Because datasets are nowadays getting bigger and bigger, the way these fuzzy associa- tion rule mining algorithms manage huge databases is essential. Some algorithms store a big amount of data while some others need to perform many database passes.
There exist several crisp association rule mining algorithms that do not store a lot of data or need only a limited number of database passes. However, most of them do not have afuzzy counterpart. In this paper, we propose an algorithm that uses the fuzzy set theory and the fuzzified version of the Closeminingalgorithm [ 1 ] to extract frequent itemsets from data with a reduced number of database passes.
Kuntz et al. 2000  introduced a new approach inspired by experimental work on behaviour during a discovery stage. The basic strategy of this approach is to start from the frequent items, similar to the Appriori algorithm. The user may then select items of interest and obtain rules involving these and other items (Figure 1.14). The rule extraction is dynamic: at each step, the user can focus on a subset of potentially interesting items and launch an algorithmfor extracting the relevant associated rules according to statistical measures. This navigation operation is called forward chain- ing, and is graphically represented by graph-based visualisation (backward chaining is also supported). Besides being user-directed this strategy avoids generating un- wanted rules. Blanchard et al. 2003  proposed a user-centred rule exploration approach, which adopts a visual metaphor of two arenas to place interesting rules. The arena holds the generalised and specialised rules separately. Each rule is repre- sented by a sphere, whose radius maps its support, and by a cone, whose base width maps its confidence. Additionally, the colours of the sphere and cone redundantly represent a weighted average of the measures, with the position of the rule at the arena represents the implication intensity. This work was extended later (Blanchard et al. 2007 ) with two complementary visualisations: the first is the 3D visual interface ( see Chapter 3) and the other is the neighbourhood relationship between rules, some of them from the already mentioned work by Kuntz et al. 2000 . Based on the neighbourhood relations, the authors proposed rules that are closer to a selected rule according to a neighbourhood relation. The available relations are: same antecedent, forward chaining, antecedent generalisation (which is opposite to forward chaining),same items, agreement specialisation, exception specialisation, generalisa- tion and same consequent.
item in the consequent term using a variant of the rule generation module of the CBA algorithm (CBA-RG) based on the classical version of the Apriori algorithm. However, it does not use attributes of users or items, because it is based solely on their occurrence. In this way, only the most frequent items are recommended and some possible items of interest, but not frequent, to the active user, are ignored. Nevertheless, they consider relationships between users as well, where associationrulesfor items and users are mined separately and items are distinguished by means of a binary rating scheme (with “like” or “dislike” values). Users are associated according to their preferences (liking or disliking) over certain items on the system. However, just one type of association rule is used: if there are few ratings given by the active user, associations between items will be used, otherwise just associations between users will be considered. Rules are mined at runtime for each specific target user, where it is not required to specify a minimum support in advance. Rather, a target range is given for the number of rules, and the algorithm adjusts the minimum support for each user in order to obtain a ruleset whose size is in the desired range. 41 However, each procedure may be very onerous when dealing with a
 F.D.R. López, A. Laurent, P. Poncelet, M. Teisseire, Fuzzy tree mining: go soft on your nodes, in: Proc. Internat. Fuzzy Systems Association World Congress (IFSA 07), Lecture Notes in Computer Science, Vol. 4529, Springer, Berlin, Heidelberg, 2007, pp. 145–154.
 Y. Chi, R.R. Muntz, S. Nijssen, J.N. Kok, Frequent subtree mining—an overview, Fundamenta Informaticae XXI (2005) 1001–1038.  C. Wang, Q. Yuan, H. Zhou, W. Wang, B. Shi, Chopper: an efficient algorithmfor tree mining, Journal of Computer Science and Technology
Associationrules are conditional implications between frequent itemsets. The problem of the usefulness and the relevance of the set of discovered associationrules is re- lated to the huge number of rules extracted and the presence of many redundancies among these rulesfor many datasets. We address this important problem using the Galois con- nection framework and we show that we can generate bases forassociationrules using the frequent closed itemsets ex- tracted by the Close  or the A-Close  algorithms.
