2,208 research outputs found
The Thermodynamics of Network Coding, and an Algorithmic Refinement of the Principle of Maximum Entropy
The principle of maximum entropy (Maxent) is often used to obtain prior
probability distributions as a method to obtain a Gibbs measure under some
restriction giving the probability that a system will be in a certain state
compared to the rest of the elements in the distribution. Because classical
entropy-based Maxent collapses cases confounding all distinct degrees of
randomness and pseudo-randomness, here we take into consideration the
generative mechanism of the systems considered in the ensemble to separate
objects that may comply with the principle under some restriction and whose
entropy is maximal but may be generated recursively from those that are
actually algorithmically random offering a refinement to classical Maxent. We
take advantage of a causal algorithmic calculus to derive a thermodynamic-like
result based on how difficult it is to reprogram a computer code. Using the
distinction between computable and algorithmic randomness we quantify the cost
in information loss associated with reprogramming. To illustrate this we apply
the algorithmic refinement to Maxent on graphs and introduce a Maximal
Algorithmic Randomness Preferential Attachment (MARPA) Algorithm, a
generalisation over previous approaches. We discuss practical implications of
evaluation of network randomness. Our analysis provides insight in that the
reprogrammability asymmetry appears to originate from a non-monotonic
relationship to algorithmic probability. Our analysis motivates further
analysis of the origin and consequences of the aforementioned asymmetries,
reprogrammability, and computation.Comment: 30 page
Community detection algorithms: a comparative analysis
Uncovering the community structure exhibited by real networks is a crucial
step towards an understanding of complex systems that goes beyond the local
organization of their constituents. Many algorithms have been proposed so far,
but none of them has been subjected to strict tests to evaluate their
performance. Most of the sporadic tests performed so far involved small
networks with known community structure and/or artificial graphs with a
simplified structure, which is very uncommon in real systems. Here we test
several methods against a recently introduced class of benchmark graphs, with
heterogeneous distributions of degree and community size. The methods are also
tested against the benchmark by Girvan and Newman and on random graphs. As a
result of our analysis, three recent algorithms introduced by Rosvall and
Bergstrom, Blondel et al. and Ronhovde and Nussinov, respectively, have an
excellent performance, with the additional advantage of low computational
complexity, which enables one to analyze large systems.Comment: 12 pages, 8 figures. The software to compute the values of our
general normalized mutual information is available at
http://santo.fortunato.googlepages.com/inthepress
Data mining using concepts of independence, unimodality and homophily
With the widespread use of information technologies, more and more complex data is generated and collected every day. Such complex data is various in structure, size, type and format, e.g. time series, texts, images, videos and graphs. Complex data is often high-dimensional and heterogeneous, which makes the separation of the wheat (knowledge) from the chaff (noise) more difficult. Clustering is a main mode of knowledge discovery from complex data, which groups objects in such a way that intra-group objects are more similar than inter-group objects. Traditional clustering methods such as k-means, Expectation-Maximization clustering (EM), DBSCAN and spectral clustering are either deceived by "the curse of dimensionality" or spoiled by heterogenous information. So, how to effectively explore complex data? In some cases, people may only have some partial information about the complex data. For example, in social networks, not every user provides his/her profile information such as the personal interests. Can we leverage the limited user information and friendship network wisely to infer the likely labels of the unlabeled users so that the advertisers can do accurate advertising? This is the problem of learning from labeled and unlabeled data, which is literarily attributed to semi-supervised classification.
