Approximated and User Steerable tSNE for Progressive Visual Analytics

Progressive Visual Analytics aims at improving the interactivity in existing analytics techniques by means of visualization as well as interaction with intermediate results. One key method for data analysis is dimensionality reduction, for example, to produce 2D embeddings that can be visualized and analyzed efficiently. t-Distributed Stochastic Neighbor Embedding (tSNE) is a well-suited technique for the visualization of several high-dimensional data. tSNE can create meaningful intermediate results but suffers from a slow initialization that constrains its application in Progressive Visual Analytics. We introduce a controllable tSNE approximation (A-tSNE), which trades off speed and accuracy, to enable interactive data exploration. We offer real-time visualization techniques, including a density-based solution and a Magic Lens to inspect the degree of approximation. With this feedback, the user can decide on local refinements and steer the approximation level during the analysis. We demonstrate our technique with several datasets, in a real-world research scenario and for the real-time analysis of high-dimensional streams to illustrate its effectiveness for interactive data analysis

Percolation Analysis of a Wiener Reconstruction of the IRAS 1.2 Jy Redshift Catalog

We present percolation analyses of Wiener Reconstructions of the IRAS 1.2 Jy Redshift Survey. There are ten reconstructions of galaxy density fields in real space spanning the range $\beta= 0.1$ to $1.0$, where ${\beta}={\Omega^{0.6}}/b$, $\Omega$ is the present dimensionless density and $b$ is the bias factor. Our method uses the growth of the largest cluster statistic to characterize the topology of a density field, where Gaussian randomized versions of the reconstructions are used as standards for analysis. For the reconstruction volume of radius, $R {\approx} 100 h^{-1}$ Mpc, percolation analysis reveals a slight `meatball' topology for the real space, galaxy distribution of the IRAS survey. cosmology-galaxies:clustering-methods:numericalComment: Revised version accepted for publication in The Astrophysical Journal, January 10, 1997 issue, Vol.47

How are galaxies assigned to halos? Searching for assembly bias in the SDSS galaxy clustering

Clustering of dark matter halos has been shown to depend on halo properties beyond mass such as halo concentration, a phenomenon referred to as halo assembly bias. Standard halo occupation models (HOD) in large scale structure studies assume that halo mass alone is sufficient in characterizing the connection between galaxies and halos. Modeling of galaxy clustering can face systematic effects if the number of galaxies within a halo is correlated with other halo properties. Using the Small MultiDark-Planck high resolution $N$-body simulation and the clustering measurements of the Sloan Digital Sky Survey (SDSS) DR7 main galaxy sample, we investigate the extent to which the concentration-dependence of halo occupation can be constrained. Furthermore, we study how allowing for the concentration dependence can improve our modeling of galaxy clustering. Our constraints on HOD with assembly bias suggest that satellite population is not correlated with halo concentration at fixed halo mass. At fixed halo mass, our constraints favor lack of correlation between the occupation of centrals and halo concentration in the most luminous samples ($M_{\rm r}<-21.5,-21$), and modest correlation in the $M_{\rm r}<-20.5,-20, -19.5$ samples. We show that in comparison with abundance-matching mock catalogs, our findings suggest qualitatively similar but modest levels of the impact of halo assembly bias on galaxy clustering. The effect is only present in the central occupation and becomes less significant in brighter galaxy samples. Furthermore, by performing model comparison based on information criteria, we find that in most cases, the standard mass-only HOD model is still favored by the observations.Comment: Accepted for publication in Ap

Improving k-nn search and subspace clustering based on local intrinsic dimensionality

In several novel applications such as multimedia and recommender systems, data is often represented as object feature vectors in high-dimensional spaces. The high-dimensional data is always a challenge for state-of-the-art algorithms, because of the so-called curse of dimensionality . As the dimensionality increases, the discriminative ability of similarity measures diminishes to the point where many data analysis algorithms, such as similarity search and clustering, that depend on them lose their effectiveness. One way to handle this challenge is by selecting the most important features, which is essential for providing compact object representations as well as improving the overall search and clustering performance. Having compact feature vectors can further reduce the storage space and the computational complexity of search and learning tasks. Support-Weighted Intrinsic Dimensionality (support-weighted ID) is a new promising feature selection criterion that estimates the contribution of each feature to the overall intrinsic dimensionality. Support-weighted ID identifies relevant features locally for each object, and penalizes those features that have locally lower discriminative power as well as higher density. In fact, support-weighted ID measures the ability of each feature to locally discriminate between objects in the dataset. Based on support-weighted ID, this dissertation introduces three main research contributions: First, this dissertation proposes NNWID-Descent, a similarity graph construction method that utilizes the support-weighted ID criterion to identify and retain relevant features locally for each object and enhance the overall graph quality. Second, with the aim to improve the accuracy and performance of cluster analysis, this dissertation introduces k-LIDoids, a subspace clustering algorithm that extends the utility of support-weighted ID within a clustering framework in order to gradually select the subset of informative and important features per cluster. k-LIDoids is able to construct clusters together with finding a low dimensional subspace for each cluster. Finally, using the compact object and cluster representations from NNWID-Descent and k-LIDoids, this dissertation defines LID-Fingerprint, a new binary fingerprinting and multi-level indexing framework for the high-dimensional data. LID-Fingerprint can be used for hiding the information as a way of preventing passive adversaries as well as providing an efficient and secure similarity search and retrieval for the data stored on the cloud. When compared to other state-of-the-art algorithms, the good practical performance provides an evidence for the effectiveness of the proposed algorithms for the data in high-dimensional spaces