t. In this paper, we give an overview of the use of Formal Con-
ept Analysis in the framework of asso
iation rule extra
tion. Using fre- quent
losed itemsets and their generators, that are dened using the Galois
losure operator, we address two major problems: response times of asso
iation rule extra
tion and the relevan
e and usefulness of dis-
iation rules. We qui
kly review the Close and the A-Close algorithms for extra
losed itemsets using their generators that redu
e response times of the extra
ially in the
or- related data. We also present denitions of the generi
and informative bases for asso
iation rules whi
h generation improves the relevan
e and usefulness of dis
results for CVD and NCVD are shown in gure 6. The rst three columns show statistics
about initial populations and the last column show the tness of best individuals after a
GA run. We can observe that mean tness of populations generated using CLOSE is 8.75
to 400 times better than those of randomly generated population. It is not surprising
itemset X is a frequent closed itemset if no other item i ∈ X is common to all objects containing X. Generators of a fre-
quent closed itemsets X are minimal (by inclusion) itemsets which closure is X. The frequent closed itemsets constitute a generating set for all frequent itemsets and thus for all as- sociation rules . This relies on the following properties: (i) The support of a frequent itemset is equal to the sup- port of its closure; (ii) The maximal frequent itemsets are maximal frequent closed itemsets. Using these properties, a new approach forminingassociationrules was proposed: (1) Extract frequent closed itemsets and their supports; (2) Derive frequent itemsets and their supports; (3) Generate all valid associationrules. The search space of the first phase is then reduced to the closed itemsets. The first algorithm based on this approach is C LOSE . Several algorithms for extracting frequent closed itemsets, using complex data structures to improve efficiency, have been proposed. How- ever, they do not extract generators and their response times, depending mainly of data density and correlation, are of the same order of magnitude.
Finding associationrules, also known as association rule mining, is an important data mining task. Since the seminal work on the Apriori algorithm , association rule mining has been a thriving field of research, which has contributed many effective techniques for detecting frequent patterns . Several methods have been proposed in the literature forminingassociationrules from large RDF knowledge graphs. These methods can be divided into two broad categories: on the one hand, we find methods inspired by inductive logic programming  or statistical relational learning ; on the other hand, methods that follow the mainstream of association rule mining are adapted and applied to RDF graphs.
Comparison of three algorithms:
These three algorithms are used all over the world on different applications, and are well known. Apart from its FP-tree, the FP- growth algorithm is very analogous to Eclat, but it uses some addi- tional steps to maintain the FP-tree structure during the recursion steps, while Eclat only needs to maintain the covers of all generated itemsets. The simple difference between Eclat and FP-growth is the way they count the support of every candidate itemset and how they represent and maintain the i-projected database. As a com- parison, Eclat basically generates candidate itemsets using only the join step from Apriori, since the itemsets necessary for the prune step are not available. If the transaction database contains a lot of large transactions of frequent items, such that Apriori needs to generate all its subsets of size 2, Eclat still outperforms Apriori. For very low support thresholds or sparse datasets, Eclat clearly outperforms all other algorithms. The main advantage FP-growth has over Eclat is that each linked list, starting from an item in the header table representing the cover of that item, is stored in a com- pressed form. The Apriori and FP-Growth Algorithms extract rules from a database but use two different approaches, where Apriori computes all possibilities; FP-Growth uses a prefix-tree structure to simplify computing. The heavy algorithm Apriori may give inter- esting results, but FP-growth is about an order of magnitude faster than Apriori, specifically with a dense data set (containing many patterns) and/or with long frequent patterns ( Goethals, 2010, chap. 16 ). It is important while implementing an association rule learn- ing system to study performance indicators. These algorithms are complex and the overall data-mining task is heavy in computing and memory consumption. The execution speed and the memory consumption are two performance indicators and should always be calculated.
As for the association rule extraction, the process consists of two steps: first frequent gradual patterns (also known as item- sets) are extracted. Then causality relations between the items are extracted. In mining frequent gradual itemsets, the goal is to discover frequent co-variations between attributes . When considering such gradual patterns and gradual rules, it is thus important to be able to count to which extent attributes co-variate. In this context, varied measures have been defined in the literature. However, few works have focused on how to exploit fuzzy orderings for handling noisy data.
All the works about the aura set cited before follow Elfadel and Picard’s seminal proposal and consider spatially-invariant neighborhoods. The underlying assumption is that the neighborhood of each site is the translate of a generic neighborhood, as for structuring elements used by mathematical morphology. The last contribution of this paper is to show that the aura set theory can drop this restriction by defining neighborhoods that are specific to each site. In the context of fuzzy sets, we illustrate that adaptive neighborhoods are useful for image analysis, with texture classification as an example. Such interest is investigated by Verd´ u-Monedero et al. [ 24 ] and by Landstr¨om and Thurley [ 25 ] with a formulation using mathematical morphology. We show that the aura definitions provide an elegant formalism as well to deal with spatially-variant neighborhoods and that the derived measures efficiently hold such adaptability.
