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This short correspondence is a reply to a recently published paper by Verlinde et al. in which the authors empirically compared fuzzy and nonfuzzy association analysis and, on the basis of their results, questioned the usefulness of a fuzzy approach. Although we highly welcome the critical examination of the topic and definitely agree that fuzzy extensions of existing methods call for a thorough justification, the empirical comparison presented in the aforementioned paper is in our opinion not objective and extensive enough to fully warrant the conclusions drawn from the results. Apart from some general comments on the claims raised in their paper, we present empirical results based on an alternative experimental setup that lead to different conclusions. Index Terms--Association rules, data mining, fuzzy sets, partitioning.

In this paper, we propose a method for retrieving promising candidate solutions in case-based problem solving. Our method, referred to as credible case-based inference, makes use of so-called similarity profiles as a formal model of the key hypothesis underlying case-based reasoning (CBR), namely, the assumption that similar problems have similar solutions. Proceeding from this formalization, it becomes possible to derive theoretical properties of the corresponding inference scheme in a rigorous way. In particular, it can be shown that, under mild technical conditions, a set of candidates covers the true solution with high probability. Thus, the approach supports an important subtask in CBR, namely, to generate potential solutions for a new target problem in a sound manner and hence contributes to the methodical foundations of CBR. Due to its generality, it can be employed for different types of performance tasks and can easily be integrated in existing CBR systems. Index Terms--Case-based reasoning, prediction, instance-based learning.

This paper introduces a framework of experienced-based decision making as an extension of case-based decision making, a recently proposed alternative to expected utility theory. In experienced-based decision making, an agent faced with a new decision problem acts on the basis of experience gathered from previous problems in the past, either through predicting the utility of potential actions or through establishing a direct relationship between decision problems and appropriate actions. In the paper, a realization of the latter approach in the form of "satisficing" decision trees is proposed. Index Terms--Bounded rationality, case-based reasoning, compilation, decision making, decision trees, machine learning.

In this article, we elaborate on the use of the Sugeno integral in the context of machine learning. More specifically, we propose a method for binary classification, in which the Sugeno integral is used as an aggregation function that combines several local evaluations of an instance, pertaining to different features, or measurements, into a single global evaluation. Due to the specific nature of the Sugeno integral, this approach is especially suitable for learning from ordinal data, i.e., when measurements are taken from ordinal scales. This is a topic that has not received much attention in machine learning so far. The core of the learning problem itself consists of identifying the capacity underlying the Sugeno integral. To tackle this problem, we develop an algorithm based on linear programming. The algorithm also includes a suitable technique for transforming the original feature values into local evaluations (local utility scores), as well as a method for tuning a threshold on the global evaluation. To control the flexibility of the classifier and mitigate the problem of overfitting the training data, we generalize our approach toward $k$ -maxitive capacities, where $k$ plays the role of a hyperparameter of the learner. We present experimental studies, in which we compare our method with competing approaches on several benchmark datasets. [ABSTRACT FROM AUTHOR]

Automated machine learning (AutoML) seeks to automatically find so-called machine learning pipelines that maximize the prediction performance when being used to train a model on a given dataset. One of the main and yet open challenges in AutoMLis an effective use of computational resources: An AutoML process involves the evaluation of many candidate pipelines, which are costly but often ineffective because they are canceled due to a timeout. In this paper, we present an approach to predict the runtime of two-step machine learning pipelines with up to one pre-processor, which can be used to anticipate whether or not a pipeline will time out. Separate runtime models are trained offline for each algorithm that may be used in a pipeline, and an overall prediction is derived from these models. We empirically show that the approach increases successful evaluations made by an AutoML tool while preserving or even improving on the previously best solutions. [ABSTRACT FROM AUTHOR]

