Personalization for the Semantic Web III

This report provides an overview of the achievements of working group A3 for bringing personalization functionality to the Semantic Web. It continues the work started in the deliverable A3-D1 and A3-D4. In the deliverable at hand, we report on a successfully held workshop on Semantic Web Personalization at the 3rd European Semantic Web Conference, and the research results on techniques and algorithms for enabling personalization in the Semantic Web, and achievements on developing suitable architectures for the personalized information systems in the Semantic Web.peer-reviewe

On (anti) conditional independence in Dempster-Shafer theory

This paper verifies a result of [9] concerning graphoidal structure of Shenoy's notion of independence for Dempster-Shafer theory of belief functions. Shenoy proved that his notion of independence has graphoidal properties for positive normal valuations. The requirement of strict positive normal valuations as prerequisite for application of graphoidal properties excludes a wide class of DS belief functions. It excludes especially so-called probabilistic belief functions. It is demonstrated that the requirement of positiveness of valuation may be weakened in that it may be required that commonality function is non-zero for singleton sets instead, and the graphoidal properties for independence of belief function variables are then preserved. This means especially that probabilistic belief functions with all singleton sets as focal points possess graphoidal properties for independenc

On (anti) conditional independence in Dempster-Shafer theory

This paper verifies a result of [9] concerning graphoidal structure of Shenoy's notion of independence for Dempster-Shafer theory of belief functions. Shenoy proved that his notion of independence has graphoidal properties for positive normal valuations. The requirement of strict positive normal valuations as prerequisite for application of graphoidal properties excludes a wide class of DS belief functions. It excludes especially so-called probabilistic belief functions. It is demonstrated that the requirement of positiveness of valuation may be weakened in that it may be required that commonality function is non-zero for singleton sets instead, and the graphoidal properties for independence of belief function variables are then preserved. This means especially that probabilistic belief functions with all singleton sets as focal points possess graphoidal properties for independenc

Towards Continuous Consistency Axiom

Development of new algorithms in the area of machine learning, especially clustering, comparative studies of such algorithms as well as testing according to software engineering principles requires availability of labeled data sets. While standard benchmarks are made available, a broader range of such data sets is necessary in order to avoid the problem of overfitting. In this context, theoretical works on axiomatization of clustering algorithms, especially axioms on clustering preserving transformations are quite a cheap way to produce labeled data sets from existing ones. However, the frequently cited axiomatic system of Kleinberg:2002, as we show in this paper, is not applicable for finite dimensional Euclidean spaces, in which many algorithms like $k$-means, operate. In particular, the so-called outer-consistency axiom fails upon making small changes in datapoint positions and inner-consistency axiom is valid only for identity transformation in general settings. Hence we propose an alternative axiomatic system, in which Kleinberg's inner consistency axiom is replaced by a centric consistency axiom and outer consistency axiom is replaced by motion consistency axiom. We demonstrate that the new system is satisfiable for a hierarchical version of $k$-means with auto-adjusted $k$, hence it is not contradictory. Additionally, as $k$-means creates convex clusters only, we demonstrate that it is possible to create a version detecting concave clusters and still the axiomatic system can be satisfied. The practical application area of such an axiomatic system may be the generation of new labeled test data from existent ones for clustering algorithm testing. %We propose the gravitational consistency as a replacement which does not have this deficiency.Comment: 42 pages, 6 tables, 9 figure

On (anti) conditional independence in Dempster-Shafer theory

This paper verifies a result of [9] concerning graphoidal structure of Shenoy's notion of independence for Dempster-Shafer theory of belief functions. Shenoy proved that his notion of independence has graphoidal properties for positive normal valuations. The requirement of strict positive normal valuations as prerequisite for application of graphoidal properties excludes a wide class of DS belief functions. It excludes especially so-called probabilistic belief functions. It is demonstrated that the requirement of positiveness of valuation may be weakened in that it may be required that commonality function is non-zero for singleton sets instead, and the graphoidal properties for independence of belief function variables are then preserved. This means especially that probabilistic belief functions with all singleton sets as focal points possess graphoidal properties for independenc

