464 research outputs found
Adaptive imputation of missing values for incomplete pattern classification
In classification of incomplete pattern, the missing values can either play a
crucial role in the class determination, or have only little influence (or
eventually none) on the classification results according to the context. We
propose a credal classification method for incomplete pattern with adaptive
imputation of missing values based on belief function theory. At first, we try
to classify the object (incomplete pattern) based only on the available
attribute values. As underlying principle, we assume that the missing
information is not crucial for the classification if a specific class for the
object can be found using only the available information. In this case, the
object is committed to this particular class. However, if the object cannot be
classified without ambiguity, it means that the missing values play a main role
for achieving an accurate classification. In this case, the missing values will
be imputed based on the K-nearest neighbor (K-NN) and self-organizing map (SOM)
techniques, and the edited pattern with the imputation is then classified. The
(original or edited) pattern is respectively classified according to each
training class, and the classification results represented by basic belief
assignments are fused with proper combination rules for making the credal
classification. The object is allowed to belong with different masses of belief
to the specific classes and meta-classes (which are particular disjunctions of
several single classes). The credal classification captures well the
uncertainty and imprecision of classification, and reduces effectively the rate
of misclassifications thanks to the introduction of meta-classes. The
effectiveness of the proposed method with respect to other classical methods is
demonstrated based on several experiments using artificial and real data sets
Median evidential c-means algorithm and its application to community detection
Median clustering is of great value for partitioning relational data. In this
paper, a new prototype-based clustering method, called Median Evidential
C-Means (MECM), which is an extension of median c-means and median fuzzy
c-means on the theoretical framework of belief functions is proposed. The
median variant relaxes the restriction of a metric space embedding for the
objects but constrains the prototypes to be in the original data set. Due to
these properties, MECM could be applied to graph clustering problems. A
community detection scheme for social networks based on MECM is investigated
and the obtained credal partitions of graphs, which are more refined than crisp
and fuzzy ones, enable us to have a better understanding of the graph
structures. An initial prototype-selection scheme based on evidential
semi-centrality is presented to avoid local premature convergence and an
evidential modularity function is defined to choose the optimal number of
communities. Finally, experiments in synthetic and real data sets illustrate
the performance of MECM and show its difference to other methods
Evidential relational clustering using medoids
In real clustering applications, proximity data, in which only pairwise
similarities or dissimilarities are known, is more general than object data, in
which each pattern is described explicitly by a list of attributes.
Medoid-based clustering algorithms, which assume the prototypes of classes are
objects, are of great value for partitioning relational data sets. In this
paper a new prototype-based clustering method, named Evidential C-Medoids
(ECMdd), which is an extension of Fuzzy C-Medoids (FCMdd) on the theoretical
framework of belief functions is proposed. In ECMdd, medoids are utilized as
the prototypes to represent the detected classes, including specific classes
and imprecise classes. Specific classes are for the data which are distinctly
far from the prototypes of other classes, while imprecise classes accept the
objects that may be close to the prototypes of more than one class. This soft
decision mechanism could make the clustering results more cautious and reduce
the misclassification rates. Experiments in synthetic and real data sets are
used to illustrate the performance of ECMdd. The results show that ECMdd could
capture well the uncertainty in the internal data structure. Moreover, it is
more robust to the initializations compared with FCMdd.Comment: in The 18th International Conference on Information Fusion, July
2015, Washington, DC, USA , Jul 2015, Washington, United State
Credal Fusion of Classifications for Noisy and Uncertain Data
This paper reports on an investigation in classification technique employed to classify noised and uncertain data. However, classification is not an easy task. It is a significant challenge to discover knowledge from uncertain data. In fact, we can find many problems. More time we don't have a good or a big learning database for supervised classification. Also, when training data contains noise or missing values, classification accuracy will be affected dramatically. So to extract groups from data is not easy to do. They are overlapped and not very separated from each other. Another problem which can be cited here is the uncertainty due to measuring devices. Consequentially classification model is not so robust and strong to classify new objects. In this work, we present a novel classification algorithm to cover these problems. We materialize our main idea by using belief function theory to do combination between classification and clustering. This theory treats very well imprecision and uncertainty linked to classification. Experimental results show that our approach has ability to significantly improve the quality of classification of generic database
