Fuzzy C-ordered medoids clustering of interval-valued data

Fuzzy clustering for interval-valued data helps us to find natural vague boundaries in such data. The Fuzzy c-Medoids Clustering (FcMdC) method is one of the most popular clustering methods based on a partitioning around medoids approach. However, one of the greatest disadvantages of this method is its sensitivity to the presence of outliers in data. This paper introduces a new robust fuzzy clustering method named Fuzzy c-Ordered-Medoids clustering for interval-valued data (FcOMdC-ID). The Huber's M-estimators and the Yager's Ordered Weighted Averaging (OWA) operators are used in the method proposed to make it robust to outliers. The described algorithm is compared with the fuzzy c-medoids method in the experiments performed on synthetic data with different types of outliers. A real application of the FcOMdC-ID is also provided

Clustering an interval data set : are the main partitions similar to a priori partition?

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.In this paper we compare the best partitions of data units (cities) obtained from different algorithms of Ascendant Hierarchical Cluster Analysis (AHCA) of a well-known data set of the literature on symbolic data analysis (“city temperature interval data set”) with a priori partition of cities given by a panel of human observers. The AHCA was based on the weighted generalised affinity with equal weights, and on the probabilistic coefficient associated with the asymptotic standardized weighted generalized affinity coefficient by the method of Wald and Wolfowitz. These similarity coefficients between elements were combined with three aggregation criteria, one classical, Single Linkage (SL), and the other ones probabilistic, AV1 and AVB, the last ones in the scope of the VL methodology. The evaluation of the partitions in order to find the partitioning that best fits the underlying data was carried out using some validation measures based on the similarity matrices. In general, global satisfactory results have been obtained using our methods, being the best partitions quite close (or even coinciding) with the a priori partition provided by the panel of human observers

Towards Formal Structural Representation of Spoken Language: An Evolving Transformation System (ETS) Approach

Speech recognition has been a very active area of research over the past twenty years. Despite an evident progress, it is generally agreed by the practitioners of the field that performance of the current speech recognition systems is rather suboptimal and new approaches are needed. The motivation behind the undertaken research is an observation that the notion of representation of objects and concepts that once was considered to be central in the early days of pattern recognition, has been largely marginalised by the advent of statistical approaches. As a consequence of a predominantly statistical approach to speech recognition problem, due to the numeric, feature vector-based, nature of representation, the classes inductively discovered from real data using decision-theoretic techniques have little meaning outside the statistical framework. This is because decision surfaces or probability distributions are difficult to analyse linguistically. Because of the later limitation it is doubtful that the gap between speech recognition and linguistic research can be bridged by the numeric representations. This thesis investigates an alternative, structural, approach to spoken language representation and categorisation. The approach pursued in this thesis is based on a consistent program, known as the Evolving Transformation System (ETS), motivated by the development and clarification of the concept of structural representation in pattern recognition and artificial intelligence from both theoretical and applied points of view. This thesis consists of two parts. In the first part of this thesis, a similarity-based approach to structural representation of speech is presented. First, a linguistically well-motivated structural representation of phones based on distinctive phonological features recovered from speech is proposed. The representation consists of string templates representing phones together with a similarity measure. The set of phonological templates together with a similarity measure defines a symbolic metric space. Representation and ETS-inspired categorisation in the symbolic metric spaces corresponding to the phonological structural representation are then investigated by constructing appropriate symbolic space classifiers and evaluating them on a standard corpus of read speech. In addition, similarity-based isometric transition from phonological symbolic metric spaces to the corresponding non-Euclidean vector spaces is investigated. Second part of this thesis deals with the formal approach to structural representation of spoken language. Unlike the approach adopted in the first part of this thesis, the representation developed in the second part is based on the mathematical language of the ETS formalism. This formalism has been specifically developed for structural modelling of dynamic processes. In particular, it allows the representation of both objects and classes in a uniform event-based hierarchical framework. In this thesis, the latter property of the formalism allows the adoption of a more physiologically-concreteapproach to structural representation. The proposed representation is based on gestural structures and encapsulates speech processes at the articulatory level. Algorithms for deriving the articulatory structures from the data are presented and evaluated

Measure based metrics for aggregated data

Aggregated data arises commonly from surveys and censuses where groups of individuals are studied as coherent entities. The aggregated data can take many forms including sets, intervals, distributions and histograms. The data analyst needs to measure the similarity between such aggregated data items and a range of metrics are reported in the literature to achieve this (e.g. the Jaccard metric for sets and the Wasserstein metric for histograms). In this paper, a unifying theory based on measure theory is developed that establishes not only that known metrics are essentially similar but also suggests new metrics

Fuzzy clustering of spatial interval-valued data

In this paper, two fuzzy clustering methods for spatial interval-valued data are proposed, i.e. the fuzzy C-Medoids clustering of spatial interval-valued data with and without entropy regularization. Both methods are based on the Partitioning Around Medoids (PAM) algorithm, inheriting the great advantage of obtaining non-fictitious representative units for each cluster. In both methods, the units are endowed with a relation of contiguity, represented by a symmetric binary matrix. This can be intended both as contiguity in a physical space and as a more abstract notion of contiguity. The performances of the methods are proved by simulation, testing the methods with different contiguity matrices associated to natural clusters of units. In order to show the effectiveness of the methods in empirical studies, three applications are presented: the clustering of municipalities based on interval-valued pollutants levels, the clustering of European fact-checkers based on interval-valued data on the average number of impressions received by their tweets and the clustering of the residential zones of the city of Rome based on the interval of price values

