Interval type-2 defuzzification using uncertainty weights

One of the most popular interval type-2 defuzzification methods is the Karnik-Mendel (KM) algorithm. Nie and Tan (NT) have proposed an approximation of the KM method that converts the interval type-2 membership functions to a single type-1 membership function by averaging the upper and lower memberships, and then applies a type-1 centroid defuzzification. In this paper we propose a modification of the NT algorithm which takes into account the uncertainty of the (interval type-2) memberships. We call this method the uncertainty weight (UW) method. Extensive numerical experiments motivated by typical fuzzy controller scenarios compare the KM, NT, and UW methods. The experiments show that (i) in many cases NT can be considered a good approximation of KM with much lower computational complexity, but not for highly unbalanced uncertainties, and (ii) UW yields more reasonable results than KM and NT if more certain decision alternatives should obtain a larger weight than more uncertain alternatives

Robust fuzzy relational clustering of non-linear data

In many practical situations data may be characterized by non-linear structures. Classical (hard or fuzzy) algorithms, usually based on the Euclidean distance, implicitly lead to spherical shape clusters and, therefore, do not identify clusters properly. In this paper we deal with non-linear structures in clustering by means of the geodesic distance, able to capture and preserve the intrinsic geometry of the data. We introduce a new fuzzy relational clustering algorithm based on the geodesic distance. Furthermore, to improve its adequacy, a robust version is proposed in order to take into account the presence of outliers

Multi-agent Based Manifold Denoising

Manifold learning plays a central role in many Machine Learning (ML) methods where it assumes information lies on a low-dimensional manifold, but the presence of high dimensional noise may defect their performance. In this contribution, we propose a novel (swarm) algorithm to suppress the noise of manifolds of potentially varying dimensionalities. Inspired by colonial insects this method employs multiple agents with different strategies moving through the data space in parallel. During this process, they use local information to reconstruct the manifolds and then move data objects close to them. Moreover, principles of evolutionary game theory are used to encourage agents to select better strategies and hence optimize the hyper-parameters automatically. While other denoising techniques can be seen as single-agent approaches, the new algorithm is a multi-agent approach which makes it more flexible and suitable for scenarios including multiple manifolds. In the experiments, we simulate several situations from a simple manifold with a specific noise level, to more complex manifolds where there are variations on the density, noise level or dimensionalities. Furthermore, we demonstrate the improvement of the proposed algorithm for the performance of the Parzen Window (PW) density estimator

Aggregation invariance in general clustering approaches

Aggregation invariance, c-Means clustering, EM algorithm, Fuzzy clustering, Model-based clustering, Mutual information, 34K20, 62P99, 65K10, 82B26, 94A17, 94D05,

Soft Clustering: Why and How-To

Despite the huge success of machine learning methods in the last decade, a crucial issue is to control the support of the data used in inference, so that data that are too far from the training set are given low confidence by default. The most important class that features this ability is that of prototype-based methods which are based on clustering or vector quantization as a representation learning model. This paper surveys a family of popular soft clustering methods, framing them in a unified formalism. It also discusses the peculiarities of each of them. A large fraction of the paper is devoted to clarifying the role of model parameters and to providing some guidelines on how to set up these parameters