Automated machine learning (AutoML) supports the algorithmic construction and data-specific customization of machine learning pipelines, including the selection, combination, and parametrization of machine learning algorithms as main constituents. Generally speaking, AutoML approaches comprise two major components: a search space model and an optimizer for traversing the space. Recent approaches have shown impressive results in the realm of supervised learning, most notably (single-label) classification (SLC). Moreover, first attempts at extending these approaches towards multi-label classification (MLC) have been made. While the space of candidate pipelines is already huge in SLC, the complexity of the search space is raised to an even higher power in MLC. One may wonder, therefore, whether and to what extent optimizers established for SLC can scale to this increased complexity, and how they compare to each other. This paper makes the following contributions: First, we survey existing approaches to AutoML for MLC. Second, we augment these approaches with optimizers not previously tried for MLC. Third, we propose a benchmarking framework that supports a fair and systematic comparison. Fourth, we conduct an extensive experimental study, evaluating the methods on a suite of MLC problems. We find a grammar-based best-first search to compare favorably to other optimizers. [ABSTRACT FROM AUTHOR]

Basic ideas and formal concepts from fuzzy sets and fuzzy logic have been used successfully in various branches of science and engineering. This paper elaborates on the use of fuzzy sets in the broad field of data analysis and statistical sciences, including modern manifestations such as data mining and machine learning. In the fuzzy logic community, this branch of research has recently gained in importance, especially due to the emergence of data science as a new scientific discipline, and the increasing relevance of machine learning as a key methodology of modern artificial intelligence. This development has been accompanied by an internal shift from largely knowledge-based to strongly data-driven fuzzy modeling and systems design. Reflecting on the historical dimension and evolution of the area, we discuss the role of fuzzy logic in data analysis and related fields, highlight existing contributions of fuzzy sets in these fields, and outline interesting directions for future work. [ABSTRACT FROM AUTHOR]

CavBase is a database containing information about the three-dimensional geometry and the physicochemical properties of putative protein binding sites. Analyzing CavBase data typically involves computing the similarity of pairs of binding sites. In contrast to sequence alignment, however, a structural comparison of protein binding sites is a computationally challenging problem, making large scale studies difficult or even infeasible. One possibility to overcome this obstacle is to precompute pairwise similarities in an all-against-all comparison, and to make these similarities subsequently accessible to data analysis methods. Pairwise similarities, once being computed, can also be used to equip CavBase with a neighborhood structure. Taking advantage of this structure, methods for problems such as similarity retrieval can be implemented efficiently. In this paper, we tackle the problem of performing an all-against-all comparison using CavBase, consisting of more than 200,000 protein cavities, by means of parallel computation and cloud computing techniques. We present the conceptual design and technical realization of a large-scale study to create a similarity database called CavSimBase. We illustrate how CavSimBase is constructed, is accessed, and is used to answer biological questions by data analysis and similarity retrieval. [ABSTRACT FROM PUBLISHER]

Fuzzy pattern trees have recently been introduced as a novel type of fuzzy system, specifically with regard to the modeling of classification functions in machine learning. Moreover, different algorithms for learning pattern trees from data have been proposed in the literature. While showing strong performance in terms of predictive accuracy, these algorithms exhibit a rather high computational complexity, and their runtime may become prohibitive for large datasets. In this paper, we therefore propose extensions of an existing state-of-the-art algorithm for fuzzy pattern tree induction, which are aimed at making this algorithm faster without compromising its predictive accuracy. These extensions include the use of adaptive sampling schemes, as well as heuristics for guiding the growth of pattern trees. The effectiveness of our modified algorithm is confirmed by means of several experimental studies. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the minimal set of axioms that overlap indices between fuzzy sets must fulfill. We also present a method to build overlap indices using overlap functions, and we carry on a theoretical study about the continuity, the invariance, and some general properties of such indices. We present a generalization of the inference algorithm for interpolative fuzzy systems using overlap indices. We also propose an algorithm for choosing, among a set of overlap indices, the best one for a considered problem. [ABSTRACT FROM AUTHOR]