Fuzzy clustering of spatial interval-valued data

In this paper, two fuzzy clustering methods for spatial intervalvalued data are proposed, i.e. the fuzzy C-Medoids clustering of spatial interval-valued data with and without entropy regularization. Both methods are based on the Partitioning Around Medoids (PAM) algorithm, inheriting the great advantage of obtaining non-fictitious representative units for each cluster. In both methods, the units are endowed with a relation of contiguity, represented by a symmetric binary matrix. This can be intended both as contiguity in a physical space and as a more abstract notion of contiguity. The performances of the methods are proved by simulation, testing the methods with different contiguity matrices associated to natural clusters of units. In order to show the effectiveness of the methods in empirical studies, three applications are presented: the clustering of municipalities based on interval-valued pollutants levels, the clustering of European fact-checkers based on interval-valued data on the average number of impressions received by their tweets and the clustering of the residential zones of the city of Rome based on the interval of price values

A Similarity Measure Based on Bidirectional Subsethood for Intervals

With a growing number of areas leveraging interval-valued data—including in the context of modelling human uncertainty (e.g., in Cyber Security), the capacity to accurately and systematically compare intervals for reasoning and computation is increasingly important. In practice, well established set-theoretic similarity measures such as the Jaccard and Sørensen-Dice measures are commonly used, while axiomatically a wide breadth of possible measures have been theoretically explored. This paper identifies, articulates, and addresses an inherent and so far not discussed limitation of popular measures—their tendency to be subject to aliasing—where they return the same similarity value for very different sets of intervals. The latter risks counter-intuitive results and poor automated reasoning in real-world applications dependent on systematically comparing interval-valued system variables or states. Given this, we introduce new axioms establishing desirable properties for robust similarity measures, followed by putting forward a novel set-theoretic similarity measure based on the concept of bidirectional subsethood which satisfies both the traditional and new axioms. The proposed measure is designed to be sensitive to the variation in the size of intervals, thus avoiding aliasing. The paper provides a detailed theoretical exploration of the new proposed measure, and systematically demonstrates its behaviour using an extensive set of synthetic and real-world data. Specifically, the measure is shown to return robust outputs that follow intuition—essential for real world applications. For example, we show that it is bounded above and below by the Jaccard and Sørensen-Dice similarity measures (when the minimum t-norm is used). Finally, we show that a dissimilarity or distance measure, which satisfies the properties of a metric, can easily be derived from the proposed similarity measure

A Novel Machine Learning Classifier Based on a Qualia Modeling Agent (QMA)

This dissertation addresses a problem found in supervised machine learning (ML) classification, that the target variable, i.e., the variable a classifier predicts, has to be identified before training begins and cannot change during training and testing. This research develops a computational agent, which overcomes this problem. The Qualia Modeling Agent (QMA) is modeled after two cognitive theories: Stanovich\u27s tripartite framework, which proposes learning results from interactions between conscious and unconscious processes; and, the Integrated Information Theory (IIT) of Consciousness, which proposes that the fundamental structural elements of consciousness are qualia. By modeling the informational relationships of qualia, the QMA allows for retaining and reasoning-over data sets in a non-ontological, non-hierarchical qualia space (QS). This novel computational approach supports concept drift, by allowing the target variable to change ad infinitum without re-training while achieving classification accuracy comparable to or greater than benchmark classifiers. Additionally, the research produced a functioning model of Stanovich\u27s framework, and a computationally tractable working solution for a representation of qualia, which when exposed to new examples, is able to match the causal structure and generate new inferences

Towards Comprehensive Foundations of Computational Intelligence

Abstract. Although computational intelligence (CI) covers a vast variety of different methods it still lacks an integrative theory. Several proposals for CI foundations are discussed: computing and cognition as compression, meta-learning as search in the space of data models, (dis)similarity based methods providing a framework for such meta-learning, and a more general approach based on chains of transformations. Many useful transformations that extract information from features are discussed. Heterogeneous adaptive systems are presented as particular example of transformation-based systems, and the goal of learning is redefined to facilitate creation of simpler data models. The need to understand data structures leads to techniques for logical and prototype-based rule extraction, and to generation of multiple alternative models, while the need to increase predictive power of adaptive models leads to committees of competent models. Learning from partial observations is a natural extension towards reasoning based on perceptions, and an approach to intuitive solving of such problems is presented. Throughout the paper neurocognitive inspirations are frequently used and are especially important in modeling of the higher cognitive functions. Promising directions such as liquid and laminar computing are identified and many open problems presented.

Multivalued type dissimilarity measure and concept of mutual dissimilarity value for clustering symbolic patterns

A successful attempt in exploring a dissimilarity measure which captures the reality is made in this paper. The proposed measure unlike other measures (Pattern Recognition 24(6) (1991) 567; Pattern Recognition Lett. 16 (1995) 647; Pattern Recognition 28(8) (1995) 1277; IEEE Trans. Syst. Man Cybern. 24(4) (1994)) is multivalued and non-symmetric. The concept of mutual dissimilarity value is introduced to make the existing conventional clustering algorithms work on the proposed unconventional dissimilarity measure