Graph convolutional network (GCN) has been successfully applied to many graph-based applications; however, training a large-scale GCN remains challenging. Current SGD-based algorithms suffer from either a high computational cost that exponentially grows with number of GCN layers, or a large space requirement for keeping the entire graph and the embedding of each node in memory. In this paper, we propose Cluster-GCN, a novel GCN algorithm that is suitable for SGD-based training by exploiting the graph clustering structure. Cluster-GCN works as the following: at each step, it samples a block of nodes that associate with a dense subgraph identified by a graph clustering algorithm, and restricts the neighborhood search within this subgraph. This simple but effective strategy leads to significantly improved memory and computational efficiency while being able to achieve comparable test accuracy with previous algorithms. To test the scalability of our algorithm, we create a new Amazon2M data with 2 million nodes and 61 million edges which is more than 5 times larger than the previous largest publicly available dataset (Reddit). For training a 3-layer GCN on this data, Cluster-GCN is faster than the previous state-of-the-art VR-GCN (1523 seconds vs 1961 seconds) and using much less memory (2.2GB vs 11.2GB). Furthermore, for training 4 layer GCN on this data, our algorithm can finish in around 36 minutes while all the existing GCN training algorithms fail to train due to the out-of-memory issue. Furthermore, Cluster-GCN allows us to train much deeper GCN without much time and memory overhead, which leads to improved prediction accuracy---using a 5-layer Cluster-GCN, we achieve state-of-the-art test F1 score 99.36 on the PPI dataset, while the previous best result was 98.71 by [16].

Graph-based clustering has shown promising performance in many tasks. A key step of graph-based approach is the similarity graph construction. In general, learning graph in kernel space can enhance clustering accuracy due to the incorporation of nonlinearity. However, most existing kernel-based graph learning mechanisms is not similarity-preserving, hence leads to sub-optimal performance. To overcome this drawback, we propose a more discriminative graph learning method which can preserve the pairwise similarities between samples in an adaptive manner for the first time. Specifically, we require the learned graph be close to a kernel matrix, which serves as a measure of similarity in raw data. Moreover, the structure is adaptively tuned so that the number of connected components of the graph is exactly equal to the number of clusters. Finally, our method unifies clustering and graph learning which can directly obtain cluster indicators from the graph itself without performing further clustering step. The effectiveness of this approach is examined on both single and multiple kernel learning scenarios in several datasets.

Machine learning has become ubiquitous and a key technology on mining electronic health records (EHRs) for facilitating clinical research and practice. Unsupervised machine learning, as opposed to supervised learning, has shown promise in identifying novel patterns and relations from EHRs without using human created labels. In this paper, we investigate the application of unsupervised machine learning models in discovering latent disease clusters and patient subgroups based on EHRs. We utilized Latent Dirichlet Allocation (LDA), a generative probabilistic model, and proposed a novel model named Poisson Dirichlet Model (PDM), which extends the LDA approach using a Poisson distribution to model patients' disease diagnoses and to alleviate age and sex factors by considering both observed and expected observations. In the empirical experiments, we evaluated LDA and PDM on three patient cohorts with EHR data retrieved from the Rochester Epidemiology Project (REP), for the discovery of latent disease clusters and patient subgroups. We compared the effectiveness of LDA and PDM in identifying latent disease clusters through the visualization of disease representations learned by two approaches. We also tested the performance of LDA and PDM in differentiating patient subgroups through survival analysis, as well as statistical analysis. The experimental results show that the proposed PDM could effectively identify distinguished disease clusters by alleviating the impact of age and sex, and that LDA could stratify patients into more differentiable subgroups than PDM in terms of p-values. However, the subgroups discovered by PDM might imply the underlying patterns of diseases of greater interest in epidemiology research due to the alleviation of age and sex. Both unsupervised machine learning approaches could be leveraged to discover patient subgroups using EHRs but with different foci.

Sequence classification is an important data mining task in many real world applications. Over the past few decades, many sequence classification methods have been proposed from different aspects. In particular, the pattern-based method is one of the most important and widely studied sequence classification methods in the literature. In this paper, we present a reference-based sequence classification framework, which can unify existing pattern-based sequence classification methods under the same umbrella. More importantly, this framework can be used as a general platform for developing new sequence classification algorithms. By utilizing this framework as a tool, we propose new sequence classification algorithms that are quite different from existing solutions. Experimental results show that new methods developed under the proposed framework are capable of achieving comparable classification accuracy to those state-of-the-art sequence classification algorithms.

