26,199 research outputs found
Batch and median neural gas
Neural Gas (NG) constitutes a very robust clustering algorithm given
euclidian data which does not suffer from the problem of local minima like
simple vector quantization, or topological restrictions like the
self-organizing map. Based on the cost function of NG, we introduce a batch
variant of NG which shows much faster convergence and which can be interpreted
as an optimization of the cost function by the Newton method. This formulation
has the additional benefit that, based on the notion of the generalized median
in analogy to Median SOM, a variant for non-vectorial proximity data can be
introduced. We prove convergence of batch and median versions of NG, SOM, and
k-means in a unified formulation, and we investigate the behavior of the
algorithms in several experiments.Comment: In Special Issue after WSOM 05 Conference, 5-8 september, 2005, Pari
Introduction to finite mixtures
Mixture models have been around for over 150 years, as an intuitively simple
and practical tool for enriching the collection of probability distributions
available for modelling data. In this chapter we describe the basic ideas of
the subject, present several alternative representations and perspectives on
these models, and discuss some of the elements of inference about the unknowns
in the models. Our focus is on the simplest set-up, of finite mixture models,
but we discuss also how various simplifying assumptions can be relaxed to
generate the rich landscape of modelling and inference ideas traversed in the
rest of this book.Comment: 14 pages, 7 figures, A chapter prepared for the forthcoming Handbook
of Mixture Analysis. V2 corrects a small but important typographical error,
and makes other minor edits; V3 makes further minor corrections and updates
following review; V4 corrects algorithmic details in sec 4.1 and 4.2, and
removes typo
Effective retrieval and new indexing method for case based reasoning: Application in chemical process design
In this paper we try to improve the retrieval step for case based reasoning for preliminary design. This improvement deals with three major parts of our CBR system. First, in the preliminary design step, some uncertainties like imprecise or unknown values remain in the description of the problem, because they need a deeper analysis to be withdrawn. To deal with this issue, the faced problem description is soften with the fuzzy sets theory. Features are described with a central value, a percentage of imprecision and a relation with respect to the central value. These additional data allow us to build a domain of possible values for each attributes. With this representation, the calculation of the similarity function is impacted, thus the characteristic function is used to calculate the local similarity between two features. Second, we focus our attention on the main goal of the retrieve step in CBR to find relevant cases for adaptation. In this second part, we discuss the assumption of similarity to find the more appropriated case. We put in highlight that in some situations this classical similarity must be improved with further knowledge to facilitate case adaptation. To avoid failure during the adaptation step, we implement a method that couples similarity measurement with adaptability one, in order to approximate the cases utility more accurately. The latter gives deeper information for the reusing of cases. In a last part, we present a generic indexing technique for the base, and a new algorithm for the research of relevant cases in the memory. The sphere indexing algorithm is a domain independent index that has performances equivalent to the decision tree ones. But its main strength is that it puts the current problem in the center of the research area avoiding boundaries issues. All these points are discussed and exemplified through the preliminary design of a chemical engineering unit operation
Query-driven learning for predictive analytics of data subspace cardinality
Fundamental to many predictive analytics tasks is the ability to estimate the cardinality (number of data items) of multi-dimensional data subspaces, defined by query selections over datasets. This is crucial for data analysts dealing with, e.g., interactive data subspace explorations, data subspace visualizations, and in query processing optimization. However, in many modern data systems, predictive analytics may be (i) too costly money-wise, e.g., in clouds, (ii) unreliable, e.g., in modern Big Data query engines, where accurate statistics are difficult to obtain/maintain, or (iii) infeasible, e.g., for privacy issues. We contribute a novel, query-driven, function estimation model of analyst-defined data subspace cardinality. The proposed estimation model is highly accurate in terms of prediction and accommodating the well-known selection queries: multi-dimensional range and distance-nearest neighbors (radius) queries. Our function estimation model: (i) quantizes the vectorial query space, by learning the analysts’ access patterns over a data space, (ii) associates query vectors with their corresponding cardinalities of the analyst-defined data subspaces, (iii) abstracts and employs query vectorial similarity to predict the cardinality of an unseen/unexplored data subspace, and (iv) identifies and adapts to possible changes of the query subspaces based on the theory of optimal stopping. The proposed model is decentralized, facilitating the scaling-out of such predictive analytics queries. The research significance of the model lies in that (i) it is an attractive solution when data-driven statistical techniques are undesirable or infeasible, (ii) it offers a scale-out, decentralized training solution, (iii) it is applicable to different selection query types, and (iv) it offers a performance that is superior to that of data-driven approaches
Robust EM algorithm for model-based curve clustering
Model-based clustering approaches concern the paradigm of exploratory data
analysis relying on the finite mixture model to automatically find a latent
structure governing observed data. They are one of the most popular and
successful approaches in cluster analysis. The mixture density estimation is
generally performed by maximizing the observed-data log-likelihood by using the
expectation-maximization (EM) algorithm. However, it is well-known that the EM
algorithm initialization is crucial. In addition, the standard EM algorithm
requires the number of clusters to be known a priori. Some solutions have been
provided in [31, 12] for model-based clustering with Gaussian mixture models
for multivariate data. In this paper we focus on model-based curve clustering
approaches, when the data are curves rather than vectorial data, based on
regression mixtures. We propose a new robust EM algorithm for clustering
curves. We extend the model-based clustering approach presented in [31] for
Gaussian mixture models, to the case of curve clustering by regression
mixtures, including polynomial regression mixtures as well as spline or
B-spline regressions mixtures. Our approach both handles the problem of
initialization and the one of choosing the optimal number of clusters as the EM
learning proceeds, rather than in a two-fold scheme. This is achieved by
optimizing a penalized log-likelihood criterion. A simulation study confirms
the potential benefit of the proposed algorithm in terms of robustness
regarding initialization and funding the actual number of clusters.Comment: In Proceedings of the 2013 International Joint Conference on Neural
Networks (IJCNN), 2013, Dallas, TX, US
Sequence Modelling For Analysing Student Interaction with Educational Systems
The analysis of log data generated by online educational systems is an
important task for improving the systems, and furthering our knowledge of how
students learn. This paper uses previously unseen log data from Edulab, the
largest provider of digital learning for mathematics in Denmark, to analyse the
sessions of its users, where 1.08 million student sessions are extracted from a
subset of their data. We propose to model students as a distribution of
different underlying student behaviours, where the sequence of actions from
each session belongs to an underlying student behaviour. We model student
behaviour as Markov chains, such that a student is modelled as a distribution
of Markov chains, which are estimated using a modified k-means clustering
algorithm. The resulting Markov chains are readily interpretable, and in a
qualitative analysis around 125,000 student sessions are identified as
exhibiting unproductive student behaviour. Based on our results this student
representation is promising, especially for educational systems offering many
different learning usages, and offers an alternative to common approaches like
modelling student behaviour as a single Markov chain often done in the
literature.Comment: The 10th International Conference on Educational Data Mining 201
A survey of outlier detection methodologies
Outlier detection has been used for centuries to detect and, where appropriate, remove anomalous observations from data. Outliers arise due to mechanical faults, changes in system behaviour, fraudulent behaviour, human error, instrument error or simply through natural deviations in populations. Their detection can identify system faults and fraud before they escalate with potentially catastrophic consequences. It can identify errors and remove their contaminating effect on the data set and as such to purify the data for processing. The original outlier detection methods were arbitrary but now, principled and systematic techniques are used, drawn from the full gamut of Computer Science and Statistics. In this paper, we introduce a survey of contemporary techniques for outlier detection. We identify their respective motivations and distinguish their advantages and disadvantages in a comparative review
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