To gain insights into these problems, this thesis focuses on developing clustering and semi-supervised classification methods that are driven by the concepts of independence, unimodality and homophily. The proposed methods leverage techniques from diverse areas, such as statistics, information theory, graph theory, signal processing, optimization and machine learning. Specifically, this thesis develops four methods, i.e. FUSE, ISAAC, UNCut, and wvGN. FUSE and ISAAC are clustering techniques to discover statistically independent patterns from high-dimensional numerical data. UNCut is a clustering technique to discover unimodal clusters in attributed graphs in which not all the attributes are relevant to the graph structure. wvGN is a semi-supervised classification technique using the theory of homophily to infer the labels of the unlabeled vertices in graphs. We have verified our clustering and semi-supervised classification methods on various synthetic and real-world data sets. The results are superior to those of the state-of-the-art.Täglich werden durch den weit verbreiteten Einsatz von Informationstechnologien mehr und mehr komplexe Daten generiert und gesammelt. Diese komplexen Daten unterscheiden sich in der Struktur, Größe, Art und Format. Häufig anzutreffen sind beispielsweise Zeitreihen, Texte, Bilder, Videos und Graphen. Dabei sind diese Daten meist hochdimensional und heterogen, was die Trennung des Weizens ( Wissen ) von der Spreu ( Rauschen ) erschwert. Die Cluster Analyse ist dabei eine der wichtigsten Methoden um aus komplexen Daten wssen zu extrahieren. Dabei werden die Objekte eines Datensatzes in einer solchen Weise gruppiert, dass intra-gruppierte Objekte ähnlicher sind als Objekte anderer Gruppen. Der Einsatz von traditionellen Clustering-Methoden wie k-Means, Expectation-Maximization (EM), DBSCAN und Spektralclustering wird dabei entweder "durch der Fluch der Dimensionalität" erschwert oder ist angesichts der heterogenen Information nicht möglich. Wie erforscht man also solch komplexe Daten effektiv? Darüber hinaus ist es oft der Fall, dass für Objekte solcher Datensätze nur partiell Informationen vorliegen. So gibt in sozialen Netzwerken nicht jeder Benutzer seine Profil-Informationen wie die persönlichen Interessen frei. Können wir diese eingeschränkten Benutzerinformation trotzdem in Kombination mit dem Freundschaftsnetzwerk nutzen, um von von wenigen, einer Klasse zugeordneten Nutzern auf die anderen zu schließen. Beispielsweise um zielgerichtete Werbung zu schalten? Dieses Problem des Lernens aus klassifizierten und nicht klassifizierten Daten wird dem semi-supversised Learning zugeordnet.
Um Einblicke in diese Probleme zu gewinnen, konzentriert sich diese Arbeit auf die Entwicklung von Clustering- und semi-überwachten Klassifikationsmethoden, die von den Konzepten der Unabhängigkeit, Unimodalität und Homophilie angetrieben werden. Die vorgeschlagenen Methoden nutzen Techniken aus verschiedenen Bereichen der Statistik, Informationstheorie, Graphentheorie, Signalverarbeitung, Optimierung und des maschinelles Lernen. Dabei stellt diese Arbeit vier Techniken vor: FUSE, ISAAC, UNCut, sowie wvGN. FUSE und ISAAC sind Clustering-Techniken, um statistisch unabhängige Muster aus hochdimensionalen numerischen Daten zu entdecken. UNCut ist eine Clustering-Technik, um unimodale Cluster in attributierten Graphen zu entdecken, in denen die Kanten und Attribute heterogene Informationen liefern. wvGN ist eine halbüberwachte Klassifikationstechnik, die Homophilie verwendet, um von gelabelten Kanten auf ungelabelte Kanten im Graphen zu schließen. Wir haben diese Clustering und semi-überwachten Klassifizierungsmethoden auf verschiedenen synthetischen und realen Datensätze überprüft. Die Ergebnisse sind denen von bisherigen State-of-the-Art-Methoden überlegen
MINDWALC : mining interpretable, discriminative walks for classification of nodes in a knowledge graph
Background Leveraging graphs for machine learning tasks can result in more expressive power as extra information is added to the data by explicitly encoding relations between entities. Knowledge graphs are multi-relational, directed graph representations of domain knowledge. Recently, deep learning-based techniques have been gaining a lot of popularity. They can directly process these type of graphs or learn a low-dimensional numerical representation. While it has been shown empirically that these techniques achieve excellent predictive performances, they lack interpretability. This is of vital importance in applications situated in critical domains, such as health care. Methods We present a technique that mines interpretable walks from knowledge graphs that are very informative for a certain classification problem. The walks themselves are of a specific format to allow for the creation of data structures that result in very efficient mining. We combine this mining algorithm with three different approaches in order to classify nodes within a graph. Each of these approaches excels on different dimensions such as explainability, predictive performance and computational runtime. Results We compare our techniques to well-known state-of-the-art black-box alternatives on four benchmark knowledge graph data sets. Results show that our three presented approaches in combination with the proposed mining algorithm are at least competitive to the black-box alternatives, even often outperforming them, while being interpretable. Conclusions The mining of walks is an interesting alternative for node classification in knowledge graphs. Opposed to the current state-of-the-art that uses deep learning techniques, it results in inherently interpretable or transparent models without a sacrifice in terms of predictive performance
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