We propose an efficient linear-time graph-based divisive cluster analysis approach called Sampling Clustering. It constructs a lite informative dendrogram by recursively dividing a graph into subgraphs. In each recursive call, a graph is sampled first with a set of vertices being removed to disconnect latent clusters, then condensed by adding edges to the remaining vertices to avoid graph fragmentation caused by vertex removals. We also present some sampling and condensing methods and discuss the effectiveness in this paper. Our implementations run in linear time and achieve outstanding performance on various types of datasets. Experimental results show that they outperform state-of-the-art clustering algorithms with significantly less computing resource requirements.

Hierarchical review aspect aggregation is an important challenge in review summarization. Currently, agglomerative clustering is widely used for hierarchical aspect aggregation. We identify an important but less studied issue in using agglomerative clustering for the aforementioned task. This paper proposes a novel approach to generate a multi-way hierarchy by adaptation of the multivariate concept. Furthermore, we propose a novel experimentation approach to evaluate the acceptability of the aspect relations obtained from the hierarchy generated.

In this work, we first attempt to replicate an earlier study on gene selection and clustering, and then we extend this work by applying a different type of hierarchical clustering to dis- cover interesting subsets of genes from breast cancer data. Replication of such studies is a known challenge and an ac- tive area of research in bioinformatics. The work presented in this paper is three-fold. First, we replicate a study conducted at the University of North Carolina to generate an initial set of genes. Second, we apply an approach called Distance Weighted Discrimination to fuse multiple, disparate breast cancer datasets into a single validation set. Third, we per- form hierarchical clustering and k-means clustering on this validation set to discover natural groupings and compare the clusters generated by both methods. While applying the hi- erarchical clustering is part of the reproduction step, we ex- tend the research by trying two different forms of hierarchi- cal clustering. We also apply k-means clustering for the same purpose and compare all three methods using Kaplan-Meier estimation and Cox proportional hazards regression. We dis- cover that among the three methods, k-means clustering gives us the best results.

Signed graphs encode positive (attractive) and negative (repulsive) relations between nodes. We extend spectral clustering to signed graphs via the one-parameter family of Signed Power Mean Laplacians, defined as the matrix power mean of normalized standard and signless Laplacians of positive and negative edges. We provide a thorough analysis of the proposed approach in the setting of a general Stochastic Block Model that includes models such as the Labeled Stochastic Block Model and the Censored Block Model. We show that in expectation the signed power mean Laplacian captures the ground truth clusters under reasonable settings where state-of-the-art approaches fail. Moreover, we prove that the eigenvalues and eigenvector of the signed power mean Laplacian concentrate around their expectation under reasonable conditions in the general Stochastic Block Model. Extensive experiments on random graphs and real world datasets confirm the theoretically predicted behaviour of the signed power mean Laplacian and show that it compares favourably with state-of-the-art methods.

In order to achieve it, we proposed and developed the classification framework EasiCS to obtain the relative stability The cervical spondylosis(CS), a common degenerative clustering results, which consists of dimension reduction, disease, harms human life and health, affects up clustering algorithm EasiSOM, spectral clustering algorithm to two-thirds of the population, and poses an serious EasiSC as shown in the Figure 1. To the best of our burden on individuals and society (Matz et al. 2009; knowledge, the EasiCS is the first effort to utilize the clustering Kotil and Bilge 2008; Cai et al. 2016; Nana Wang; algorithm and sEMG. Compared with the seven commonly Wang et al. 2018). Currently, the neck disability index used clustering algorithms, the novelty framework (Howard Vernon) is the most commonly used tool EasiCS provide the best overall performance. The cervical to assess the neck dysfunction (Vernon and Mior 1991), spondylosis(CS), a common degenerative disease, harms human The availability of which are mainly undermined by the life and health, affects up to two-thirds of the population, coarse-grained and unreasonable classification, despite that and poses an serious burden on individuals and society the NDI information is subjective and not accurate enough.

This paper presents a novel time series clustering method, the self-organising eigenspace map (SOEM), based on a generalisation of the well-known self-organising feature map (SOFM). The SOEM operates on the eigenspaces of the embedded covariance structures of time series which are related directly to modes in those time series. Approximate joint diagonalisation acts as a pseudo-metric across these spaces allowing us to generalise the SOFM to a neural network with matrix input. The technique is empirically validated against three sets of experiments; univariate and multivariate time series clustering, and application to (clustered) multi-variate time series forecasting. Results indicate that the technique performs a valid topologically ordered clustering of the time series. The clustering is superior in comparison to standard benchmarks when the data is non-aligned, gives the best clustering stage for when used in forecasting, and can be used with partial/non-overlapping time series, multivariate clustering and produces a topological representation of the time series objects.