Enhanced clustering analysis pipeline for performance analysis of parallel applications

Clustering analysis is widely used to stratify data in the same cluster when they are similar according to the specific metrics. We can use the cluster analysis to group the CPU burst of a parallel application, and the regions on each process in-between communication calls or calls to the parallel runtime. The resulting clusters obtained are the different computational trends or phases that appear in the application. These clusters are useful to understand the behavior of the computation part of the application and focus the analyses on those that present performance issues. Although density-based clustering algorithms are a powerful and efficient tool to summarize this type of information, their traditional user-guided clustering methodology has many shortcomings and deficiencies in dealing with the complexity of data, the diversity of data structures, high-dimensionality of data, and the dramatic increase in the amount of data. Consequently, the majority of DBSCAN-like algorithms have weaknesses to handle high-dimensionality and/or Multi-density data, and they are sensitive to their hyper-parameter configuration. Furthermore, extracting insight from the obtained clusters is an intuitive and manual task. To mitigate these weaknesses, we have proposed a new unified approach to replace the user-guided clustering with an automated clustering analysis pipeline, called Enhanced Cluster Identification and Interpretation (ECII) pipeline. To build the pipeline, we propose novel techniques including Robust Independent Feature Selection, Feature Space Curvature Map, Organization Component Analysis, and hyper-parameters tuning to feature selection, density homogenization, cluster interpretation, and model selection which are the main components of our machine learning pipeline. This thesis contributes four new techniques to the Machine Learning field with a particular use case in Performance Analytics field. The first contribution is a novel unsupervised approach for feature selection on noisy data, called Robust Independent Feature Selection (RIFS). Specifically, we choose a feature subset that contains most of the underlying information, using the same criteria as the Independent component analysis. Simultaneously, the noise is separated as an independent component. The second contribution of the thesis is a parametric multilinear transformation method to homogenize cluster densities while preserving the topological structure of the dataset, called Feature Space Curvature Map (FSCM). We present a new Gravitational Self-organizing Map to model the feature space curvature by plugging the concepts of gravity and fabric of space into the Self-organizing Map algorithm to mathematically describe the density structure of the data. To homogenize the cluster density, we introduce a novel mapping mechanism to project the data from the non-Euclidean curved space to a new Euclidean flat space. The third contribution is a novel topological-based method to study potentially complex high-dimensional categorized data by quantifying their shapes and extracting fine-grain insights from them to interpret the clustering result. We introduce our Organization Component Analysis (OCA) method for the automatic arbitrary cluster-shape study without an assumption about the data distribution. Finally, to tune the DBSCAN hyper-parameters, we propose a new tuning mechanism by combining techniques from machine learning and optimization domains, and we embed it in the ECII pipeline. Using this cluster analysis pipeline with the CPU burst data of a parallel application, we provide the developer/analyst with a high-quality SPMD computation structure detection with the added value that reflects the fine grain of the computation regions.El análisis de conglomerados se usa ampliamente para estratificar datos en el mismo conglomerado cuando son similares según las métricas específicas. Nosotros puede usar el análisis de clúster para agrupar la ráfaga de CPU de una aplicación paralela y las regiones en cada proceso intermedio llamadas de comunicación o llamadas al tiempo de ejecución paralelo. Los clusters resultantes obtenidos son las diferentes tendencias computacionales o fases que aparecen en la solicitud. Estos clusters son útiles para entender el comportamiento de la parte de computación del aplicación y centrar los análisis en aquellos que presenten problemas de rendimiento. Aunque los algoritmos de agrupamiento basados en la densidad son una herramienta poderosa y eficiente para resumir este tipo de información, su La metodología tradicional de agrupación en clústeres guiada por el usuario tiene muchas deficiencias y deficiencias al tratar con la complejidad de los datos, la diversidad de estructuras de datos, la alta dimensionalidad de los datos y el aumento dramático en la cantidad de datos. En consecuencia, el La mayoría de los algoritmos similares a DBSCAN tienen debilidades para manejar datos de alta dimensionalidad y/o densidad múltiple, y son sensibles a su configuración de hiperparámetros. Además, extraer información de los clústeres obtenidos es una forma intuitiva y tarea manual Para mitigar estas debilidades, hemos propuesto un nuevo enfoque unificado para reemplazar el agrupamiento guiado por el usuario con un canalización de análisis de agrupamiento automatizado, llamada canalización de identificación e interpretación de clúster mejorada (ECII). para construir el tubería, proponemos técnicas novedosas que incluyen la selección robusta de características independientes, el mapa de curvatura del espacio de características, Análisis de componentes de la organización y ajuste de hiperparámetros para la selección de características, homogeneización de densidad, agrupación interpretación y selección de modelos, que son los componentes principales de nuestra canalización de aprendizaje automático. Esta tesis aporta cuatro nuevas técnicas al campo de Machine Learning con un caso de uso particular en el campo de Performance Analytics. La primera contribución es un enfoque novedoso no supervisado para la selección de características en datos ruidosos, llamado Robust Independent Feature. Selección (RIFS).Específicamente, elegimos un subconjunto de funciones que contiene la mayor parte de la información subyacente, utilizando el mismo criterios como el análisis de componentes independientes. Simultáneamente, el ruido se separa como un componente independiente. La segunda contribución de la tesis es un método de transformación multilineal paramétrica para homogeneizar densidades de clústeres mientras preservando la estructura topológica del conjunto de datos, llamado Mapa de Curvatura del Espacio de Características (FSCM). Presentamos un nuevo Gravitacional Mapa autoorganizado para modelar la curvatura del espacio característico conectando los conceptos de gravedad y estructura del espacio en el Algoritmo de mapa autoorganizado para describir matemáticamente la estructura de densidad de los datos. Para homogeneizar la densidad del racimo, introducimos un mecanismo de mapeo novedoso para proyectar los datos del espacio curvo no euclidiano a un nuevo plano euclidiano espacio. La tercera contribución es un nuevo método basado en topología para estudiar datos categorizados de alta dimensión potencialmente complejos mediante cuantificando sus formas y extrayendo información detallada de ellas para interpretar el resultado de la agrupación. presentamos nuestro Método de análisis de componentes de organización (OCA) para el estudio automático de forma arbitraria de conglomerados sin una suposición sobre el distribución de datos.Postprint (published version

