Finding communities in sparse networks

Spectral algorithms based on matrix representations of networks are often used to detect communities but classic spectral methods based on the adjacency matrix and its variants fail to detect communities in sparse networks. New spectral methods based on non-backtracking random walks have recently been introduced that successfully detect communities in many sparse networks. However, the spectrum of non-backtracking random walks ignores hanging trees in networks that can contain information about the community structure of networks. We introduce the reluctant backtracking operators that explicitly account for hanging trees as they admit a small probability of returning to the immediately previous node unlike the non-backtracking operators that forbid an immediate return. We show that the reluctant backtracking operators can detect communities in certain sparse networks where the non-backtracking operators cannot while performing comparably on benchmark stochastic block model networks and real world networks. We also show that the spectrum of the reluctant backtracking operator approximately optimises the standard modularity function similar to the flow matrix. Interestingly, for this family of non- and reluctant-backtracking operators the main determinant of performance on real-world networks is whether or not they are normalised to conserve probability at each node.Comment: 11 pages, 4 figure

Recent Advances in Graph Partitioning

We survey recent trends in practical algorithms for balanced graph partitioning together with applications and future research directions

An exploration of evolutionary computation applied to frequency modulation audio synthesis parameter optimisation

With the ever-increasing complexity of sound synthesisers, there is a growing demand for automated parameter estimation and sound space navigation techniques. This thesis explores the potential for evolutionary computation to automatically map known sound qualities onto the parameters of frequency modulation synthesis. Within this exploration are original contributions in the domain of synthesis parameter estimation and, within the developed system, evolutionary computation, in the form of the evolutionary algorithms that drive the underlying optimisation process. Based upon the requirement for the parameter estimation system to deliver multiple search space solutions, existing evolutionary algorithmic architectures are augmented to enable niching, while maintaining the strengths of the original algorithms. Two novel evolutionary algorithms are proposed in which cluster analysis is used to identify and maintain species within the evolving populations. A conventional evolution strategy and cooperative coevolution strategy are defined, with cluster-orientated operators that enable the simultaneous optimisation of multiple search space solutions at distinct optima. A test methodology is developed that enables components of the synthesis matching problem to be identified and isolated, enabling the performance of different optimisation techniques to be compared quantitatively. A system is consequently developed that evolves sound matches using conventional frequency modulation synthesis models, and the effectiveness of different evolutionary algorithms is assessed and compared in application to both static and timevarying sound matching problems. Performance of the system is then evaluated by interview with expert listeners. The thesis is closed with a reflection on the algorithms and systems which have been developed, discussing possibilities for the future of automated synthesis parameter estimation techniques, and how they might be employed

Toward a direct and scalable identification of reduced models for categorical processes

The applicability of many computational approaches is dwelling on the identification of reduced models defined on a small set of collective variables (colvars). A methodology for scalable probability-preserving identification of reduced models and colvars directly from the data is derived—not relying on the availability of the full relation matrices at any stage of the resulting algorithm, allowing for a robust quantification of reduced model uncertainty and allowing us to impose a priori available physical information. We show two applications of the methodology: (i) to obtain a reduced dynamical model for a polypeptide dynamics in water and (ii) to identify diagnostic rules from a standard breast cancer dataset. For the first example, we show that the obtained reduced dynamical model can reproduce the full statistics of spatial molecular configurations—opening possibilities for a robust dimension and model reduction in molecular dynamics. For the breast cancer data, this methodology identifies a very simple diagnostics rule—free of any tuning parameters and exhibiting the same performance quality as the state of the art machine-learning applications with multiple tuning parameters reported for this problem

