Robust k -Means-Type Clustering for Noisy Data.

Data clustering is a fundamental machine learning task that seeks to categorize a dataset into homogeneous groups. However, real data usually contain noise, which poses significant challenges to clustering algorithms. In this article, motivated by how the k -means algorithm is derived from a Gaussian mixture model (GMM), we propose a robust k -means-type algorithm, named k -means-type clustering based on t -distribution (KMTD), by assuming that the data points are drawn from a special multivariate t -mixture model (TMM). Compared to the Gaussian distribution, the t -distribution has a fatter tail. The proposed algorithm is more robust to noise. Like the k -means algorithm, the proposed algorithm is simpler than those based on a full TMM. Both synthetic and actual data are used to illustrate the proposed algorithm's performance and efficiency. The experimental results demonstrated that the proposed algorithm operates more quickly than other sophisticated algorithms and, in most cases, achieves higher accuracy than the other algorithms.

Multicentre, randomized comparison of two-stent and provisional stenting techniques in patients with complex coronary bifurcation lesions: the DEFINITION II trial.

AIM: The present study aimed to assess the benefits of two-stent techniques for patients with DEFINITION criteria-defined complex coronary bifurcation lesions. METHODS AND RESULTS: In total, 653 patients with complex bifurcation lesions at 49 international centres were randomly assigned to undergo the systematic two-stent technique (two-stent group) or provisional stenting (provisional group). The primary endpoint was the composite of target lesion failure (TLF) at the 1-year follow-up, including cardiac death, target vessel myocardial infarction (TVMI), and clinically driven target lesion revascularization (TLR). The safety endpoint was definite or probable stent thrombosis. At the 1-year follow-up, TLF occurred in 37 (11.4%) and 20 (6.1%) patients in the provisional and two-stent groups, respectively [77.8%: double-kissing crush; hazard ratio (HR) 0.52, 95% confidence interval (CI) 0.30-0.90; P = 0.019], largely driven by increased TVMI (7.1%, HR 0.43, 95% CI 0.20-0.90; P = 0.025) and clinically driven TLR (5.5%, HR 0.43, 95% CI 0.19-1.00; P = 0.049) in the provisional group. At the 1 year after indexed procedures, the incidence of cardiac death was 2.5% in the provisional group, non-significant to 2.1% in the two-stent group (HR 0.86, 95% CI 0.31-2.37; P = 0.772). CONCLUSION: For DEFINITION criteria-defined complex coronary bifurcation lesions, the systematic two-stent approach was associated with a significant improvement in clinical outcomes compared with the provisional stenting approach. Further study is urgently warranted to identify the mechanisms contributing to the increased rate of TVMI after provisional stenting. STUDY REGISTRATION: http://www.clinicaltrials.com; Identifier: NCT02284750.

Correlation-based iterative clustering methods for time course data: The identification of temporal gene response modules for influenza infection in humans.

Many pragmatic clustering methods have been developed to group data vectors or objects into clusters so that the objects in one cluster are very similar and objects in different clusters are distinct based on some similarity measure. The availability of time course data has motivated researchers to develop methods, such as mixture and mixed-effects modelling approaches, that incorporate the temporal information contained in the shape of the trajectory of the data. However, there is still a need for the development of time-course clustering methods that can adequately deal with inhomogeneous clusters (some clusters are quite large and others are quite small). Here we propose two such methods, hierarchical clustering (IHC) and iterative pairwise-correlation clustering (IPC). We evaluate and compare the proposed methods to the Markov Cluster Algorithm (MCL) and the generalised mixed-effects model (GMM) using simulation studies and an application to a time course gene expression data set from a study containing human subjects who were challenged by a live influenza virus. We identify four types of temporal gene response modules to influenza infection in humans, i.e., single-gene modules (SGM), small-size modules (SSM), medium-size modules (MSM) and large-size modules (LSM). The LSM contain genes that perform various fundamental biological functions that are consistent across subjects. The SSM and SGM contain genes that perform either different or similar biological functions that have complex temporal responses to the virus and are unique to each subject. We show that the temporal response of the genes in the LSM have either simple patterns with a single peak or trough a consequence of the transient stimuli sustained or state-transitioning patterns pertaining to developmental cues and that these modules can differentiate the severity of disease outcomes. Additionally, the size of gene response modules follows a power-law distribution with a consistent exponent across all subjects, which reveals the presence of universality in the underlying biological principles that generated these modules.