Enzyme sequences and structures are routinely used in the biological sciences as queries to search for functionally related enzymes in online databases. To this end, one usually departs from some notion of similarity, comparing two enzymes by looking for correspondences in their sequences, structures or surfaces. For a given query, the search operation results in a ranking of the enzymes in the database, from very similar to dissimilar enzymes, while information about the biological function of annotated database enzymes is ignored. In this work, we show that rankings of that kind can be substantially improved by applying kernel-based learning algorithms. This approach enables the detection of statistical dependencies between similarities of the active cleft and the biological function of annotated enzymes. This is in contrast to search-based approaches, which do not take annotated training data into account. Similarity measures based on the active cleft are known to outperform sequence-based or structure-based measures under certain conditions. We consider the Enzyme Commission (EC) classification hierarchy for obtaining annotated enzymes during the training phase. The results of a set of sizeable experiments indicate a consistent and significant improvement for a set of similarity measures that exploit information about small cavities in the surface of enzymes. [ABSTRACT FROM PUBLISHER]

To calculate similarities between molecular structures, measures based on the maximum common subgraph are frequently applied. For the comparison of protein binding sites, these measures are not fully appropriate since graphs representing binding sites on a detailed atomic level tend to get very large. In combination with an NP-hard problem, a large graph leads to a computationally demanding task. Therefore, for the comparison of binding sites, a less detailed coarse graph model is used building upon so-called pseudocenters. Consistently, a loss of structural data is caused since many atoms are discarded and no information about the shape of the binding site is considered. This is usually resolved by performing subsequent calculations based on additional information. These steps are usually quite expensive, making the whole approach very slow. The main drawback of a graph-based model solely based on pseudocenters, however, is the loss of information about the shape of the protein surface. In this study, we propose a novel and efficient modeling formalism that does not increase the size of the graph model compared to the original approach, but leads to graphs containing considerably more information assigned to the nodes. More specifically, additional descriptors considering surface characteristics are extracted from the local surface and attributed to the pseudocenters stored in Cavbase. These properties are evaluated as additional node labels, which lead to a gain of information and allow for much faster but still very accurate comparisons between different structures. [ABSTRACT FROM PUBLISHER]

We propose a novel method for preference learning or, more specifically, learning to rank, where the task is to learn a ranking model that takes a subset of alternatives as input and produces a ranking of these alternatives as output. Just like in the case of conventional classifier learning, training information is provided in the form of a set of labeled instances, with labels or, say, preference degrees taken from an ordered categorical scale. This setting is known as multipartite ranking in the literature. Our approach is based on the idea of using the (discrete) Choquet integral as an underlying model for representing ranking functions. Being an established aggregation function in fields such as multiple criteria decision making and information fusion, the Choquet integral offers a number of interesting properties that make it attractive from a machine learning perspective, too. The learning problem itself comes down to properly specifying the fuzzy measure on which the Choquet integral is defined. This problem is formalized as a margin maximization problem and solved by means of a cutting plane algorithm. The performance of our method is tested on a number of benchmark datasets. [ABSTRACT FROM PUBLISHER]

In this paper, we introduce a fuzzy extension of a class of measures to compare clustering structures, namely, measures that are based on the number of concordant and the number of discordant pairs of data points. This class includes the well-known Rand index but also commonly used alternatives, such as the Jaccard measure. In contrast with previous proposals, our extension exhibits desirable metrical properties. Apart from elaborating on formal properties of this kind, we present an experimental study in which we compare different fuzzy extensions of the Rand index and the Jaccard measure. [ABSTRACT FROM AUTHOR]

In this paper, we propose new aggregation functions for the pairwise comparison of alternatives in fuzzy preference modeling. More specifically, we introduce the concept of a grouping function, i.e., a specific type of aggregation function that combines two degrees of support (weak preference) into a degree of information or, say, a degree of comparability between two alternatives, and we relate this new concept to that of incomparability. Grouping functions of this type complement the existing concept of overlap functions in a natural way, since the latter can be used to turn two degrees of weak preference into a degree of indifference. We also define the so-called generalized bientropic functions that allow for a unified representation of overlap and grouping functions. Apart from analyzing mathematical properties of these types of functions and exploring relationships between them, we elaborate on their use in fuzzy preference modeling and decision making. We present an algorithm to elaborate on an alternative preference ranking that penalizes those alternatives for which the expert is not sure of his/her preference. [ABSTRACT FROM AUTHOR]

