Christophe Marsala

Interpolative reasoning based on graduality

We propose a new method to use an incomplete rule base with imprecise descriptions of variables. We extend classical interpolative reasoning to this case, under the assumption of graduality in variations of the variables, by using an analogical fuzzy approach.

Independence and Possibilistic Conditioning

There is not a unique definition of a conditional possibility distribution since the concept of conditioning is complex and many papers have been conducted to define conditioning in a possibilistic framework. In most cases, independence has been also defined and studied by means of a kind of analogy with the probabilistic case. In [2,4], we introduce conditional possibility as a primitive concept by means of a function whose domain is a set of conditional events. In this paper, we define a concept of independence associated with this form of conditional possibility and we show that classical properties required for independence concepts are satisfied.

Conditional possibility and necessity

We introduce the definition of a conditional possibility (and a conditional necessity by duality) as a primitive concept, i.e. a function whose domain is a set of conditional events. The starting point is a definition of conditional event E|H which differs from many seemingly similar ones adopted in the relevant literature, which makes the third value depending on E|H. It turns out that this function t(E|H) can be taken as a conditional possibility by requiring natural property of closure of truth-values of the conditional events with respect to max and min. We show that other definitions of conditional possibility measures, present in the literature, are particular cases of the one proposed here. Moreover, we introduce a concept of coherence for conditional possibility and a relevant characterization theorem, given in terms of a class of unconditional possibility measures.

Graded multi-label classification: Compromise between handling label relations and limiting error propagation

In graded multi-label classification (GMLC), each data can be assigned to multiple labels according to a degree of membership on an ordinal scale, and with respect to label relations. For example, in a movie catalog web page, a five stars action movie should be at least a one star suspense movie. Ignoring those relations can lead to inconsistent predictions, but if they are considered, then a prediction error for one label will be propagated to all related labels. Most of existing approaches either ignore label relations, or can learn only relations fitting a predefined imposed structure. This paper is motivated by the lack of a study analysing the compromise between handling label relations and limiting error propagation in GMLC, and by the fact that there is no known approach giving a control on that compromise to allow such a study. In this paper, a new meta-classifier with two main advantages is proposed for GMLC. Firstly, no predefined structure is imposed for learning label relations, and secondly, the meta-classifier is based on three measures giving control on the studied compromise. The studied compromise is analysed according to its impact on the classifier complexity and on hamming-loss evaluation measure. A comparison to three existing approaches shows that the proposed meta-classifier is competitive according to hamming-loss evaluation measure, and it is the most stable classifier according to hamming-loss standard deviation.

Classification with a reject option under Concept Drift: The Droplets algorithm

In this paper a new on-line algorithm is proposed (the Droplets algorithm) for dealing with concept drifts and to produce reliable predictions. The two main characteristics of this algorithm are that it is able to adapt to different types of drifts without making any assumptions regarding their type or when they occur, and can provide reliable predictions in a non-stationary environment without using a fixed confidence threshold. Experimental results on five datasets based on Random RBF and Rotating Hyperplane generators as well as a new semi-synthetic dataset based weather temperatures show that, by discarding difficult observations, the Droplets algorithm manages to obtain the best average accuracy against ten classifiers. The results also indicate that the algorithm manages to provide reliable prediction by accurately distinguishing which observations are easily classifiable.

Entropy Measures and Views of Information

Among the countless papers written by Ronald R. Yager, those on Entropies and measures of information are considered, keeping in mind the notion of view of a set, in order to point out a similarity between the quantities introduced in various frameworks to evaluate a kind of entropy. We define the concept of entropy measure and we show that its main characteristic is a form of monotonicity, satisfied by quantities scrutinised by R.R. Yager.

A distributed graph based approach for rough classifications considering dominance relations between overlapping classes

Several data from real world applications involves overlapping classes. Data is allowed to belong to multiple classes with different membership degrees. In this paper, we explore a different concept characterizing social networks, documents, and most of biological and chemical datasets: data could have multiple classes, but dominant classes are better noticed than dominated classes. For example, a document could discuss economy and politics, but it would be more focused on politics. A molecule could have multiple odors, but experts could notice some odors better than others. We are interested in this type of data, where a dominance relation exists between classes. Experts could easily make mistakes because dominated classes are hardly noticed. Data incoherence is a serious problem but not the only one. There is too much irrelevant and redundant attributes. Unfortunately this increases the computational time of generating classifiers. Our first challenge is to find an adapted model to overlapping classes considering dominance relations. The second challenge is to find the most relevant attributes. Finally the third challenge is to ensure that the approach gives results in an acceptable time. We address those challenges by taking advantage of the rough set theory, which is suited for incoherent data and allows multiple classes and attributes selection. The proposed approach works in a parallel and decentralized way to reduce the computational time. We tested it on real chemical data and the collected results are very promising.

Droplet Ensemble Learning on Drifting Data Streams

Ensemble learning methods for evolving data streams are extremely powerful learning methods since they combine the predictions of a set of classifiers, to improve the performance of the best single classifier inside the ensemble. In this paper we introduce the Droplet Ensemble Algorithm (DEA), a new method for learning on data streams subject to concept drifts which combines ensemble and instance based learning. Contrarily to state of the art ensemble methods which select the base learners according to their performances on recent observations, DEA dynamically selects the subset of base learners which is the best suited for the region of the feature space where the latest observation was received. Experiments on 25 datasets (most of which being commonly used as benchmark in the literature) reproducing different type of drifts show that this new method achieves excellent results on accuracy and ranking against SAM KNN [1], all of its base learners and a majority vote algorithm using the same base learners.

Laplacian regularization for fuzzy subspace clustering

This paper studies a well-established fuzzy subspace clustering paradigm and identifies a discontinuity in the produced solutions, which assigns neighbor points to different clusters and fails to identify the expected subspaces in these situations. To alleviate this drawback, a regularization term is proposed, inspired from clustering tasks for graphs such as spectral clustering. A new cost function is introduced, and a new algorithm based on an alternate optimization algorithm, called Weighted Laplacian Fuzzy Clustering, is proposed and experimentally studied.

Proximal Optimization for Fuzzy Subspace Clustering

This paper proposes a fuzzy partitioning subspace clustering algorithm that minimizes a variant of the FCM cost function with a weighted Euclidean distance and a penalty term. To this aim it considers the framework of proximal optimization. It establishes the expression of the proximal operator for the considered cost function and derives PFSCM, an algorithm combining proximal descent and alternate optimization. Experiments show the relevance of the proposed approach.