Narrow Results

The amplitudes of R and T waves of the electrocardiogram (ECG) recorded during the exercise test show both large inter- and intra-individual variability in response to stress. We analyze a dataset of 65 normal subjects undergoing ambulatory test. We model the dataset of R and T series in the framework of functional data, assuming that the individual series are realizations of a non-stationary process, centered at the population trend. We test the time variability of this trend computing a simultaneous confidence band and the zero crossing of its derivative. The analysis shows that the amplitudes of the R and T waves have opposite responses to stress, consisting respectively in a bump and a dip at the early recovery stage. Our findings support the existence of a relationship between R and T wave amplitudes and respectively diastolic and systolic ventricular volumes.

We present two strategies for detecting patterns and clusters in high-dimensional time-dependent functional data. The use on wavelet-based similarity measures, since wavelets are well suited for identifying highly discriminant local time and scale features. The multiresolution aspect of the wavelet transform provides a time-scale decomposition of the signals allowing to visualize and to cluster the functional data into homogeneous groups. For each input function, through its empirical orthogonal wavelet transform the first strategy uses the distribution of energy across scales to generate a representation that can be sufficient to make the signals well distinguishable. Our new similarity measure combined with an efficient feature selection technique in the wavelet domain is then used within more or less classical clustering algorithms to effectively differentiate among high-dimensional populations. The second strategy uses a similarity measure between the whole time-scale representations that is based on wavelet-coherence tools. The clustering is then performed using a k-centroid algorithm starting from these similarities. Practical performance is illustrated through simulations as well as daily profiles of the French electricity power demand.

Functional linear regression is one of the main modeling tools for working with functional data. Since functional data are usually stream data essentially and there are some noises in functional data. Many numerical research studies of machine learning indicate that the noise samples not only increase the amount of storage space, but also affect the performance of algorithm. Therefore, in this paper we consider a new learning strategy by introducing incremental learning, Markov sampling for functional linear regression and propose a novel functional incremental linear square regression algorithm based on Markov sampling (FILSR-MS). To have a better understanding of the proposed FILSR-MS, we not only estimate the generalization bound of the proposed algorithm and establish the fast learning rate, but also present some useful discussions. The performance of the proposed algorithm is validated by the numerical experiments for benchmark repository.

The subset selection problem of linear algebra is applied to identify independent patterns of COVID-19 evolution within Brazil. The data consist of a set of mortality curves in states of Brazil. A subset of the most independent curves is selected by using a functional version of the QR matrix decomposition technique with column pivoting. The selected subset is used next as a basis to represent the remaining curves filtering out any data redundancy. For each independent curve, an associated epidemiological region of influence is defined. The results show two main independent curves with a similar two-peak pattern and a 50-day shift between the patterns. Two main epidemiological regions are next identified: one encompassing most of the country from the center and northeast states to the south, an another one containing the Amazonian region at the northwest.

In this paper we propose a new method for constructing single-asset investment strategies that can be used for hedging and risk management, with emphasis on the highly volatile energy asset class. The method consists of exploiting three stylized facts of asset returns, momentum, mean reversion and bubbles, by taking non-overlapping segments of the data that are used in a functional-type of analysis. We illustrate the workings of the proposed method with real data on two of the largest energy ETFs and the ETF for the S&P500. Our results show that the proposed method can perform substantially better than a simple rebalancing strategy or the buy and hold benchmark as it exhibits better risk return characteristics. More importantly, it appears that it can identify turning points relatively fast and is thus suitable for being used as a hedging and risk management tool in the highly unstable energy markets.

Functional logistic regression is one of the methods that have raised great interest in the emerging statistical field of functional data analysis and particularly the one of functional regression analysis when the predictor is functional and the response is binary. The aim of this paper is to generalize the solutions exposed in the literature to the different problems that arise in the functional logit model (as multicollinearity), to the multinomial case where the response variable has a finite set of categories bigger than two.

Multi-dimensional functional data, such as time series data and images from manufacturing processes, have been used for fault detection and quality improvement in many engineering applications such as automobile manufacturing, semiconductor manufacturing, and nano-machining systems. Extracting interesting and useful features from multi-dimensional functional data for manufacturing fault diagnosis is more difficult than extracting the corresponding patterns from traditional numeric and categorical data due to the complexity of functional data types, high correlation, and nonstationary nature of the data. This chapter discusses accomplishments and research issues of multi-dimensional functional data mining in the following areas: dimensionality reduction for functional data, multi-scale fault diagnosis, misalignment prediction of rotating machinery, and agricultural product inspection based on hyperspectral image analysis.