Graphs are frequently used to describe the geometry and also the physicochemical composition of protein active sites. Here, the concept of graph alignment as a novel method for the structural analysis of protein binding pockets is presented. Using inexact graph-matching techniques, one is able to identify both conserved areas and regions of difference among different binding pockets. Thus, using multiple graph alignments, it is possible to characterize functional protein families and to examine differences among related protein families independent of sequence or fold homology. Optimized algorithms are described for the efficient calculation of multiple graph alignments for the analysis of physicochemical descriptors representing protein binding pockets. Additionally, it is shown how the calculated graph alignments can be analyzed to identify structural features that are characteristic for a given protein family and also features that are discriminative among related families. The methods are applied to a substantial high-quality subset of the PDB database and their ability to successfully characterize and classify 10 highly populated functional protein families is shown. Additionally, two related protein families from the group of serine proteases are examined and important structural differences are detected automatically and efficiently. [ABSTRACT FROM PUBLISHER]

Queries to a database can be made more powerful by allowing flexibility in the specification of what has to be retrieved, and by referring to cases either for expressing the request, or for computing the answer. In this paper, we present an implemented information system (applied to a database describing houses to let), based on an approach developed in the fuzzy set and possibility theory setting. This provides a unified framework for expressing users' preferences about what they are looking for, for weighting the importance of requirements, for referring to examples that they like and/or counterexamples that they dislike, and for making case-based predictions. Thus information querying goes beyond the retrieving of items from a database, and involves associated tools which help the user to figure out the actual contents of the database. [ABSTRACT FROM AUTHOR]

Geometric objects are often represented approximately in terms of a finite set of points in three-dimensional euclidean space. In this paper, we extend this representation to what we call labeled point clouds. A labeled point cloud is a finite set of points, where each point is not only associated with a position in three-dimensional space, but also with a discrete class label that represents a specific property. This type of model is especially suitable for modeling biomolecules such as proteins and protein binding sites, where a label may represent an atom type or a physico-chemical property. Proceeding from this representation, we address the question of how to compare two labeled points clouds in terms of their similarity. Using fuzzy modeling techniques, we develop a suitable similarity measure as well as an efficient evolutionary algorithm to compute it. Moreover, we consider the problem of establishing an alignment of the structures in the sense of a one-to-one correspondence between their basic constituents. From a biological point of view, alignments of this kind are of great interest, since mutually corresponding molecular constituents offer important information about evolution and heredity, and can also serve as a means to explain a degree of similarity. In this paper, we therefore develop a method for computing pairwise or multiple alignments of labeled point clouds. To this end, we proceed from an optimal superposition of the corresponding point clouds and construct an alignment which is as much as possible in agreement with the neighborhood structure established by this superposition. We apply our methods to the structural analysis of protein binding sites. [ABSTRACT FROM PUBLISHER]

Comparative analysis is a topic of utmost importance in structural bioinformatics. Recently, a structural counterpart to sequence alignment, called multiple graph alignment, was introduced as a tool for the comparison of protein structures in general and protein binding sites in particular. Using approximate graph matching techniques, this method enables the identification of approximately conserved patterns in functionally related structures. In this paper, we introduce a new method for computing graph alignments motivated by two problems of the original approach, a conceptual and a computational one. First, the existing approach is of limited usefulness for structures that only share common substructures. Second, the goal to find a globally optimal alignment leads to an optimization problem that is computationally intractable. To overcome these disadvantages, we propose a semiglobal approach to graph alignment in analogy to semiglobal sequence alignment that combines the advantages of local and global graph matching. [ABSTRACT FROM PUBLISHER]