A nonparametric multiclass partitioning method for classification

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1982.MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERINGIncludes bibliographical references.by Saul Brian Gelfand.M.S

Tree-Structured Nonlinear Adaptive Signal Processing

In communication systems, nonlinear adaptive filtering has become increasingly popular in a variety of applications such as channel equalization, echo cancellation and speech coding. However, existing nonlinear adaptive filters such as polynomial (truncated Volterra series) filters and multilayer perceptrons suffer from a number of problems. First, although high Order polynomials can approximate complex nonlinearities, they also train very slowly. Second, there is no systematic and efficient way to select their structure. As for multilayer perceptrons, they have a very complicated structure and train extremely slowly Motivated by the success of classification and regression trees on difficult nonlinear and nonparametfic problems, we propose the idea of a tree-structured piecewise linear adaptive filter. In the proposed method each node in a tree is associated with a linear filter restricted to a polygonal domain, and this is done in such a way that each pruned subtree is associated with a piecewise linear filter. A training sequence is used to adaptively update the filter coefficients and domains at each node, and to select the best pruned subtree and the corresponding piecewise linear filter. The tree structured approach offers several advantages. First, it makes use of standard linear adaptive filtering techniques at each node to find the corresponding Conditional linear filter. Second, it allows for efficient selection of the subtree and the corresponding piecewise linear filter of appropriate complexity. Overall, the approach is computationally efficient and conceptually simple. The tree-structured piecewise linear adaptive filter bears some similarity to classification and regression trees. But it is actually quite different from a classification and regression tree. Here the terminal nodes are not just assigned a region and a class label or a regression value, but rather represent: a linear filter with restricted domain, It is also different in that classification and regression trees are determined in a batch mode offline, whereas the tree-structured adaptive filter is determined recursively in real-time. We first develop the specific structure of a tree-structured piecewise linear adaptive filter and derive a stochastic gradient-based training algorithm. We then carry out a rigorous convergence analysis of the proposed training algorithm for the tree-structured filter. Here we show the mean-square convergence of the adaptively trained tree-structured piecewise linear filter to the optimal tree-structured piecewise linear filter. Same new techniques are developed for analyzing stochastic gradient algorithms with fixed gains and (nonstandard) dependent data. Finally, numerical experiments are performed to show the computational and performance advantages of the tree-structured piecewise linear filter over linear and polynomial filters for equalization of high frequency channels with severe intersymbol interference, echo cancellation in telephone networks and predictive coding of speech signals

Heart valve disease: investigation by cardiovascular magnetic resonance

Cardiovascular magnetic resonance (CMR) has become a valuable investigative tool in many areas of cardiac medicine. Its value in heart valve disease is less well appreciated however, particularly as echocardiography is a powerful and widely available technique in valve disease. This review highlights the added value that CMR can bring in valve disease, complementing echocardiography in many areas, but it has also become the first-line investigation in some, such as pulmonary valve disease and assessing the right ventricle. CMR has many advantages, including the ability to image in any plane, which allows full visualisation of valves and their inflow/outflow tracts, direct measurement of valve area (particularly for stenotic valves), and characterisation of the associated great vessel anatomy (e.g. the aortic root and arch in aortic valve disease). A particular strength is the ability to quantify flow, which allows accurate measurement of regurgitation, cardiac shunt volumes/ratios and differential flow volumes (e.g. left and right pulmonary arteries). Quantification of ventricular volumes and mass is vital for determining the impact of valve disease on the heart, and CMR is the 'Gold standard' for this. Limitations of the technique include partial volume effects due to image slice thickness, and a low ability to identify small, highly mobile objects (such as vegetations) due to the need to acquire images over several cardiac cycles. The review examines the advantages and disadvantages of each imaging aspect in detail, and considers how CMR can be used optimally for each valve lesion

Analysis of simulated annealing type algorithms

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1987.MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERINGBibliography: leaves 101-103.by Saul B. Gelfand.Ph.D

and

Discrete Markov random fields (MRF's) defined on a finite lattice have seen significant application as stochastic models for images [1], [2]. There are two fundamental problems associated with image processing based on such random field models. First, we want to generate realizations of the random fields to determine their suitability as models of our prior knowledge. Second, we want t

Modified dynamic time warping (MDTW) for estimating temporal dietary patterns

Nitin Khanna, Heather A. Eicher-Miller, Hemant K. Verma, Carol J. Boushey,, Saul B. Gelfand and Edward Del

The Discovery of Data-Driven Temporal Dietary Patterns and a Validation of Their Description Using Energy and Time Cut-Offs

Data-driven temporal dietary patterning (TDP) methods were previously developed. The objectives were to create data-driven temporal dietary patterns and assess concurrent validity of energy and time cut-offs describing the data-driven TDPs by determining their relationships to BMI and waist circumference (WC). The first day 24-h dietary recall timing and amounts of energy for 17,915 U.S. adults of the National Health and Nutrition Examination Survey 2007–2016 were used to create clusters representing four TDPs using dynamic time warping and the kernel k-means clustering algorithm. Energy and time cut-offs were extracted from visualization of the data-derived TDPs and then applied to the data to find cut-off-derived TDPs. The strength of TDP relationships with BMI and WC were assessed using adjusted multivariate regression and compared. Both methods showed a cluster, representing a TDP with proportionally equivalent average energy consumed during three eating events/day, associated with significantly lower BMI and WC compared to the other three clusters that had one energy intake peak/day at 13:00, 18:00, and 19:00 (all p < 0.0001). Participant clusters of the methods were highly overlapped (>83%) and showed similar relationships with obesity. Data-driven TDP was validated using descriptive cut-offs and hold promise for obesity interventions and translation to dietary guidance