Performance analysis is an essential task in High-Performance Computing (HPC) systems and it is applied for different purposes such as anomaly detection, optimal resource allocation, and budget planning. HPC monitoring tasks generate a huge number of Key Performance Indicators (KPIs) to supervise the status of the jobs running in these systems. KPIs give data about CPU usage, memory usage, network (interface) traffic, or other sensors that monitor the hardware. Analyzing this data, it is possible to obtain insightful information about running jobs, such as their characteristics, performance, and failures. The main contribution in this paper is to identify which metric/s (KPIs) is/are the most appropriate to identify/classify different types of jobs according to their behavior in the HPC system. With this aim, we have applied different clustering techniques (partition and hierarchical clustering algorithms) using a real dataset from the Galician Computation Center (CESGA). We have concluded that (i) those metrics (KPIs) related to the Network (interface) traffic monitoring provide the best cohesion and separation to cluster HPC jobs, and (ii) hierarchical clustering algorithms are the most suitable for this task. Our approach was validated using a different real dataset from the same HPC center.

Among ensemble clustering methods, Evidence Accumulation Clustering is one of the simplest technics. In this approach, a co-association (CA) matrix representing the co-clustering frequency is built and then clustered to extract consensus clusters. Compared to other approaches, this one is simple as there is no need to find matches between clusters obtained from two different partitionings. Nevertheless, this method suffers from computational issues, as it requires to compute and store a matrix of size n x n, where n is the number of items. Due to the quadratic cost, this approach is reserved for small datasets. This work describes a trick which mimic the behavior of average linkage clustering. We found a way of computing efficiently the density of a partitioning, reducing the cost from a quadratic to linear complexity. Additionally, we proved that the k-means maximizes naturally the density. We performed experiments on several benchmark datasets where we compared the k-means and the bisecting version to other state-of-the-art consensus algorithms. The k-means results are comparable to the best state of the art in terms of NMI while keeping the computational cost low. Additionally, the k-means led to the best results in terms of density. These results provide evidence that consensus clustering can be solved with simple algorithms.

Matrix valued data has become increasingly prevalent in many applications. Most of the existing clustering methods for this type of data are tailored to the mean model and do not account for the dependence structure of the features, which can be very informative, especially in high-dimensional settings. To extract the information from the dependence structure for clustering, we propose a new latent variable model for the features arranged in matrix form, with some unknown membership matrices representing the clusters for the rows and columns. Under this model, we further propose a class of hierarchical clustering algorithms using the difference of a weighted covariance matrix as the dissimilarity measure. Theoretically, we show that under mild conditions, our algorithm attains clustering consistency in the high-dimensional setting. While this consistency result holds for our algorithm with a broad class of weighted covariance matrices, the conditions for this result depend on the choice of the weight. To investigate how the weight affects the theoretical performance of our algorithm, we establish the minimax lower bound for clustering under our latent variable model. Given these results, we identify the optimal weight in the sense that using this weight guarantees our algorithm to be minimax rate-optimal in terms of the magnitude of some cluster separation metric. The practical implementation of our algorithm with the optimal weight is also discussed. Finally, we conduct simulation studies to evaluate the finite sample performance of our algorithm and apply the method to a genomic dataset.

We investigate a natural generalization of the classical clustering problem, considering clustering tasks in which different instances may have different weights. We conduct the first extensive theoretical analysis on the influence of weighted data on standard clustering algorithms in both the partitional and hierarchical settings, characterizing the conditions under which algorithms react to weights. Extending a recent framework for clustering algorithm selection, we propose intuitive properties that would allow users to choose between clustering algorithms in the weighted setting and classify algorithms accordingly.

Selecting a clustering algorithm is a perplexing task. Yet since different algorithms may yield dramatically different outputs on the same data, the choice of algorithm is crucial. When selecting a clustering algorithm, users tend to focus on cost-related considerations (software purchasing costs, running times, etc). Differences concerning the output of the algorithms are not usually considered. Recently, a formal approach for selecting a clustering algorithm has been proposed (Ackerman, Ben-David, and Loker, NIPS 2010). The approach involves distilling abstract properties of the input-output behavior of different clustering paradigms and classifying algorithms based on these properties. In this paper, we extend this approach into the hierarchical setting. The class of linkage-based algorithms is perhaps the most popular class of hierarchical algorithms. We identify two properties of hierarchical algorithms, and prove that linkage-based algorithms are the only ones that satisfy both of these properties. Our characterization clearly delineates the difference between linkage-based algorithms and other hierarchical algorithms. We formulate an intuitive notion of locality of a hierarchical algorithm that distinguishes between linkage-based and "global" hierarchical algorithms like bisecting k-means, and prove that popular divisive hierarchical algorithms produce clusterings that cannot be produced by any linkage-based algorithm.