{"59991":{"#nid":"59991","#data":{"type":"news","title":"Wavelet Bootstrapping: Statistical Technique Helps Researchers Gain More Information from Single Data Run","body":[{"value":"\u003Cp\u003EFor certain classes of data that may be very expensive or difficult to obtain, a new statistical technique may provide useful information from a single data run by allowing meaningful re-sampling. \n\u003C\/p\u003E\n\u003Cp\u003EThe technique, known as \u0022wavelet bootstrapping\u0022 or \u0022wavestrapping,\u0022 has applications in the geophysical sciences, bioinformatics, medical imaging, nanotechnology and other areas. It can also be useful for rapidly obtaining information from small data sets in such applications as medical diagnostics.\n\u003C\/p\u003E\n\u003Cp\u003EWavelets are mathematical functions that have become increasingly important to researchers because of their ability to analyze data sets that are difficult to understand using traditional techniques such as Fast Fourier Transform. For instance, signals within noisy data recorded in the time domain can become more meaningful when analyzed in the wavelet domain.\n\u003C\/p\u003E\n\u003Cp\u003EWavestrapping was pioneered by University of Washington researchers, who applied wavelet transforms to an established statistical re-sampling technique known as bootstrapping, which is used to extract additional information from single data runs. The marriage of bootstrapping and wavelets offers a new tool for the analysis of data sets that would otherwise be difficult to study because of correlation and time-dependency issues.\n\u003C\/p\u003E\n\u003Cp\u003E\u0022The new thing here is re-sampling, but not in the time domain, which would be nearly impossible because of the strong dependence of data or correlation of data,\u0022 said \u003Ca href=\u0022http:\/\/www.isye.gatech.edu\/faculty-staff\/profile.php?entry=bv20\u0022\u003EBrani Vidakovic\u003C\/a\u003E, professor at the Georgia Institute of Technology\u0027s School of Industrial and Systems Engineering. \u0022By transferring the data to the wavelet domain, applying re-sampling methods and then returning the re-sampled data as variants in the time domain, you can then proceed as if you had a data ensemble rather than a single run.\u0022\n\u003C\/p\u003E\n\u003Cp\u003EVidakovic discussed his research on validating wavelet bootstrapping strategies and assessing their variability bounds at the annual meeting of the American Association for the Advancement of Science (AAAS) in Seattle. His presentation \u0022What Does a Single Run Tell about the Ensemble?\u0022 was part of a session \u0022Wavelet-Based Statistical Analysis of Multiscale Geophysical Data\u0022 held on February 16.\n\u003C\/p\u003E\n\u003Cp\u003E\u0022Sometimes scientists have a single measurement and they are unable to get another measurement,\u0022 Vidakovic explained. \u0022Sometimes they would like to have an ensemble of measurements with similar boundary conditions so the heterogeneity caused by external factors - such as different regimes, times of day or climate conditions - are taken into account. Wavestrapping can help make inferences from a single run.\u0022\n\u003C\/p\u003E\n\u003Cp\u003EOne example might be a study of atmospheric turbulence in which an additional flight to gather data under similar conditions could be impossible. \u0022Atmospheric scientists are very excited about wavelets because not only are they local and able to efficiently describe organized structures in turbulence, but they are also able to assess the self-similarity and scaling indices of turbulence,\u0022 Vidakovic said.\n\u003C\/p\u003E\n\u003Cp\u003EIn such instances, converting the data into a wavelet domain before re-sampling can produce information for which error bounds can be reliably assessed, Vidakovic said. Though the bootstrapping technique is controversial, he believes it offers important opportunities when used with appropriate data sets.\n\u003C\/p\u003E\n\u003Cp\u003E\u0022This is very effective when data in the time domain are not good for bootstrapping because of dependency,\u0022 he said. \u0022It can solve one difficult problem, and in that respect it is new and exciting.\u0022\n\u003C\/p\u003E\n\u003Cp\u003EWavestrapping was proposed and developed by Don Percival and other researchers at the University of Washington\u0027s Applied Physics Lab. Vidakovic\u0027s research, sponsored by the National Science Foundation, builds on that work in assessing the technique\u0027s validity and where its use is appropriate.