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NOVEL TECHNIQUES FOR INTRINSIC DIMENSION ESTIMATION
Full text linkSince the 1950s, the rapid pace of technological advances allows to measure
and record increasing amounts of data, motivating the urgent need to develop
dimensionality reduction systems to be applied on datasets comprising high-
dimensional points.
To this aim, a fundamental information is provided by the intrinsic di-
mension (id) defined by Bennet [1] as the minimum number of parameters
needed to generate a data description by maintaining the “intrinsic” structure
characterizing the dataset, so that the information loss is minimized.
More recently, a quite intuitive definition employed by several authors in the
past has been reported by Bishop in [2] where the author writes that “a set in
D dimensions is said to have an id equal to d if the data lies entirely within a
d-dimensional subspace of D ”.
Though more specific and different id definitions have been proposed in dif-
ferent research fieldsthroughout the pattern recognition literature the presently
prevailing id definition views a point set as a sample set uniformly drawn from
an unknown smooth (or locally smooth) manifold structure, eventually embed-
ded in an higher dimensional space through a non-linear smooth mapping; in
this case, the id to be estimated is the manifold’s topological dimension.
Due to the importance of id in several theoretical and practical application
fields, in the last two decades a great deal of research effort has been devoted
to the development of effective id estimators. Though several techniques have
been proposed in literature, the problem is still open for the following main
reasons.
1At first, it must be highlighted that though Lebesgue’s definition of topo-
logical dimension (reported by [5]) is quite clear, in practice its estimation is
difficult if only a finite set of points is available. Therefore, id estimation tech-
niques proposed in literature are either founded on different notions of dimen-
sion (e.g. fractal dimensions) approximating the topological one, or on various
techniques aimed at preserving the characteristics of data-neighborhood distri-
butions, which reflect the topology of the underlying manifold. Besides, the
estimated id value markedly changes as the scale used to analyze the input
dataset changes, and being the number of available points practically limited,
several methods underestimate id when its value is sufficiently high (namely id
10). Other serious problems arise when the dataset is embedded in higher
dimensional spaces through a non-linear map. Finally, the too high computa-
tional complexity of most estimators makes them unpractical when the need is
to process datasets comprising huge amounts of high-dimensional data.
The main subject of this thesis work is the development of efficient and ef-
fective id estimators. Precisely, two novel estimators, named MiND (Minimum
Neighbor Distance estimators of intrinsic dimension, [6]) and DANCo (Dimension-
ality from Angle and Norm Concentration, [4]) are described. The aforemen-
tioned techniques are based on the exploitation of statistics characterizing the
hidden structure of high dimensional spaces, such as the distribution of norms
and angles, which are informative of the id and could therefore be exploited for
its estimation. A simple practical example to show the informatory power of
these features, is the clustering system proposed in [3]; based on the assumption
that each class is represented by one manifold, the clustering procedure codes
the input data by means of local id estimates and features related to them. This
coding allows to obtain reliable results by applying classic and basic clustering
algorithms.
To evaluate the proposed estimators by objectively comparing them with
relevant state-of-the-art techniques, a benchmark framework is proposed. The
need of this framework is highlighted by the fact that in literature each method
has been assessed on different datasets and by employing different evaluation
measures; therefore it is difficult to provide an objective comparison by solely
analyzing the results reported by the authors. Based on this observation, the
proposed benchmark employs publicly available, synthetic and real, datasets
that have been used by several authors in the literature for their interesting, and
challenging, peculiarities. Moreover, some synthetic datasets have been added,
to more deeply test the estimators’ performance on high dimensional datasets
being characterized by similarly high id. The application of this benchmark has
shown to provide an objective comparative assessment in terms of robustness
w.r.t. parameter settings, high dimensional datasets, datasets being character-
ized by an high intrinsic dimension, and noisy datasets. The achieved results
show that DANCo provides the most reliable estimates on both synthetic and real
datasets.
