8,616 research outputs found
Analysis of sensory data using graph signal processing
Air pollution monitoring is an important topic that has been researched in the past few years thanks to the massive deployment of IoT platforms, as it affects the lives of both children and adults, and it kills millions of people worldwide every year. A new framework of tools called Graph Signal Processing was presented recently and it allows, among other things, the ability to predict data on a node that belongs to a network of sensors using both the data itself and the topology of the graph, which is based on the Laplacian matrix. This thesis is a comparative study on different prediction techniques for pollutant signals, such as Linear Combination, Multiple Linear Regression and GSP and it presents the results of all three methods in different scenarios, using RMSE and R2 indicators, and focusing the efforts on the understanding of how different parameters (such as the distance between nodes) affect the performances of these new tools. The results of the study show that pollutants O3 and NO2 are lowpass signals, and as the number of edges between nodes increases, GSP obtains a close performances to MRL. For PM10, we conclude that is not a low-pass signal, and the performance of the indicators drop massively compared with the previous ones. Linear combination is the worst of all three and MLR has a stable performance during all the scenarios
A pattern language for parallelizing irregular algorithms
Dissertação apresentada na Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa para obtenção do grau de Mestre em Engenharia InformáticaIn irregular algorithms, data set’s dependences and distributions cannot be statically predicted.
This class of algorithms tends to organize computations in terms of data locality instead of parallelizing control in multiple threads. Thus, opportunities for exploiting parallelism vary dynamically, according to how the algorithm changes data dependences. As such, effective parallelization of such algorithms requires new approaches that account for that dynamic nature.
This dissertation addresses the problem of building efficient parallel implementations of irregular algorithms by proposing to extract, analyze and document patterns of concurrency and parallelism present in the Galois parallelization framework for irregular algorithms.
Patterns capture formal representations of a tangible solution to a problem that arises in a well defined context within a specific domain.
We document the said patterns in a pattern language, i.e., a set of inter-dependent patterns that compose well-documented template solutions that can be reused whenever a certain problem arises in a well-known context
On morphological hierarchical representations for image processing and spatial data clustering
Hierarchical data representations in the context of classi cation and data
clustering were put forward during the fties. Recently, hierarchical image
representations have gained renewed interest for segmentation purposes. In this
paper, we briefly survey fundamental results on hierarchical clustering and
then detail recent paradigms developed for the hierarchical representation of
images in the framework of mathematical morphology: constrained connectivity
and ultrametric watersheds. Constrained connectivity can be viewed as a way to
constrain an initial hierarchy in such a way that a set of desired constraints
are satis ed. The framework of ultrametric watersheds provides a generic scheme
for computing any hierarchical connected clustering, in particular when such a
hierarchy is constrained. The suitability of this framework for solving
practical problems is illustrated with applications in remote sensing
Functional Regression
Functional data analysis (FDA) involves the analysis of data whose ideal
units of observation are functions defined on some continuous domain, and the
observed data consist of a sample of functions taken from some population,
sampled on a discrete grid. Ramsay and Silverman's 1997 textbook sparked the
development of this field, which has accelerated in the past 10 years to become
one of the fastest growing areas of statistics, fueled by the growing number of
applications yielding this type of data. One unique characteristic of FDA is
the need to combine information both across and within functions, which Ramsay
and Silverman called replication and regularization, respectively. This article
will focus on functional regression, the area of FDA that has received the most
attention in applications and methodological development. First will be an
introduction to basis functions, key building blocks for regularization in
functional regression methods, followed by an overview of functional regression
methods, split into three types: [1] functional predictor regression
(scalar-on-function), [2] functional response regression (function-on-scalar)
and [3] function-on-function regression. For each, the role of replication and
regularization will be discussed and the methodological development described
in a roughly chronological manner, at times deviating from the historical
timeline to group together similar methods. The primary focus is on modeling
and methodology, highlighting the modeling structures that have been developed
and the various regularization approaches employed. At the end is a brief
discussion describing potential areas of future development in this field
Graph-Based Analysis and Visualisation of Mobility Data
Urban mobility forecast and analysis can be addressed through grid-based and
graph-based models. However, graph-based representations have the advantage of
more realistically depicting the mobility networks and being more robust since
they allow the implementation of Graph Theory machinery, enhancing the analysis
and visualisation of mobility flows. We define two types of mobility graphs:
Region Adjacency graphs and Origin-Destination graphs. Several node centrality
metrics of graphs are applied to identify the most relevant nodes of the
network in terms of graph connectivity. Additionally, the Perron vector
associated with a strongly connected graph is applied to define a circulation
function on the mobility graph. Such node values are visualised in the
geographically embedded graphs, showing clustering patterns within the network.
Since mobility graphs can be directed or undirected, we define several Graph
Laplacian for both cases and show that these matrices and their spectral
properties provide insightful information for network analysis. The computation
of node centrality metrics and Perron-induced circulation functions for three
different geographical regions demonstrate that basic elements from Graph
Theory applied to mobility networks can lead to structure analysis for graphs
of different connectivity, size, and orientation properties.Comment: 19 pages, 7 figure
Fast Robust PCA on Graphs
Mining useful clusters from high dimensional data has received significant
attention of the computer vision and pattern recognition community in the
recent years. Linear and non-linear dimensionality reduction has played an
important role to overcome the curse of dimensionality. However, often such
methods are accompanied with three different problems: high computational
complexity (usually associated with the nuclear norm minimization),
non-convexity (for matrix factorization methods) and susceptibility to gross
corruptions in the data. In this paper we propose a principal component
analysis (PCA) based solution that overcomes these three issues and
approximates a low-rank recovery method for high dimensional datasets. We
target the low-rank recovery by enforcing two types of graph smoothness
assumptions, one on the data samples and the other on the features by designing
a convex optimization problem. The resulting algorithm is fast, efficient and
scalable for huge datasets with O(nlog(n)) computational complexity in the
number of data samples. It is also robust to gross corruptions in the dataset
as well as to the model parameters. Clustering experiments on 7 benchmark
datasets with different types of corruptions and background separation
experiments on 3 video datasets show that our proposed model outperforms 10
state-of-the-art dimensionality reduction models. Our theoretical analysis
proves that the proposed model is able to recover approximate low-rank
representations with a bounded error for clusterable data
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