1 FBK–IRST, Trento, Italy
2 Universit´e Nice Sophia Antipolis, I3S, UMR 7271, Sophia Antipolis, France
Abstract. An emerging field within Sentiment Analysis concerns the investiga- tion about how sentiment concepts have to be adapted with respect to the different domains in which they are used. In the context of the Concept-Level Sentiment Analysis Challenge, we presented a system whose aims are twofold: (i) the imple- mentation of a learning approach able to model fuzzy functions used for build- ing the relationships graph representing the appropriateness between sentiment concepts and different domains (Task 1); and (ii) the development of a semantic resource based on the connection between an extended version of WordNet, Sen- ticNet, and ConceptNet, that has been used both for extracting concepts (Task 2) and for classifying sentences within specific domains (Task 3).
Abstract—This paper proposes a notion of fuzzy graph database and describes afuzzy query algebra that makes it possible to handle such database, which may be fuzzy or not, in a flexible way. The algebra, based on fuzzy set theory and the concept of afuzzy graph, is composed of a set of operators that can be used to express preference queries on fuzzy graph databases. The preferences concern i) the content of the vertices of the graph and ii) the structure of the graph. In a similar way as relational algebra constitutes the basis of SQL , the fuzzy algebra proposed here underlies a user-oriented query language and an associated tool implementing this language that are also presented in the paper.
Figure 2: (a)(b) Images of a real scene. Views of the 3D data obtained by stereovision algorithms on this images are shown in figure 4(a)(d). (c) Synthetic point of view of the registered models (see figure 4(c)(f)) on which the original image (a) is reprojected.
One advantage of the proposed method is its robustness, allowing to produce registrations with several objects. For example, on 3D data (figure 4(a)(d)) obtained with stereovision algorithms on real images (figure 2(a)(b)), models of a ball and of a planar object are registered and accurately fitted with the proposed method (figure 4). The relevance of the method is demonstrated in figure 2(c) showing a synthetic point of view of the registered models .
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We address deconvolution and segmentation of blurry im- ages. We propose to use Fuzzy C-Means (FCM) for regulariz- ing Maximum Likelihood Expectation Maximization decon- volution approach. Regularization is performed by focusing the intensity of voxels around cluster centroids during decon- volution process. It is used to deconvolve extremely blurry images. It allows us retrieving sharp edges without impact- ing small structures. Thanks to FCM, by specifying the de- sired number of clusters, heterogeneities are taken into ac- count and segmentation can be performed. Our method is evaluated on both simulated and Fluorescence Di ffuse Opti- cal Tomography biomedical blurry images. Results show our method is well designed for segmenting extremely blurry im- ages, and outperforms the Total Variation regularization ap- proach. Moreover, we demonstrate it is well suited for image quantification.
O pen A rchive T OULOUSE A rchive O uverte ( OATAO )
OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible.
This is an author-deposited version published in : http://oatao.univ-toulouse.fr/
multi-core and SIMD properties of modern processors. The fuzzy dilation generates afuzzy landscape  (also known as directional map  or spatial template ). In afuzzy landscape, the value of each pixel represents to what extent it verifies the relation under study, as shown in Fig. 1b for the relation to the left of the right lung. Fora given reference object, this fuzzy landscape is gener- ated once and then used to evaluate all the relations of the type x to the left of the right lung with all other objects. To generate explanations as in Fig. 1a  on a set of images, the most relevant relations between objects are extracted from a training set of images by computing one landscape per image, per object and per investigated relation. For reference, with 7 objects like in Fig. 1a and considering 5 relations (left, right, above, under, close to), 35 fuzzy landscapes are necessary for one image. With the com- plexity of the scene and the size of the training set, the number of landscapes to compute can then easily escalate hence the importance of computing them faster.
valid approximate asso
iation rules is for the four datasets very signi
e it varies of almost 20,000 rulesfor T20I6D100K to more than 2,000,000 rulesfor C73D10K. It is thus essential to redu
e the set of extra
ted rules in order to make it usable by the user. F or T20I6D100K, this basis represents a division by a fa
tor of 5 approximately of the number of extra
ted approximate rules. For Mushrooms, C20D10K, and C73D10K, the total number of valid approximate asso
iation rules is mu
h more important than for the syntheti
e these data are dense and
orrelated and thus the number of frequent itemsets is mu
h higher. As a
e, it is the same for the number of valid approximate rules. The proportion of frequent
losed itemsets among the frequent itemsets being weak, the redu
tion of the informative basis for approximate rules makes it possible to redu
onsiderably (by a fa
tor varying from 40 to 500) the number of extra