A Framework for Approximate Optimization of BoT Application Deployment in Hybrid Cloud Environment

We adopt a systematic approach to investigate the efficiency of near-optimal deployment of large-scale CPU-intensive Bag-of-Task applications running on cloud resources with the non-proportional cost to performance ratios. Our analytical solutions perform in both known and unknown running time of the given application. It tries to optimize users' utility by choosing the most desirable tradeoff between the make-span and the total incurred expense. We propose a schema to provide a near-optimal deployment of BoT application regarding users' preferences. Our approach is to provide user with a set of Pareto-optimal solutions, and then she may select one of the possible scheduling points based on her internal utility function. Our framework can cope with uncertainty in the tasks' execution time using two methods, too. First, an estimation method based on a Monte Carlo sampling called AA algorithm is presented. It uses the minimum possible number of sampling to predict the average task running time. Second, assuming that we have access to some code analyzer, code profiling or estimation tools, a hybrid method to evaluate the accuracy of each estimation tool in certain interval times for improving resource allocation decision has been presented. We propose approximate deployment strategies that run on hybrid cloud. In essence, proposed strategies first determine either an estimated or an exact optimal schema based on the information provided from users' side and environmental parameters. Then, we exploit dynamic methods to assign tasks to resources to reach an optimal schema as close as possible by using two methods. A fast yet simple method based on First Fit Decreasing algorithm, and a more complex approach based on the approximation solution of the transformed problem into a subset sum problem. Extensive experiment results conducted on a hybrid cloud platform confirm that our framework can deliver a near optimal solution respecting user's utility function

A Training Set Subsampling Strategy for the Reduced Basis Method

We present a subsampling strategy for the offline stage of the Reduced Basis Method. The approach is aimed at bringing down the considerable offline costs associated with using a finely-sampled training set. The proposed algorithm exploits the potential of the pivoted QR decomposition and the discrete empirical interpolation method to identify important parameter samples. It consists of two stages. In the first stage, we construct a low-fidelity approximation to the solution manifold over a fine training set. Then, for the available low-fidelity snapshots of the output variable, we apply the pivoted QR decomposition or the discrete empirical interpolation method to identify a set of sparse sampling locations in the parameter domain. These points reveal the structure of the parametric dependence of the output variable. The second stage proceeds with a subsampled training set containing a by far smaller number of parameters than the initial training set. Different subsampling strategies inspired from recent variants of the empirical interpolation method are also considered. Tests on benchmark examples justify the new approach and show its potential to substantially speed up the offline stage of the Reduced Basis Method, while generating reliable reduced-order models.Comment: 31 pages, 10 figures, 6 table