Ranked List Loss for Deep Metric Learning

The objective of deep metric learning (DML) is to learn embeddings that can capture semantic similarity and dissimilarity information among data points. Existing pairwise or tripletwise loss functions used in DML are known to suffer from slow convergence due to a large proportion of trivial pairs or triplets as the model improves. To improve this, ranking-motivated structured losses are proposed recently to incorporate multiple examples and exploit the structured information among them. They converge faster and achieve state-of-the-art performance. In this work, we unveil two limitations of existing ranking-motivated structured losses and propose a novel ranked list loss to solve both of them. First, given a query, only a fraction of data points is incorporated to build the similarity structure. Consequently, some useful examples are ignored and the structure is less informative. To address this, we propose to build a set-based similarity structure by exploiting all instances in the gallery. The learning setting can be interpreted as few-shot retrieval: given a mini-batch, every example is iteratively used as a query, and the rest ones compose the gallery to search, i.e., the support set in few-shot setting. The rest examples are split into a positive set and a negative set. For every mini-batch, the learning objective of ranked list loss is to make the query closer to the positive set than to the negative set by a margin. Second, previous methods aim to pull positive pairs as close as possible in the embedding space. As a result, the intraclass data distribution tends to be extremely compressed. In contrast, we propose to learn a hypersphere for each class in order to preserve useful similarity structure inside it, which functions as regularisation. Extensive experiments demonstrate the superiority of our proposal by comparing with the state-of-the-art methods.Comment: Accepted to T-PAMI. Therefore, to read the offical version, please go to IEEE Xplore. Fine-grained image retrieval task. Our source code is available online: https://github.com/XinshaoAmosWang/Ranked-List-Loss-for-DM

Evaluating subset selection methods for use case points estimation

When the Use Case Points method is used for software effort estimation, users are faced with low model accuracy which impacts on its practical application. This study investigates the significance of using subset selection methods for the prediction accuracy of Multiple Linear Regression models, obtained by the stepwise approach. K-means, Spectral Clustering, the Gaussian Mixture Model and Moving Window are evaluated as appropriate subset selection techniques. The methods were evaluated according to several evaluation criteria and then statistically tested. Evaluation was performing on two independent datasets-which differ in project types and size. Both were cut by the hold-out method. If clustering were used, the training sets were clustered into 3 classes; and, for each of class, an independent regression model was created. These were later used for the prediction of testing sets. If Moving Window was used, then window of sizes 5, 10 and 15 were tested. The results show that clustering techniques decrease prediction errors significantly when compared to Use Case Points or moving windows methods. Spectral Clustering was selected as the best-performing solution, because it achieves a Sum of Squared Errors reduction of 32% for the first dataset, and 98% for the second dataset. The Mean Absolute Percentage Error is less than 1% for the second dataset for Spectral Clustering; 9% for moving window; and 27% for Use Case Points. When the first dataset is used, then prediction errors are significantly higher -53% for Spectral Clustering, but Use Case Points produces a 165% result. It can be concluded that this study proves subset selection techniques as a significant method for improving the prediction ability of linear regression models - which are used for software development effort prediction. It can also be concluded that the clustering method performs better than the moving window method

Higher-order Projected Power Iterations for Scalable Multi-Matching

The matching of multiple objects (e.g. shapes or images) is a fundamental problem in vision and graphics. In order to robustly handle ambiguities, noise and repetitive patterns in challenging real-world settings, it is essential to take geometric consistency between points into account. Computationally, the multi-matching problem is difficult. It can be phrased as simultaneously solving multiple (NP-hard) quadratic assignment problems (QAPs) that are coupled via cycle-consistency constraints. The main limitations of existing multi-matching methods are that they either ignore geometric consistency and thus have limited robustness, or they are restricted to small-scale problems due to their (relatively) high computational cost. We address these shortcomings by introducing a Higher-order Projected Power Iteration method, which is (i) efficient and scales to tens of thousands of points, (ii) straightforward to implement, (iii) able to incorporate geometric consistency, (iv) guarantees cycle-consistent multi-matchings, and (iv) comes with theoretical convergence guarantees. Experimentally we show that our approach is superior to existing methods