The thesis is organized as follows: in Chapter 1 a brief theoretical description
of the various definitions of dimension is presented, along with the problems re-
lated to id estimation and interesting application domains profitably exploiting
the knowledge of id; in Chapter 2 notable state-of-the-art intrinsic id are sur-
veyed, and grouped according to the employed methods; in Chapter 3 MinD, and
DANCo are described; in Chapter 4, after summarizing mostly used experimental
settings, we propose a benchmark framework and we employ it to objectively
assess and compare relevant intrinsic dimensionality estimators; in Chapter 5
conclusions and open research problems are shortly reported.
References
[1] R. S. Bennett. The Intrinsic Dimensionality of Signal Collections. IEEE
Trans. on Information Theory, IT-15(5):517–525, 1969.
[2] C. M. Bishop. Neural Networks for Pattern Recognition. Oxford University
Press, Oxford, 1995.
[3] P. Campadelli, E. Casiraghi, C. Ceruti, G. Lombardi, and A. Rozza. Local
intrinsic dimensionality based features for clustering. In Alfredo Petrosino,
editor, ICIAP (1), volume 8156 of Lecture Notes in Computer Science, pages
41–50. Springer, 2013.
[4] C. Ceruti, S. Bassis, A Rozza, G. Lombardi, E. Casiraghi, and P. Campadelli.
DANCo: an intrinsic Dimensionalty estimator exploiting Angle and Norm
Concentration. Pattern recognition, 2014.
[5] M. Katetov and P. Simon. Origins of dimension theory. Handbook of the
History of General Topology, 1997.
[6] A. Rozza, G. Lombardi, C. Ceruti, E. Casiraghi, and P. Campadelli. Novel
high intrinsic dimensionality estimators. Machine Learning Journal, 89(1-
2):37–65, May 2012
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Novel high intrinsic dimensionality estimators
No full textRecently, a great deal of research work has been devoted to the development of algorithms to estimate the intrinsic dimensionality (id) of a given dataset, that is the minimum number of parameters needed to represent the data without information loss. id estimation is important for the following reasons: the capacity and the generalization capability of discriminant methods depend on it; id is a necessary information for any dimensionality reduction technique; in neural network design the number of hidden units in the encoding middle layer should be chosen according to the id of data; the id value is strongly related to the model order in a time series, that is crucial to obtain reliable time series predictions.Although many estimation techniques have been proposed in the literature, most of them fail on noisy data, or compute underestimated values when the id is sufficiently high. In this paper, after reviewing some of the most important id estimators related to our work, we provide a theoretical motivation of the bias that causes the underestimation effect, and we present two id estimators based on the statistical properties of manifold neighborhoods, which have been developed in order to reduce this effect. We exhaustively evaluate the proposed techniques on synthetic and real datasets, by employing an objective evaluation measure to compare their performance with those achieved by state of the art algorithms; the results show that the proposed methods are promising, and produce reliable estimates also in the difficult case of datasets drawn from non-linearly embedded manifolds, characterized by high id
Intrinsic dimension estimation : relevant techniques and a Benchmark Framework
No full textWhen dealing with datasets comprising high-dimensional points, it is
usually advantageous to discover some data structure. A fundamental
information needed to this aim is the minimum number of parameters
required to describe the data while minimizing the information loss. This
number, usually called intrinsic dimension, can be interpreted as the dimension
of the manifold from which the input data are supposed to be
drawn.
Due to its usefulness in many theoretical and practical problems, in
the last decades the concept of intrinsic dimension has gained considerable
attention in the scientific community, motivating the large number
of intrinsic dimensionality estimators proposed in literature. However,
the problem is still open since most techniques cannot efficiently deal
with datasets drawn from manifolds of high intrinsic dimension and nonlinearly
embedded in higher dimensional spaces.
This paper surveys some of the most interesting, widespread used,
and advanced state-of-the-art methodologies. Unfortunately, since no
benchmark database exists in this research field, an objective comparison
among different techniques is not possible. Consequently, we suggest
a benchmark framework and apply it to comparatively evaluate relevant
state-of-the-art estimators
Una metodologia per la valutazione ambientale strategica di nuove linee elettriche ad alta tensione applicata al territorio sardo
No full textVariations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Dispelling the Myths Behind First-author Citation Counts
Full text linkWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
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