Functional Clustering Approach Research Articles

Unsupervised Anomaly Detection and Diagnosis in Power Electronic Networks: Informative Leverage and Multivariate Functional Clustering Approaches

Unsupervised Anomaly Detection and Diagnosis in Power Electronic Networks: Informative Leverage and Multivariate Functional Clustering Approaches

Functional clustering of neuronal signals with FMM mixture models

The identification of unlabeled neuronal electric signals is one of the most challenging open problems in neuroscience, widely known as Spike Sorting. Motivated to solve this problem, we propose a model-based approach within the mixture modeling framework for clustering oscillatory functional data called MixFMM. The core of the approach is the FMM (Frequency Modulated Möbius) waves, which are non-linear parametric time functions, flexible enough to describe different oscillatory patterns and simple enough to be estimated efficiently. In particular, specific model parameters describe the phase, amplitude and shape of the waveforms. A mixture model is defined using FMM waves as basic functions and gaussian errors, and an EM algorithm is proposed for estimating the parameters. Spike Sorting (SS) has received considerable attention in the literature, and different functional clustering approaches have been considered. We have conducted a fair comparative analysis of the MixFMM with three competitors. Two of them are traditional methods in functional clustering and widely used in Spike Sorting. The third is an approach that has proven superior to many others solving Spike Sorting problems. The datasets used for validation include benchmarking simulated and real cases. The internal and external validation indexes confirm a better performance of the MixFMM on real data sets against the three competitors and an outstanding performance in simulated data against traditional approaches.

Clustering-based simultaneous forecasting of life expectancy time series through Long-Short Term Memory Neural Networks

In this paper, we apply a functional clustering method to the multivariate time series of life expectancy at birth of the female populations collected in the Human Mortality Database. We reconstruct the functional form of life expectancy from the available discrete observations and derive the curves through non-parametric smoothing. Once the clustering is realized, we perform the life expectancy simultaneous forecasting of the countries inside each cluster implementing a multivariate Long-Short Term Memory neural network. Although functional clustering has already been used in the actuarial literature, in this work it is applied for the first time to the study of life expectancy. The originality of the work also lies in the combination of a functional clustering approach with simultaneous forecasting obtained through the Long-Short Term Memory. We point out that such a combination provides a more informative outlook of the evolution of life expectancy, allowing us to depict country-specific longevity consistently with acknowledged mortality profiles. The results show that the evolution of developed countries follows a homogeneous pattern and supports the persisting homogeneity within the high longevity cluster over time. Moreover, we find a remarkable cross-country heterogeneity in the medium-low longevity cluster. By exploiting the cluster information, we improve the simultaneous forecasting of life expectancy time series using Long Short Term Memory neural networks and compare the error forecast of our approach with those of the classical VAR model, showing a better performance of the former when considering the cluster average errors.

Functional data clustering using principal curve methods

In this paper we propose a novel clustering method for functional data based on the principal curve clustering approach. By this method functional data are approximated using functional principal component analysis (FPCA) and the principal curve clustering is then performed on the principal scores. The proposed method makes use of the nonparametric principal curves to summarize the features of the principal scores extracted from the original functional data, and a probabilistic model combined with Bayesian Information Criterion is employed to automatically and simultaneously find the appropriate number of features, the optimal degree of smoothing and the corresponding cluster members. The simulation studies show that the proposed method outperforms the existing functional clustering approaches considered. The capability of this method is also demonstrated by the applications in the human mortality and fertility data.

Clustering functional data with application to electronic medication adherence monitoring in HIV prevention trials.

