indicate the advantage of the machine learning methods over the traditional estimating the degree of self-similarity.Comment: 4 pages, 2 figures, 3 equations, 1 tabl

Analyzing imputed financial data: a new approach to cluster analysis

The authors introduce a novel statistical modeling technique to cluster analysis and apply it to financial data. Their two main goals are to handle missing data and to find homogeneous groups within the data. Their approach is flexible and handles large and complex data structures with missing observations and with quantitative and qualitative measurements. The authors achieve this result by mapping the data to a new structure that is free of distributional assumptions in choosing homogeneous groups of observations. Their new method also provides insight into the number of different categories needed for classifying the data. The authors use this approach to partition a matched sample of stocks. One group offers dividend reinvestment plans, and the other does not. Their method partitions this sample with almost 97 percent accuracy even when using only easily available financial variables. One interpretation of their result is that the misclassified companies are the best candidates either to adopt a dividend reinvestment plan (if they have none) or to abandon one (if they currently offer one). The authors offer other suggestions for applications in the field of finance.

Spectral redemption: clustering sparse networks

Spectral algorithms are classic approaches to clustering and community detection in networks. However, for sparse networks the standard versions of these algorithms are suboptimal, in some cases completely failing to detect communities even when other algorithms such as belief propagation can do so. Here we introduce a new class of spectral algorithms based on a non-backtracking walk on the directed edges of the graph. The spectrum of this operator is much better-behaved than that of the adjacency matrix or other commonly used matrices, maintaining a strong separation between the bulk eigenvalues and the eigenvalues relevant to community structure even in the sparse case. We show that our algorithm is optimal for graphs generated by the stochastic block model, detecting communities all the way down to the theoretical limit. We also show the spectrum of the non-backtracking operator for some real-world networks, illustrating its advantages over traditional spectral clustering.Comment: 11 pages, 6 figures. Clarified to what extent our claims are rigorous, and to what extent they are conjectures; also added an interpretation of the eigenvectors of the 2n-dimensional version of the non-backtracking matri