A sufficient condition for belief function construction from conditional belief functions

It is commonly acknowledged that we need to accept and handle uncertainty when reasoning with real world data. The most profoundly studied measure of uncertainty is the probability. However, the general feeling is that probability cannot express all types of uncertainty, including vagueness and incompleteness of knowledge. The Mathematical Theory of Evidence or the Dempster-Shafer Theory (DST) [1, 12] has been intensely investigated in the past as a means of expressing incomplete knowledge. The interesting property in this context is that DST formally fits into the framework of graphoidal structures [13] which implies possibilities of efficient reasoning by local computations in large multivariate belief distributions given a factorization of the belief distribution into low dimensional component conditional belief functions. But the concept of conditional belief functions is generally not usable because composition of conditional belief functions is not granted to yield joint multivariate belief distribution, as some values of the belief distribution may turn out to be negative [4, 13, 15]. To overcome this problem creation of an adequate frequency model is needed. In this paper we suggest that a Dempster-Shafer distribution results from ''clustering'' (merging) of objects sharing common features. Upon ''clustering'' two (or more) objects become indistinguishable (will be counted as one) but some attributes will behave as if they have more than one value at once. The next elements of the model needed are the concept of conditional independence and that of merger conditions. It is assumed that before merger the objects move closer in such a way that conditional distributions of features for the objects to merge are identical. The traditional conditional independence of feature variables is assumed before merger (thereafter only the DST conditional independence holds). Furthermore it is necessary that the objects get ''closer'' before the merger independly for each feature variable and only those areas merge where the conditional distributions get identical in each variable. The paper demonstrates that within this model, the graphoidal properties hold and a sufficient condition for non-negativity of the graphoidally represented belief function is presented and its validity demonstrated.V Workshop sobre Aspectos Teóricos de la Inteligencia Artificial (ATIA)Red de Universidades con Carreras en Informática (RedUNCI

A sufficient condition for belief function construction from conditional belief functions

It is commonly acknowledged that we need to accept and handle uncertainty when reasoning with real world data. The most profoundly studied measure of uncertainty is the probability. However, the general feeling is that probability cannot express all types of uncertainty, including vagueness and incompleteness of knowledge. The Mathematical Theory of Evidence or the Dempster-Shafer Theory (DST) [1, 12] has been intensely investigated in the past as a means of expressing incomplete knowledge. The interesting property in this context is that DST formally fits into the framework of graphoidal structures [13] which implies possibilities of efficient reasoning by local computations in large multivariate belief distributions given a factorization of the belief distribution into low dimensional component conditional belief functions. But the concept of conditional belief functions is generally not usable because composition of conditional belief functions is not granted to yield joint multivariate belief distribution, as some values of the belief distribution may turn out to be negative [4, 13, 15]. To overcome this problem creation of an adequate frequency model is needed. In this paper we suggest that a Dempster-Shafer distribution results from ''clustering'' (merging) of objects sharing common features. Upon ''clustering'' two (or more) objects become indistinguishable (will be counted as one) but some attributes will behave as if they have more than one value at once. The next elements of the model needed are the concept of conditional independence and that of merger conditions. It is assumed that before merger the objects move closer in such a way that conditional distributions of features for the objects to merge are identical. The traditional conditional independence of feature variables is assumed before merger (thereafter only the DST conditional independence holds). Furthermore it is necessary that the objects get ''closer'' before the merger independly for each feature variable and only those areas merge where the conditional distributions get identical in each variable. The paper demonstrates that within this model, the graphoidal properties hold and a sufficient condition for non-negativity of the graphoidally represented belief function is presented and its validity demonstrated.V Workshop sobre Aspectos Teóricos de la Inteligencia Artificial (ATIA)Red de Universidades con Carreras en Informática (RedUNCI