Model-Based Clustering and Classification of Functional Data

The problem of complex data analysis is a central topic of modern statistical science and learning systems and is becoming of broader interest with the increasing prevalence of high-dimensional data. The challenge is to develop statistical models and autonomous algorithms that are able to acquire knowledge from raw data for exploratory analysis, which can be achieved through clustering techniques or to make predictions of future data via classification (i.e., discriminant analysis) techniques. Latent data models, including mixture model-based approaches are one of the most popular and successful approaches in both the unsupervised context (i.e., clustering) and the supervised one (i.e, classification or discrimination). Although traditionally tools of multivariate analysis, they are growing in popularity when considered in the framework of functional data analysis (FDA). FDA is the data analysis paradigm in which the individual data units are functions (e.g., curves, surfaces), rather than simple vectors. In many areas of application, the analyzed data are indeed often available in the form of discretized values of functions or curves (e.g., time series, waveforms) and surfaces (e.g., 2d-images, spatio-temporal data). This functional aspect of the data adds additional difficulties compared to the case of a classical multivariate (non-functional) data analysis. We review and present approaches for model-based clustering and classification of functional data. We derive well-established statistical models along with efficient algorithmic tools to address problems regarding the clustering and the classification of these high-dimensional data, including their heterogeneity, missing information, and dynamical hidden structure. The presented models and algorithms are illustrated on real-world functional data analysis problems from several application area

Bayesian neural network learning for repeat purchase modelling in direct marketing.

We focus on purchase incidence modelling for a European direct mail company. Response models based on statistical and neural network techniques are contrasted. The evidence framework of MacKay is used as an example implementation of Bayesian neural network learning, a method that is fairly robust with respect to problems typically encountered when implementing neural networks. The automatic relevance determination (ARD) method, an integrated feature of this framework, allows to assess the relative importance of the inputs. The basic response models use operationalisations of the traditionally discussed Recency, Frequency and Monetary (RFM) predictor categories. In a second experiment, the RFM response framework is enriched by the inclusion of other (non-RFM) customer profiling predictors. We contribute to the literature by providing experimental evidence that: (1) Bayesian neural networks offer a viable alternative for purchase incidence modelling; (2) a combined use of all three RFM predictor categories is advocated by the ARD method; (3) the inclusion of non-RFM variables allows to significantly augment the predictive power of the constructed RFM classifiers; (4) this rise is mainly attributed to the inclusion of customer\slash company interaction variables and a variable measuring whether a customer uses the credit facilities of the direct mailing company.Marketing; Companies; Models; Model; Problems; Neural networks; Networks; Variables; Credit;

Revisiting Data Complexity Metrics Based on Morphology for Overlap and Imbalance: Snapshot, New Overlap Number of Balls Metrics and Singular Problems Prospect

Data Science and Machine Learning have become fundamental assets for companies and research institutions alike. As one of its fields, supervised classification allows for class prediction of new samples, learning from given training data. However, some properties can cause datasets to be problematic to classify. In order to evaluate a dataset a priori, data complexity metrics have been used extensively. They provide information regarding different intrinsic characteristics of the data, which serve to evaluate classifier compatibility and a course of action that improves performance. However, most complexity metrics focus on just one characteristic of the data, which can be insufficient to properly evaluate the dataset towards the classifiers' performance. In fact, class overlap, a very detrimental feature for the classification process (especially when imbalance among class labels is also present) is hard to assess. This research work focuses on revisiting complexity metrics based on data morphology. In accordance to their nature, the premise is that they provide both good estimates for class overlap, and great correlations with the classification performance. For that purpose, a novel family of metrics have been developed. Being based on ball coverage by classes, they are named after Overlap Number of Balls. Finally, some prospects for the adaptation of the former family of metrics to singular (more complex) problems are discussed.Comment: 23 pages, 9 figures, preprin

Computer aided diagnosis for cardiovascular diseases based on ECG signals : a survey

The interpretation of Electroencephalography (ECG) signals is difficult, because even subtle changes in the waveform can indicate a serious heart disease. Furthermore, these waveform changes might not be present all the time. As a consequence, it takes years of training for a medical practitioner to become an expert in ECG-based cardiovascular disease diagnosis. That training is a major investment in a specific skill. Even with expert ability, the signal interpretation takes time. In addition, human interpretation of ECG signals causes interoperator and intraoperator variability. ECG-based Computer-Aided Diagnosis (CAD) holds the promise of improving the diagnosis accuracy and reducing the cost. The same ECG signal will result in the same diagnosis support regardless of time and place. This paper introduces both the techniques used to realize the CAD functionality and the methods used to assess the established functionality. This survey aims to instill trust in CAD of cardiovascular diseases using ECG signals by introducing both a conceptional overview of the system and the necessary assessment method

Adaptive algorithms for real-world transactional data mining.

The accurate identification of the right customer to target with the right product at the right time, through the right channel, to satisfy the customer’s evolving needs, is a key performance driver and enhancer for businesses. Data mining is an analytic process designed to explore usually large amounts of data (typically business or market related) in search of consistent patterns and/or systematic relationships between variables for the purpose of generating explanatory/predictive data models from the detected patterns. It provides an effective and established mechanism for accurate identification and classification of customers. Data models derived from the data mining process can aid in effectively recognizing the status and preference of customers - individually and as a group. Such data models can be incorporated into the business market segmentation, customer targeting and channelling decisions with the goal of maximizing the total customer lifetime profit. However, due to costs, privacy and/or data protection reasons, the customer data available for data mining is often restricted to verified and validated data,(in most cases,only the business owned transactional data is available). Transactional data is a valuable resource for generating such data models. Transactional data can be electronically collected and readily made available for data mining in large quantity at minimum extra cost. Transactional data is however, inherently sparse and skewed. These inherent characteristics of transactional data give rise to the poor performance of data models built using customer data based on transactional data. Data models for identifying, describing, and classifying customers, constructed using evolving transactional data thus need to effectively handle the inherent sparseness and skewness of evolving transactional data in order to be efficient and accurate. Using real-world transactional data, this thesis presents the findings and results from the investigation of data mining algorithms for analysing, describing, identifying and classifying customers with evolving needs. In particular, methods for handling the issues of scalability, uncertainty and adaptation whilst mining evolving transactional data are analysed and presented. A novel application of a new framework for integrating transactional data binning and classification techniques is presented alongside an effective prototype selection algorithm for efficient transactional data model building. A new change mining architecture for monitoring, detecting and visualizing the change in customer behaviour using transactional data is proposed and discussed as an effective means for analysing and understanding the change in customer buying behaviour over time. Finally, the challenging problem of discerning between the change in the customer profile (which may necessitate the effective change of the customer’s label) and the change in performance of the model(s) (which may necessitate changing or adapting the model(s)) is introduced and discussed by way of a novel flexible and efficient architecture for classifier model adaptation and customer profiles class relabeling