This paper proposes a one-step spectral clustering method by learning an intrinsic affinity matrix (i.e., the clustering result) from the low-dimensional space (i.e., intrinsic subspace) of original data. Specifically, the intrinsic affinitymatrix is learnt by: 1) the alignment of the initial affinity matrix learnt from original data; 2) the adjustment of the transformation matrix, which transfers the original feature space into its intrinsic subspace by simultaneously conducting feature selection and subspace learning; and 3) the clustering result constraint, i.e., the graph constructed by the intrinsic affinity matrix has exact c connected components where c is the number of clusters. In this way, two affinity matrices and a transformation matrix are iteratively updated until achieving their individual optimum, so that these two affinity matrices are consistent and the intrinsic subspace is learnt via the transformation matrix. Experimental results on both synthetic and benchmark datasets verified that our proposed method outputted more effective clustering result than the previous clustering methods.

Community detection is a task of fundamental importance in social network analysis that can be used in a variety of knowledge-based domains. While there exist many works on community detection based on connectivity structures, they suffer from either considering the overlapping or non-overlapping communities. In this work, we propose a novel approach for general community detection through an integrated framework to extract the overlapping and non-overlapping community structures without assuming prior structural connectivity on networks. Our general framework is based on a primary node based criterion which consists of the internal association degree along with the external association degree. The evaluation of the proposed method is investigated through the extensive simulation experiments and several benchmark real network datasets. The experimental results show that the proposed method outperforms the earlier state-of-the-art algorithms based on the well-known evaluation criteria.

A cluster tree provides a highly-interpretable summary of a density function by representing the hierarchy of its high-density clusters. It is estimated using the empirical tree, which is the cluster tree constructed from a density estimator. This paper addresses the basic question of quantifying our uncertainty by assessing the statistical significance of topological features of an empirical cluster tree. We first study a variety of metrics that can be used to compare different trees, analyze their properties and assess their suitability for inference. We then propose methods to construct and summarize confidence sets for the unknown true cluster tree. We introduce a partial ordering on cluster trees which we use to prune some of the statistically insignificant features of the empirical tree, yielding interpretable and parsimonious cluster trees. Finally, we illustrate the proposed methods on a variety of synthetic examples and furthermore demonstrate their utility in the analysis of a Graft-versus-Host Disease (GvHD) data set.

Convex clustering, a convex relaxation of k-means clustering and hierarchical clustering, has drawn recent attentions since it nicely addresses the instability issue of traditional nonconvex clustering methods. Although its computational and statistical properties have been recently studied, the performance of convex clustering has not yet been investigated in the high-dimensional clustering scenario, where the data contains a large number of features and many of them carry no information about the clustering structure. In this paper, we demonstrate that the performance of convex clustering could be distorted when the uninformative features are included in the clustering. To overcome it, we introduce a new clustering method, referred to as Sparse Convex Clustering, to simultaneously cluster observations and conduct feature selection. The key idea is to formulate convex clustering in a form of regularization, with an adaptive group-lasso penalty term on cluster centers. In order to optimally balance the tradeoff between the cluster fitting and sparsity, a tuning criterion based on clustering stability is developed. In theory, we provide an unbiased estimator for the degrees of freedom of the proposed sparse convex clustering method. Finally, the effectiveness of the sparse convex clustering is examined through a variety of numerical experiments and a real data application.

The Lloyd-Max algorithm is a classical approach to perform K-means clustering. Unfortunately, its cost becomes prohibitive as the training dataset grows large. We propose a compressive version of K-means (CKM), that estimates cluster centers from a sketch, i.e. from a drastically compressed representation of the training dataset. We demonstrate empirically that CKM performs similarly to Lloyd-Max, for a sketch size proportional to the number of cen-troids times the ambient dimension, and independent of the size of the original dataset. Given the sketch, the computational complexity of CKM is also independent of the size of the dataset. Unlike Lloyd-Max which requires several replicates, we further demonstrate that CKM is almost insensitive to initialization. For a large dataset of 10^7 data points, we show that CKM can run two orders of magnitude faster than five replicates of Lloyd-Max, with similar clustering performance on artificial data. Finally, CKM achieves lower classification errors on handwritten digits classification.

Clustering is one of the most common unsupervised learning tasks in machine learning and data mining. Clustering algorithms have been used in a plethora of applications across several scientific fields. However, there has been limited research in the clustering of point patterns - sets or multi-sets of unordered elements - that are found in numerous applications and data sources. In this paper, we propose two approaches for clustering point patterns. The first is a non-parametric method based on novel distances for sets. The second is a model-based approach, formulated via random finite set theory, and solved by the Expectation-Maximization algorithm. Numerical experiments show that the proposed methods perform well on both simulated and real data.

In this work a robust clustering algorithm for stationary time series is proposed. The algorithm is based on the use of estimated spectral densities, which are considered as functional data, as the basic characteristic of stationary time series for clustering purposes. A robust algorithm for functional data is then applied to the set of spectral densities. Trimming techniques and restrictions on the scatter within groups reduce the effect of noise in the data and help to prevent the identification of spurious clusters. The procedure is tested in a simulation study, and is also applied to a real data set.

Consumer Demand Response (DR) is an important research and industry problem, which seeks to categorize, predict and modify consumer's energy consumption. Unfortunately, traditional clustering methods have resulted in many hundreds of clusters, with a given consumer often associated with several clusters, making it difficult to classify consumers into stable representative groups and to predict individual energy consumption patterns. In this paper, we present a shape-based approach that better classifies and predicts consumer energy consumption behavior at the household level. The method is based on Dynamic Time Warping. DTW seeks an optimal alignment between energy consumption patterns reflecting the effect of hidden patterns of regular consumer behavior. Using real consumer 24-hour load curves from Opower Corporation, our method results in a 50% reduction in the number of representative groups and an improvement in prediction accuracy measured under DTW distance. We extend the approach to estimate which electrical devices will be used and in which hours.

One of the key information pieces in improving energy efficiency of buildings is the appliance level breakdown of energy consumption. Energy disaggregation is the process of obtaining this breakdown from a building level aggregate data using computational techniques. Most of the current research focuses on residential buildings, obtaining this information from a single smart meter and often relying on high frequency data. This work is directed at commercial buildings equipped with building management and automation systems providing low frequency operational and contextual data. This paper presents a machine learning method to disaggregate energy consumption of the building using this operational data as input features. Experimental results on two publicly available datasets demonstrate the effectiveness of the approach, which surpasses existing methods. For all but one appliance of House 2 of the publicly available REDD dataset, improvements in normalized error in assigned power range between 20% (Lighting) and 220% (Stove). For another dataset from an educational facility in Singapore, disaggregation accuracy of 92% is reported for the facility's cooling system.

Current practice in whole time series clustering of residential meter data focuses on aggregated or subsampled load data at the customer level, which ignores day-to-day differences within customers. This information is critical to determine each customer’s suitability to various demand side management strategies that support intelligent power grids and smart energy management. Clustering daily load shapes provides fine-grained information on customer attributes and sources of variation for subsequent models and customer segmentation. In this paper, we apply 11 clustering methods to daily residential meter data. We evaluate their parameter settings and suitability based on 6 generic performance metrics and post-checking of resulting clusters. Finally, we recommend suitable techniques and parameters based on the goal of discovering diverse daily load patterns among residential customers. To the authors’ knowledge, this paper is the first robust comparative review of clustering techniques applied to daily residential load shape time series in the power systems’ literature.