Maintaining high medication adherence is essential for achieving desired efficacy in clinical trials, especially prevention trials. However, adherence is traditionally measured by self-reports that are subject to reporting biases and measurement error. Recently, electronic medication dispenser devices have been adopted in several HIV pre-exposure prophylaxis prevention studies. These devices are capable of collecting objective, frequent, and timely drug adherence data. The device opening signals generated by such devices are often represented as regularly or irregularly spaced discrete functional data, which are challenging for statistical analysis. In this paper we focus on clustering the adherence monitoring data from such devices. We first pre-process the raw discrete functional data into smoothed functional data. Parametric mixture models with change-points, as well as several non-parametric and semi-parametric functional clustering approaches are adapted and applied to the smoothed adherence data. Simulation studies were conducted to evaluate finite sample performances, on the choices of tuning parameters in the pre-processing step as well as the relative performance of different clustering algorithms. We applied these methods to the HIV Prevention Trials Network(HPTN) 069 study for identifying subgroups with distinct adherence behavior over the study period.

Multiscale Functional Clustering Reveals Frequency Dependent Brain Organization in Type II Focal Cortical Dysplasia With Sleep Hypermotor Epilepsy.

A multiscale functional clustering approach is proposed to investigate the organization of the epileptic networks during different sleep stages and in relation with the occurrence of seizures. Stereo-electroencephalographic signals from seven pharmaco-resistant epileptic patients (focal cortical dysplasia type II) were analyzed. The discrete wavelet transform provided a multiscale framework on which a data-driven functional clustering procedure was applied, based on multivariate measures of integration and mutual information. The most interacting functional clusters (FCs) within the sampled brain areas were extracted. FCs characterized by strongly integrated activity were observed mostly in the beta and alpha frequency bands, immediately before seizure onset and in deep sleep stages. These FCs generally included the electrodes from the epileptogenic zone. Furthermore, repeatable patterns were found across ictal events in the same patient. In line with previous studies, our findings provide evidence of the important role of beta and alpha activity in seizures generation and support the relation between epileptic activity and sleep stages. Despite the small number of subjects included in the study, the present results suggest that the proposed multiscale functional clustering approach is a useful tool for the identification of the frequency-dependent mechanisms underlying seizure generation.

Shape invariant mixture model for clustering non-linear longitudinal growth trajectories.

In longitudinal studies, it is often of great interest to cluster individual trajectories based on repeated measurements taken over time. Non-linear growth trajectories are often seen in practice, and the individual data can also be measured sparsely, and at irregular time points, which may complicate the modeling process. Motivated by a study of pregnant women hormone profiles, we proposed a shape invariant growth mixture model for clustering non-linear growth trajectories. Bayesian inference via Monte Carlo Markov Chain was employed to estimate the parameters of interest. We compared our model to the commonly used growth mixture model and functional clustering approach by simulation studies. Results from analyzing the real data and simulated data were presented and discussed.

Functional Clustering of Accelerometer Data Via Transformed Input Variables

Summary The paper considers the clustering problem of physical activity data measured by a computerized accelerometer. Classical methods such as K-means clustering and partitioning around medoids are not efficient in handling accelerometer data that are high dimensional with inherent multiscale structures. Existing functional clustering approaches do not naturally utilize the dynamic structures of accelerometer data that may be necessary to form homogeneous clusters in a meaningful way. The paper introduces new input variables for clustering the accelerometer data based on the rank-based transformation and thick pen transformation, which reflect specific structures of the data such as the amount and the pattern of physical activity while preserving a functional form. The clustering methods proposed are obtained by coupling the transformed input variables with functional clustering that considers a marginal representation of the data for building clustering criteria. We suggest several clustering schemes using the proposed methods and apply the schemes to a real data set of 365 subjects. A simulation study is performed to evaluate the empirical performance of the methods proposed, which are shown to be superior to some existing methods.

