Finding representative electrocardiogram beat morphologies with CUR.

In this paper, we use the CUR matrix factorization as a means of dimension reduction to identify important subsequences in electrocardiogram (ECG) time series. As opposed to other factorizations typically used in dimension reduction that characterize data in terms of abstract representatives (for example, an orthogonal basis), the CUR factorization describes the data in terms of actual instances within the original data set. Therefore, the CUR characterization can be directly related back to the clinical setting. We apply CUR to a synthetic ECG data set as well as to data from the MIT-BIH Arrhythmia, MGH-MF, and Incart databases using the discrete empirical interpolation method (DEIM) and an incremental QR factorization. In doing so, we demonstrate that CUR is able to identify beat morphologies that are representative of the data set, including rare-occurring beat events, providing a robust summarization of the ECG data. We also see that using CUR-selected beats to label the remaining unselected beats via 1-nearest neighbor classification produces results comparable to those presented in other works. While the electrocardiogram is of particular interest here, this work demonstrates the utility of CUR in detecting representative subsequences in quasiperiodic physiological time series.

An Extended DEIM Algorithm for Subset Selection and Class Identification.

The discrete empirical interpolation method (DEIM) has been shown to be a viable index-selection technique for identifying representative subsets in data. Having gained some popularity in reducing dimensionality of physical models involving differential equations, its use in subset-/pattern-identification tasks is not yet broadly known within the machine learning community. While it has much to offer as is, the DEIM algorithm is limited in that the number of selected indices cannot exceed the rank of the corresponding data matrix. Although this is not an issue for many data sets, there are cases in which the number of classes represented in a given data set is greater than the rank of the data matrix; in such cases, it is impossible for the standard DEIM algorithm to identify all classes. To overcome this issue, we present a novel extension of DEIM, called E-DEIM. With the proposed algorithm, we also provide some theoretical results for using extensions of DEIM to form the CUR matrix factorization in identifying both rows and columns to approximate the original data matrix. Results from applying variations of E-DEIM to two different data sets indicate that the presented extension can indeed allow for the identification of additional classes along with those selected by standard DEIM. In addition, comparing these results to those of some more familiar methods demonstrates that the proposed deterministic E-DEIM approach including coherence performs comparably to or better than the other evaluated methods and should be considered in future class-identification tasks.