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Fast, Scalable, and Accurate Algorithms for Time-Series Analysis
Time is a critical element for the understanding of natural processes (e.g., earthquakes and weather) or human-made artifacts (e.g., stock market and speech signals). The analysis of time series, the result of sequentially collecting observations of such processes and artifacts, is becoming increasingly prevalent across scientific and industrial applications. The extraction of non-trivial features (e.g., patterns, correlations, and trends) in time series is a critical step for devising effective time-series mining methods for real-world problems and the subject of active research for decades. In this dissertation, we address this fundamental problem by studying and presenting computational methods for efficient unsupervised learning of robust feature representations from time series. Our objective is to (i) simplify and unify the design of scalable and accurate time-series mining algorithms; and (ii) provide a set of readily available tools for effective time-series analysis. We focus on applications operating solely over time-series collections and on applications where the analysis of time series complements the analysis of other types of data, such as text and graphs.
For applications operating solely over time-series collections, we propose a generic computational framework, GRAIL, to learn low-dimensional representations that natively preserve the invariances offered by a given time-series comparison method. GRAIL represents a departure from classic approaches in the time-series literature where representation methods are agnostic to the similarity function used in subsequent learning processes. GRAIL relies on the attractive idea that once we construct the data-to-data similarity matrix most time-series mining tasks can be trivially solved. To overcome scalability issues associated with approaches relying on such matrices, GRAIL exploits time-series clustering to construct a small set of landmark time series and learns representations to reduce the data-to-data matrix to a data-to-landmark points matrix. To demonstrate the effectiveness of GRAIL, we first present domain-independent, highly accurate, and scalable time-series clustering methods to facilitate exploration and summarization of time-series collections. Then, we show that GRAIL representations, when combined with suitable methods, significantly outperform, in terms of efficiency and accuracy, state-of-the-art methods in major time-series mining tasks, such as querying, clustering, classification, sampling, and visualization. Overall, GRAIL rises as a new primitive for highly accurate, yet scalable, time-series analysis.
For applications where the analysis of time series complements the analysis of other types of data, such as text and graphs, we propose generic, simple, and lightweight methodologies to learn features from time-varying measurements. Such applications often organize operations over different types of data in a pipeline such that one operation provides input---in the form of feature vectors---to subsequent operations. To reason about the temporal patterns and trends in the underlying features, we need to (i) track the evolution of features over different time periods; and (ii) transform these time-varying features into actionable knowledge (e.g., forecasting an outcome). To address this challenging problem, we propose principled approaches to model time-varying features and study two large-scale, real-world, applications. Specifically, we first study the problem of predicting the impact of scientific concepts through temporal analysis of characteristics extracted from the metadata and full text of scientific articles. Then, we explore the promise of harnessing temporal patterns in behavioral signals extracted from web search engine logs for early detection of devastating diseases. In both applications, combinations of features with time-series relevant features yielded the greatest impact than any other indicator considered in our analysis. We believe that our simple methodology, along with the interesting domain-specific findings that our work revealed, will motivate new studies across different scientific and industrial settings
Analysis of FMRI Exams Through Unsupervised Learning and Evaluation Index
In the last few years, the clustering of time series has seen significant growth and has proven effective in
providing useful information in various domains of use. This growing interest in time series clustering is the
result of the effort made by the scientific community in the context of time data mining.
For these reasons, the first phase of the thesis focused on the study of the data obtained from fMRI exams
carried out in task-based and resting state mode, using and comparing different clustering algorithms: SelfOrganizing map (SOM), the Growing Neural Gas (GNG) and Neural Gas (NG) which are crisp-type
algorithms, a fuzzy algorithm, the Fuzzy C algorithm, was also used (FCM). The evaluation of the results
obtained by using clustering algorithms was carried out using the Davies Bouldin evaluation index (DBI or
DB index).