Profiling Occupancy Patterns to Calibrate Urban Building Energy Models (UBEMs) Using Measured Data Clustering

Uncertainty in predicting occupancy patterns leads to discrepancies in simulated building energy when compared to measured data. Typical simulation models represent occupants through identical schedules and repetitive behavior. However, users’ activity patterns comprise numerous variations, especially when focusing on interactions in buildings on the neighborhood scale. Urban-scale simulations inform design decisions, and one of the major challenges is identifying representable inputs for occupancy behavior. This paper presents a framework for modeling occupancy and consequent energy loads in residential buildings using measured data for calibration; it employs a functional clustering approach to profile energy use, which generates inputs for Urban Energy Models (UBEMs). The framework is demonstrated on a residential neighborhood and reveals that the generated inputs can more accurately predict community energy load patterns.

Learning the evolution of disciplines from scientific literature: A functional clustering approach to normalized keyword count trajectories

The growing availability of large diachronic corpora of scientific literature offers the opportunity of reading the temporal evolution of concepts, methods and applications, i.e., the history of disciplines involved in the strand under investigation. After a retrieval process of the most relevant keywords, bag-of-words approaches produce words × time-points contingency tables, i.e. the frequencies of each word in the set of texts grouped by time-points. Through the analysis of word counts over the observed period of time, main purpose of the study is, after reconstructing the “life-cycle” of words, clustering words that have similar life-cycles and, thus, detecting prototypical or exemplary temporal patterns. Unveiling such relevant and (through expert opinion) meaningful inner dynamics enables us to trace a historical narrative of the discipline of interest. However, different history readings are possible depending on the type of data normalization, which is needed to account for the fluctuating size of texts across time and the general problems of data sparsity and strong asymmetry. This study proposes a methodology consisting of (1) a stepwise information retrieval procedure for keywords’ selection and (2) a functional clustering two-stage approach for statistical learning. Moreover, a sample of possible normalizations of word frequencies is considered, showing that the different concept of curve similarity induced in clustering by the type of transformation heavily affects groups’ composition and size. The corpus of titles of scientific papers published by the American Statistical Association journals in the time span 1888–2012 is examined for illustration.

Modeling and clustering water demand patterns from real-world smart meter data

Abstract. Nowadays, drinking water utilities need an acute comprehension of the water demand on their distribution network, in order to efficiently operate the optimization of resources, manage billing and propose new customer services. With the emergence of smart grids, based on automated meter reading (AMR), a better understanding of the consumption modes is now accessible for smart cities with more granularities. In this context, this paper evaluates a novel methodology for identifying relevant usage profiles from the water consumption data produced by smart meters. The methodology is fully data-driven using the consumption time series which are seen as functions or curves observed with an hourly time step. First, a Fourier-based additive time series decomposition model is introduced to extract seasonal patterns from time series. These patterns are intended to represent the customer habits in terms of water consumption. Two functional clustering approaches are then used to classify the extracted seasonal patterns: the functional version of K-means, and the Fourier REgression Mixture (FReMix) model. The K-means approach produces a hard segmentation and K representative prototypes. On the other hand, the FReMix is a generative model and also produces K profiles as well as a soft segmentation based on the posterior probabilities. The proposed approach is applied to a smart grid deployed on the largest water distribution network (WDN) in France. The two clustering strategies are evaluated and compared. Finally, a realistic interpretation of the consumption habits is given for each cluster. The extensive experiments and the qualitative interpretation of the resulting clusters allow one to highlight the effectiveness of the proposed methodology.

Functional Clustering approach for the analysis of Stereo-EEG activity patterns in correspondence of epileptic seizures.

In this study, a functional clustering approach is proposed and tested for the identification of brain functional networks emerging during sleep-related seizures. Stereo-EEG signals recorded in patients with Type II Focal Cortical Dysplasia (FCD type II), were analyzed. This novel approach is able to identify the network configuration changes in pre-ictal and early ictal periods, by grouping Stereo-EEG signals on the basis of the Cluster Index, after wavelet multiscale decomposition. Results showed that the proposed method is able to detect clusters of interacting leads, mainly overlapped on the Epileptogenic Zone (EZ) identified by a clinical expert, with distinctive configurations related to analyzed frequency ranges. This suggested the presence of coupling activities between the elements of the epileptic system at different frequency scales.