\n\u003C\/p\u003E\n\u003Cp\u003E\u003Cem\u003ESome examples of wavestrapping applications include:\u003C\/em\u003E\n\u003C\/p\u003E\n\u003Cul\u003E\n\u003Cli\u003ERapid analysis of changes in pupil diameter to reveal clues about the health of patients. Using measurements taken 21 times per second, Vidakovic is helping Georgia Tech researchers Julie Jacko and Francois Sainfort analyze data that may provide quick detection of specific medical conditions.\u003C\/li\u003E\n\u003Cli\u003EStatistical study of new types of nanometer-scale materials. \u0022Nano materials science is increasingly multiscale because people are looking at the problem at different scales,\u0022 said Vidakovic. \u0022The modeling should therefore be done at different scales because the materials are very different at the different scales.\u0022\u003C\/li\u003E\n\u003Cli\u003EAnalysis of genomic data, especially in the rapid determination of which genetic sequences are coding and which are not.\u003C\/li\u003E\n\u003Cli\u003EMedical imaging, such as the detection of details in mammography data where small differences in calcification shapes are important to diagnosis.\u003C\/li\u003E\n\u003C\/ul\u003E\n\u003Cp\u003E\u003Cem\u003EWavelets offer advantages over traditional statistical analysis techniques, including:\u003C\/em\u003E\n\u003C\/p\u003E\n\u003Cul\u003E\n\u003Cli\u003EAbility to remove noise from complex data sets;\u003C\/li\u003E\n\u003Cli\u003ESensitivity to the fractal nature and self-similarity of data;\u003C\/li\u003E\n\u003Cli\u003EAbility to minimize correlation and time-dependency of data;\u003C\/li\u003E\n\u003Cli\u003ELocality of the analysis and ability to handle multi-scale information; and\u003C\/li\u003E\n\u003Cli\u003EComputational simplicity, which permits faster analysis.\u003C\/li\u003E\n\u003C\/ul\u003E\n\u003Cp\u003EAlthough the beginnings of wavelets can be traced back almost a century, their wide use began only about 15 years ago when new wavelet bases were discovered and their implementation was connected with fast-filtering computational procedures.\n\u003C\/p\u003E\n\u003Cp\u003E\u0022The interest in wavelets is their speed and locality,\u0022 said Vidakovic. \u0022Locality is the most important, because many natural phenomena are non-stationary and very local. Wavelets are able to economically describe phenomena that are inhomogeneous. For some phenomena, it would be impossible to make sense of the data without wavelets.\u0022\n\u003C\/p\u003E\n\u003Cp\u003EWavelets also help researchers with a major problem of the computer age - large volumes of data mixed with noise. \u0022Their dimension reduction and ability to deal with huge data sets are also strengths of wavelets,\u0022 he added. \u0022Very nasty data can be de-noised almost in real-time by selecting a few of the important wavelet coefficients that can retain the main trend in the signal.\u0022\n\u003C\/p\u003E\n\u003Cp\u003EMany different wavelets exist, and selecting the right ones is a vital part of developing the new technique, Vidakovic said. \u0022Wavelets are not a miracle tool for everything,\u0022 he warned. \u0022But if the data are amenable to wavelet analysis, then they can be very helpful.\u0022\n\u003C\/p\u003E\n\n\u003Cstrong\u003ERelated Website: \u003Ca href=\u0022http:\/\/www.isye.gatech.edu\/lhci\/\u0022 target=\u0022_blank\u0022\u003ELaboratory for Human-Computer Interaction and Health Care Informatics (HCI Lab)\u003C\/a\u003E\u003Cbr \/\u003E\n\u003Cbr \/\u003E\nReprinted with permission from the \u003Ca href=\u0022http:\/\/gtresearchnews.gatech.edu\/\u0022 target=\u0022_blank\u0022\u003EGeorgia Tech Research News \u0026amp; Publications Office\u003C\/a\u003E\u003C\/strong\u003E","summary":null,"format":"limited_html"}],"field_subtitle":"","field_summary":"","field_summary_sentence":"","uid":"27279","created_gmt":"2004-03-16 01:00:00","changed_gmt":"2016-10-08 03:07:08","author":"Barbara Christopher","boilerplate_text":"","field_publication":"","field_article_url":"","dateline":{"date":"2004-03-16T00:00:00-05:00","iso_date":"2004-03-16T00:00:00-05:00","tz":"America\/New_York"},"extras":[],"groups":[{"id":"1242","name":"School of Industrial and Systems Engineering (ISYE)"}],"categories":[{"id":"145","name":"Engineering"},{"id":"135","name":"Research"}],"keywords":[],"core_research_areas":[],"news_room_topics":[],"event_categories":[],"invited_audience":[],"affiliations":[],"classification":[],"areas_of_expertise":[],"news_and_recent_appearances":[],"phone":[],"contact":[{"value":"\u003Cstrong\u003EBarbara Christopher\u003C\/strong\u003E\u003Cbr \/\u003EIndustrial and Systems Engineering\u003Cbr \/\u003E\u003Ca href=\u0022http:\/\/www.gatech.edu\/contact\/index.html?id=bt3\u0022\u003EContact Barbara Christopher\u003C\/a\u003E\u003Cbr \/\u003E\u003Cstrong\u003E404.385.3102\u003C\/strong\u003E","format":"limited_html"}],"email":["bchristopher@isye.gatech.edu"],"slides":[],"orientation":[],"userdata":""}}}