Probabilistic Logic Programming with Beta-Distributed Random Variables
We enable aProbLog---a probabilistic logical programming approach---to reason
in presence of uncertain probabilities represented as Beta-distributed random
variables. We achieve the same performance of state-of-the-art algorithms for
highly specified and engineered domains, while simultaneously we maintain the
flexibility offered by aProbLog in handling complex relational domains. Our
motivation is that faithfully capturing the distribution of probabilities is
necessary to compute an expected utility for effective decision making under
uncertainty: unfortunately, these probability distributions can be highly
uncertain due to sparse data. To understand and accurately manipulate such
probability distributions we need a well-defined theoretical framework that is
provided by the Beta distribution, which specifies a distribution of
probabilities representing all the possible values of a probability when the
exact value is unknown.Comment: Accepted for presentation at AAAI 201
Updating beliefs with incomplete observations
Currently, there is renewed interest in the problem, raised by Shafer in
1985, of updating probabilities when observations are incomplete. This is a
fundamental problem in general, and of particular interest for Bayesian
networks. Recently, Grunwald and Halpern have shown that commonly used updating
strategies fail in this case, except under very special assumptions. In this
paper we propose a new method for updating probabilities with incomplete
observations. Our approach is deliberately conservative: we make no assumptions
about the so-called incompleteness mechanism that associates complete with
incomplete observations. We model our ignorance about this mechanism by a
vacuous lower prevision, a tool from the theory of imprecise probabilities, and
we use only coherence arguments to turn prior into posterior probabilities. In
general, this new approach to updating produces lower and upper posterior
probabilities and expectations, as well as partially determinate decisions.
This is a logical consequence of the existing ignorance about the
incompleteness mechanism. We apply the new approach to the problem of
classification of new evidence in probabilistic expert systems, where it leads
to a new, so-called conservative updating rule. In the special case of Bayesian
networks constructed using expert knowledge, we provide an exact algorithm for
classification based on our updating rule, which has linear-time complexity for
a class of networks wider than polytrees. This result is then extended to the
more general framework of credal networks, where computations are often much
harder than with Bayesian nets. Using an example, we show that our rule appears
to provide a solid basis for reliable updating with incomplete observations,
when no strong assumptions about the incompleteness mechanism are justified.Comment: Replaced with extended versio
The belief noisy-or model applied to network reliability analysis
One difficulty faced in knowledge engineering for Bayesian Network (BN) is
the quan-tification step where the Conditional Probability Tables (CPTs) are
determined. The number of parameters included in CPTs increases exponentially
with the number of parent variables. The most common solution is the
application of the so-called canonical gates. The Noisy-OR (NOR) gate, which
takes advantage of the independence of causal interactions, provides a
logarithmic reduction of the number of parameters required to specify a CPT. In
this paper, an extension of NOR model based on the theory of belief functions,
named Belief Noisy-OR (BNOR), is proposed. BNOR is capable of dealing with both
aleatory and epistemic uncertainty of the network. Compared with NOR, more rich
information which is of great value for making decisions can be got when the
available knowledge is uncertain. Specially, when there is no epistemic
uncertainty, BNOR degrades into NOR. Additionally, different structures of BNOR
are presented in this paper in order to meet various needs of engineers. The
application of BNOR model on the reliability evaluation problem of networked
systems demonstrates its effectiveness
Credal Valuation Networks for Machine Reasoning Under Uncertainty
Contemporary undertakings provide limitless opportunities for widespread
application of machine reasoning and artificial intelligence in situations
characterised by uncertainty, hostility and sheer volume of data. The paper
develops a valuation network as a graphical system for higher-level fusion and
reasoning under uncertainty in support of the human operators. Valuations,
which are mathematical representation of (uncertain) knowledge and collected
data, are expressed as credal sets, defined as coherent interval probabilities
in the framework of imprecise probability theory. The basic operations with
such credal sets, combination and marginalisation, are defined to satisfy the
axioms of a valuation algebra. A practical implementation of the credal
valuation network is discussed and its utility demonstrated on a small scale
example.Comment: 16 pages, 3 figure
Generalized Evidence Theory
Conflict management is still an open issue in the application of Dempster
Shafer evidence theory. A lot of works have been presented to address this
issue. In this paper, a new theory, called as generalized evidence theory
(GET), is proposed. Compared with existing methods, GET assumes that the
general situation is in open world due to the uncertainty and incomplete
knowledge. The conflicting evidence is handled under the framework of GET. It
is shown that the new theory can explain and deal with the conflicting evidence
in a more reasonable way.Comment: 39 pages, 5 figure
- …