Renata M. C. R. Souza

Hybrid methods for fuzzy clustering based on fuzzy c-means and improved particle swarm optimization

We present two new hybrids of FCM and improved self-adaptive PSO.The methods are based on the FCM-PSO algorithm.We use FCM to initialize one particle to achieve better results in less iterations.The new methods are compared to FCM-PSO using many real and synthetic datasets.The proposed methods consistently outperform FCM-PSO in three evaluation metrics. Fuzzy clustering has become an important research field with many applications to real world problems. Among fuzzy clustering methods, fuzzy c-means (FCM) is one of the best known for its simplicity and efficiency, although it shows some weaknesses, particularly its tendency to fall into local minima. To tackle this shortcoming, many optimization-based fuzzy clustering methods have been proposed in the literature. Some of these methods are based solely on a metaheuristic optimization, such as particle swarm optimization (PSO) whereas others are hybrid methods that combine a metaheuristic with a traditional partitional clustering method such as FCM. It is demonstrated in the literature that methods that hybridize PSO and FCM for clustering have an improved accuracy over traditional partitional clustering approaches. On the other hand, PSO-based clustering methods have poor execution time in comparison to partitional clustering techniques. Another problem with PSO-based clustering is that the current PSO algorithms require tuning a range of parameters before they are able to find good solutions. In this paper we introduce two hybrid methods for fuzzy clustering that aim to deal with these shortcomings. The methods, referred to as FCM-IDPSO and FCM2-IDPSO, combine FCM with a recent version of PSO, the IDPSO, which adjusts PSO parameters dynamically during execution, aiming to provide better balance between exploration and exploitation, avoiding falling into local minima quickly and thereby obtaining better solutions. Experiments using two synthetic data sets and eight real-world data sets are reported and discussed. The experiments considered the proposed methods as well as some recent PSO-based fuzzy clustering methods. The results show that the methods introduced in this paper provide comparable or in many cases better solutions than the other methods considered in the comparison and were much faster than the other state of the art PSO-based methods.

IFKCN: Applying fuzzy Kohonen clustering network to interval data

The recording of interval data has become a common practice in real world applications and nowadays this kind of data is often used to describe objects. In this paper, we introduce a new fuzzy Kohonen clustering network for symbolic interval data (IFKCN). The network combine the idea of fuzzy membership values for learning rates and the algorithm is able to show superiority in processing the ambiguity and the uncertainty present in data sets. Experiments with benchmark interval data sets and an artificial interval data set for evaluating the usefulness of the proposed method were carried out.

A parametrized approach for linear regression of interval data

Abstract Interval symbolic data is a complex data type that can often be obtained by summarizing large datasets. All existing linear regression approaches for interval data use certain fixed reference points to model intervals, such as midpoints, ranges and lower and upper bounds. This is a limitation, because different datasets might be better represented by different reference points. In this paper, we propose a new method for extracting knowledge from interval data. Our parametrized approach automatically extracts the best reference points from the regressor variables. These reference points are then used to build two linear regressions: one for the lower bounds of the response variable and another for its upper bounds. Before the regressions are applied, we compute a criterion to verify the mathematical coherence of predicted values. Mathematical coherence means that the upper bounds are greater than the lower bounds. If the criterion shows that the coherence is not guaranteed, we suggest the use of a novel interval Box-Cox transformation of the response variable. Experimental evaluations with synthetic and real interval datasets illustrate the advantages and the usefulness of the proposed method to perform interval linear regression.

Fuzzy learning vector quantization approaches for interval data

Symbolic data analysis deals with complex data types, capable of modeling internal data variability and imprecise data. This paper introduces two Fuzzy Learning Vector Quantization algorithms for interval symbolic data. One algorithm employs an interval Euclidean distance. The second uses a weighted interval Euclidean distance to try and achieve a better performance of classification when the data set is composed of classes with varying sizes, shapes and structures. The algorithms are evaluated for their performances with synthetic and real data sets. This paper aims at contributing to the area of Supervised Learning within Symbolic Data Analysis.

A swarm-trained k-nearest prototypes adaptive classifier with automatic feature selection for interval data

Some complex data types are capable of modeling data variability and imprecision. These data types are studied in the symbolic data analysis field. One such data type is interval data, which represents ranges of values and is more versatile than classic point data for many domains. This paper proposes a new prototype-based classifier for interval data, trained by a swarm optimization method. Our work has two main contributions: a swarm method which is capable of performing both automatic selection of features and pruning of unused prototypes and a generalized weighted squared Euclidean distance for interval data. By discarding unnecessary features and prototypes, the proposed algorithm deals with typical limitations of prototype-based methods, such as the problem of prototype initialization. The proposed distance is useful for learning classes in interval datasets with different shapes, sizes and structures. When compared to other prototype-based methods, the proposed method achieves lower error rates in both synthetic and real interval datasets.

Zero-inflated prediction model in software-fault data

Software fault data with many zeroes in addition to large non-zero values are common in the software estimation area. A two-component prediction approach that provides a robust way to predict this type of data is introduced in this study. This approach allows to combine parametric and non-parametric models to improve the prediction accuracy. This way provides a more flexible structure to understand data. To show the usefulness of the proposed approach, experiments using eight projects from the NASA repository are considered. In addition, this method is compared with methods from the machine learning and statistical literature. The performance of the methods is measured by the prediction accuracy that is assessed based on the mean magnitude of relative errors.

Effort Drivers Estimation for Brazilian Geographically Distributed Software Development

To meet the requirements of today’s fast paced markets, it is important to develop projects on time and with the minimum use of resources. A good estimate is the key to achieve this goal. Several companies have started to work with geographically distributed teams due to cost reduction and time-to-market. Some researchers indicate that this approach introduces new challenges, because the teams work in different time zones and have possible differences in culture and language. It is already known that the multisite development increases the software cycle time. Data from 15 DSD projects from 10 distinct companies were collected. The analysis shows drivers that impact significantly the total effort planned to develop systems using DSD approach in Brazil.

Polygonal data analysis: A new framework in symbolic data analysis

Abstract This paper introduces a new framework for polygonal data analysis in the symbolic data analysis paradigm. We show that polygonal data generalizes bivariate interval data. A way for aggregating data in classes is presented to obtain symbolic datasets and, descriptive statistics (for instance, mean, variance, covariance, and histogram) and a linear regression model are proposed for symbolic polygonal data. A simulation study to available the performance of the polygonal linear regression based on a mean square error of area is done. The proposed methodology is applied to two real symbolic datasets represented by classes, and the results illustrate the usefulness of the statistical techniques.

Investigating Different Fitness Criteria for Swarm-based Clustering

Swarm-based optimisation methods have been previously used for tackling clustering tasks, with good results. However, the results obtained by this kind of algorithm are highly dependent on the chosen fitness criterion. In this work, we investigate the influence of four different fitness criteria on swarm-based clustering performance. The first function is the typical sum of distances between instances and their cluster centroids, which is the most used clustering criterion. The remaining functions are based on three different types of data dispersion: total dispersion, within-group dispersion and between-groups dispersion. We use a swarm-based algorithm to optimise these criteria and perform clustering tasks with nine real and artificial datasets. For each dataset, we select the best criterion in terms of adjusted Rand index and compare it with three state-of-the-art swarm-based clustering algorithms, trained with their proposed criteria. Numerical results confirm the importance of selecting an appropriate fitness criterion for each clustering task.