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 **a** **fuzzy** counterpart. In this paper, we propose an **algorithm** that uses the **fuzzy** set theory and the fuzzified version of the **Close** **mining** **algorithm** [ 1 ] to extract frequent itemsets from data with **a** reduced number of database passes.

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Kuntz et al. 2000 [174] 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 **algorithm** **for** 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 [28] 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 [31]) 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 [174]. 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.

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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 **association** **rules** **for** 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**

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[10] 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.
[11] Y. Chi, R.R. Muntz, S. Nijssen, J.N. Kok, Frequent subtree **mining**—an overview, Fundamenta Informaticae XXI (2005) 1001–1038. [12] C. Wang, Q. Yuan, H. Zhou, W. Wang, B. Shi, Chopper: an efficient **algorithm** **for** tree **mining**, Journal of Computer Science and Technology

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1. Introduction
**Association** **rules** are conditional implications between frequent itemsets. The problem of the usefulness and the relevance of the set of discovered **association** **rules** is re- lated to the huge number of **rules** extracted and the presence of many redundancies among these **rules** **for** many datasets. We address this important problem using the Galois con- nection framework and we show that we can generate bases **for** **association** **rules** using the frequent closed itemsets ex- tracted by the **Close** [4] or the **A**-**Close** [5] algorithms.

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pasquierlibd2.univ-bp
lermont.fr
Abstra
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-
overed asso
iation **rules**. We qui
kly review the **Close** and the **A**-**Close** algorithms **for** extra
ting frequent
losed itemsets using their generators that redu
e response times of the extra
tion, spe
ially in the
ase of
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
overed asso
iation **rules**.

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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** [27]. 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 **for** **mining** **association** **rules** was proposed: (1) Extract frequent closed itemsets and their supports; (2) Derive frequent itemsets and their supports; (3) Generate all valid **association** **rules**. The search space of the first phase is then reduced to the closed itemsets. The first **algorithm** based on this approach is C LOSE [27]. 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.

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Finding **association** **rules**, also known as **association** rule **mining**, is an important data **mining** task. Since the seminal work on the Apriori **algorithm** [4], **association** rule **mining** has been **a** thriving field of research, which has contributed many effective techniques **for** detecting frequent patterns [5]. Several methods have been proposed in the literature **for** **mining** **association** **rules** 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 [6] or statistical relational learning [7]; on the other hand, methods that follow the mainstream of **association** rule **mining** are adapted and applied to RDF graphs.

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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.

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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[10] [11]. 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.

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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.

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1 FBK–IRST, Trento, Italy
2 Universit´e Nice Sophia Antipolis, I3S, UMR 7271, Sophia Antipolis, France
dragoni@fbk.eu andrea.tettamanzi|celia.pereira@unice.fr
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).

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Abstract—This paper proposes **a** notion of **fuzzy** graph database and describes **a** **fuzzy** 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 **a** **fuzzy** 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.

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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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Let y p (y ) : be **a** smooth manifold of statistical distribution parameterized 821
by an open set k , the Fisher information matrix **for** the value of the parameter is
822

18 route du Panorama, 92260 Fontenay-aux-Roses, France
ABSTRACT
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.

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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 **a** **fuzzy** landscape [3] (also known as directional map [16] or spatial template [23]). In **a** **fuzzy** 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. **For** **a** 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 [18] 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.

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valid approximate asso
iation **rules** is **for** the four datasets very signi
ant sin
e it varies of almost 20,000 **rules** **for** T20I6D100K to more than 2,000,000 **rules** **for** 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
data sin
e these data are dense and
orrelated and thus the number of frequent itemsets is mu
h higher. As **a**
onsequen
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
e
onsiderably (by **a** fa
tor varying from 40 to 500) the number of extra
ted **rules**.

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