Probabilistic model-based functional parcellation reveals a robust, fine-grained subdivision of the striatum

The striatum is involved in many different aspects of behaviour, reflected by the variety of cortical areas that provide input to this structure. This input is topographically organized and is likely to result in functionally specific signals. Such specificity can be examined using functional clustering approaches. Here, we propose a Bayesian model-based functional clustering approach applied solely to resting state striatal functional MRI timecourses to identify intrinsic striatal functional modules. Data from two sets of ten participants were used to obtain parcellations and examine their robustness. This stable clustering was used to initialize a more constrained model in order to obtain individualized parcellations in 57 additional participants. Resulting cluster time courses were used to examine functional connectivity between clusters and related to the rest of the brain in a GLM analysis. We find six distinct clusters in each hemisphere, with clear inter-hemispheric correspondence and functional relevance. These clusters exhibit functional connectivity profiles that further underscore their homologous nature and are consistent with existing notions on segregation and integration in parallel cortico-basal ganglia loops. Our findings suggest that multiple territories within both the affective and motor regions can be distinguished solely using resting state functional MRI from these regions.

A supply network optimisation with functional clustering of industrial resources

Abstract This paper presents a functional clustering approach integrated in an industrial resources optimisation. Industrial processing hub formation through functional clustering of involved facilities is presented. A palm biomass case study is developed in this paper to illustrate the functional clustering model. Production facilities are identified and processing hub allocation is determined in the case study. Two models are developed: (i) biomass supply network optimisation and synthesis and (ii) biomass supply network with functional clustering. The former acts as a base case for optimal supply network synthesis. The following reforms the former by integrating a functional clustering concept. The second model functionally clusters the industrial facilities based on their material interactions. Each cluster formed consists of a centralised processing hub, which acts as the backbone/seed of a functional cluster. Strategic locations of centralised processing hubs are determined and functional clusters are formed by optimisation modelling. Optimised biomass supply networks are developed from the optimisation activities. The optimisation result favours centralised processing hub formation. Lowered machinery capital investment and transportation cost are achieved in the functional clustered model.

Functional clustering for Italian climate zones identification

This work presents a functional clustering procedure applied to meteorological time series. Our proposal combines time series interpolation with smoothing penalized B-spline and the partitioning around medoids clustering algorithm. Our final goal is to obtain homogeneous climate zones of Italy. We compare this approach to standard methods based on a combination of principal component analysis and Cluster Analysis (CA) and we discuss it in relation to other functional clustering approaches based on Fourier analysis and CA. We show that a functional approach is simpler than the standard methods from a methodological and interpretability point of view. Indeed, it becomes natural to find a clear connection between mathematical results and physical variability mechanisms. We discuss how the choice of the basis expansion (splines, Fourier) affects the analysis and propose some comments on their use. The basis for classification is formed by monthly values of temperature and precipitation recorded during the period 1971–2000 over 95 and 94 Italian monitoring stations, respectively. An assessment based on climatic patterns is presented to prove the consistency of the clustering and a comparison of results obtained with different methods is used to judge the functional data approach.

Functional Clustering and Identifying Substructures of Longitudinal Data

SummaryA functional clustering (FC) method, k-centres FC, for longitudinal data is proposed. The k-centres FC approach accounts for both the means and the modes of variation differentials between clusters by predicting cluster membership with a reclassification step. The cluster membership predictions are based on a non-parametric random-effect model of the truncated Karhunen–Loève expansion, coupled with a non-parametric iterative mean and covariance updating scheme. We show that, under the identifiability conditions derived, the k-centres FC method proposed can greatly improve cluster quality as compared with conventional clustering algorithms. Moreover, by exploring the mean and covariance functions of each cluster, thek-centres FC method provides an additional insight into cluster structures which facilitates functional cluster analysis. Practical performance of the k-centres FC method is demonstrated through simulation studies and data applications including growth curve and gene expression profile data.