Clustering evaluation is the second topic of this thesis. To evaluate the validity of the clustering, there are
specific techniques, but none of these is already consolidated for the study of fMRI exams. Furthermore,
the evaluation of evaluation techniques is still an open research field. Eight clustering validation indexes
(CVIs) applied to fMRI data clustering will be analysed. The validation indices that have been used are
Pakhira Bandyopadhyay Maulik Index (crisp and fuzzy), Fukuyama Sugeno Index, Rezaee Lelieveldt Reider
Index, Wang Sun Jiang Index, Xie Beni Index, Davies Bouldin Index, Soft Davies Bouldin Index. Furthermore,
an evaluation of the evaluation indices will be carried out, which will take into account the sub-optimal
performance obtained by the indices, through the introduction of new metrics. Finally, a new methodology
for the evaluation of CVIs will be introduced, which will use an ANFIS model
Recent advances in directional statistics
Mainstream statistical methodology is generally applicable to data observed
in Euclidean space. There are, however, numerous contexts of considerable
scientific interest in which the natural supports for the data under
consideration are Riemannian manifolds like the unit circle, torus, sphere and
their extensions. Typically, such data can be represented using one or more
directions, and directional statistics is the branch of statistics that deals
with their analysis. In this paper we provide a review of the many recent
developments in the field since the publication of Mardia and Jupp (1999),
still the most comprehensive text on directional statistics. Many of those
developments have been stimulated by interesting applications in fields as
diverse as astronomy, medicine, genetics, neurology, aeronautics, acoustics,
image analysis, text mining, environmetrics, and machine learning. We begin by
considering developments for the exploratory analysis of directional data
before progressing to distributional models, general approaches to inference,
hypothesis testing, regression, nonparametric curve estimation, methods for
dimension reduction, classification and clustering, and the modelling of time
series, spatial and spatio-temporal data. An overview of currently available
software for analysing directional data is also provided, and potential future
developments discussed.Comment: 61 page
Vertical wind profile characterization and identification of patterns based on a shape clustering algorithm
Wind power plants are becoming a generally accepted resource in the generation mix of many utilities. At the same time, the size and the power rating of individual wind turbines have increased considerably. Under these circumstances, the sector is increasingly demanding an accurate characterization of vertical wind speed profiles to estimate properly the incoming wind speed at the rotor swept area and, consequently, assess the potential for a wind power plant site. The present paper describes a shape-based clustering characterization and visualization of real vertical wind speed data. The proposed solution allows us to identify the most likely vertical wind speed patterns for a specific location based on real wind speed measurements. Moreover, this clustering approach also provides characterization and classification of such vertical wind profiles. This solution is highly suitable for a large amount of data collected by remote sensing equipment, where wind speed values at different heights within the rotor swept area are available for subsequent analysis. The methodology is based on z-normalization, shape-based distance metric solution and the Ward-hierarchical clustering method. Real vertical wind speed profile data corresponding to a Spanish wind power plant and collected by using a commercialWindcube equipment during several months are used to assess the proposed characterization and clustering process, involving more than 100000 wind speed data values. All analyses have been implemented using open-source R-software. From the results, at least four different vertical wind speed patterns are identified to characterize properly over 90% of the collected wind speed data along the day. Therefore, alternative analytical function criteria should be subsequently proposed for vertical wind speed characterization purposes.The authors are grateful for the financial support from the Spanish Ministry of the Economy and Competitiveness and the European Union âENE2016-78214-C2-2-Râand the Spanish Education, Culture and Sport Ministry âFPU16/042
Development Of Climate Classification Through Hierarchical Clustering For Building Energy Simulation
Climate classification plays an important role for the identification of homogeneous groups of climates, from which representative locations can be extracted and used for building energy simulation analyses. Nevertheless, according to the current state-of-the-art, the main reference systems consider just a fraction of those weather quantities which are relevant in the building energy balance, i.e., ambient temperature and humidity and solar radiation. To overcome this issue, in previous researches a new methodology was defined, based on monthly series of weather quantities, statistical analyses and data-mining techniques for climate clustering. In this work, with the aim of further developing such approach, a shorter time-discretization of weather quantities, i.e., a weekly discretization, was tested, alongside additional variables describing the daily range of ambient temperature and humidity. In order to investigate the potential of those modifications, a dataset with more than 300 European reference climates was analyzed and subdivided into climate classes according to the proposed clustering procedure
Compressive Mining: Fast and Optimal Data Mining in the Compressed Domain
Real-world data typically contain repeated and periodic patterns. This
suggests that they can be effectively represented and compressed using only a
few coefficients of an appropriate basis (e.g., Fourier, Wavelets, etc.).
However, distance estimation when the data are represented using different sets
of coefficients is still a largely unexplored area. This work studies the
optimization problems related to obtaining the \emph{tightest} lower/upper
bound on Euclidean distances when each data object is potentially compressed
using a different set of orthonormal coefficients. Our technique leads to
tighter distance estimates, which translates into more accurate search,
learning and mining operations \textit{directly} in the compressed domain.
We formulate the problem of estimating lower/upper distance bounds as an
optimization problem. We establish the properties of optimal solutions, and
leverage the theoretical analysis to develop a fast algorithm to obtain an
\emph{exact} solution to the problem. The suggested solution provides the
tightest estimation of the -norm or the correlation. We show that typical
data-analysis operations, such as k-NN search or k-Means clustering, can
operate more accurately using the proposed compression and distance
reconstruction technique. We compare it with many other prevalent compression
and reconstruction techniques, including random projections and PCA-based
techniques. We highlight a surprising result, namely that when the data are
highly sparse in some basis, our technique may even outperform PCA-based
compression.
The contributions of this work are generic as our methodology is applicable
to any sequential or high-dimensional data as well as to any orthogonal data
transformation used for the underlying data compression scheme.Comment: 25 pages, 20 figures, accepted in VLD
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