Improving Density Estimation by Incorporating Spatial Information
<p/> <p>Given discrete event data, we wish to produce a probability density that can model the relative probability of events occurring in a spatial region. Common methods of density estimation, such as Kernel Density Estimation, do not incorporate geographical information. Using these m...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2010-01-01
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| Series: | EURASIP Journal on Advances in Signal Processing |
| Online Access: | http://asp.eurasipjournals.com/content/2010/265631 |
| _version_ | 1818229484319408128 |
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| author | Smith LauraM Keegan MatthewS Wittman Todd Mohler GeorgeO Bertozzi AndreaL |
| author_facet | Smith LauraM Keegan MatthewS Wittman Todd Mohler GeorgeO Bertozzi AndreaL |
| author_sort | Smith LauraM |
| collection | DOAJ |
| description | <p/> <p>Given discrete event data, we wish to produce a probability density that can model the relative probability of events occurring in a spatial region. Common methods of density estimation, such as Kernel Density Estimation, do not incorporate geographical information. Using these methods could result in nonnegligible portions of the support of the density in unrealistic geographic locations. For example, crime density estimation models that do not take geographic information into account may predict events in unlikely places such as oceans, mountains, and so forth. We propose a set of Maximum Penalized Likelihood Estimation methods based on Total Variation and <inline-formula> <graphic file="1687-6180-2010-265631-i1.gif"/></inline-formula> Sobolev norm regularizers in conjunction with a priori high resolution spatial data to obtain more geographically accurate density estimates. We apply this method to a residential burglary data set of the San Fernando Valley using geographic features obtained from satellite images of the region and housing density information.</p> |
| first_indexed | 2024-12-12T10:19:20Z |
| format | Article |
| id | doaj.art-d36631a5887e458da473de871a81ee3d |
| institution | Directory Open Access Journal |
| issn | 1687-6172 1687-6180 |
| language | English |
| last_indexed | 2024-12-12T10:19:20Z |
| publishDate | 2010-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | EURASIP Journal on Advances in Signal Processing |
| spelling | doaj.art-d36631a5887e458da473de871a81ee3d2022-12-22T00:27:35ZengSpringerOpenEURASIP Journal on Advances in Signal Processing1687-61721687-61802010-01-0120101265631Improving Density Estimation by Incorporating Spatial InformationSmith LauraMKeegan MatthewSWittman ToddMohler GeorgeOBertozzi AndreaL<p/> <p>Given discrete event data, we wish to produce a probability density that can model the relative probability of events occurring in a spatial region. Common methods of density estimation, such as Kernel Density Estimation, do not incorporate geographical information. Using these methods could result in nonnegligible portions of the support of the density in unrealistic geographic locations. For example, crime density estimation models that do not take geographic information into account may predict events in unlikely places such as oceans, mountains, and so forth. We propose a set of Maximum Penalized Likelihood Estimation methods based on Total Variation and <inline-formula> <graphic file="1687-6180-2010-265631-i1.gif"/></inline-formula> Sobolev norm regularizers in conjunction with a priori high resolution spatial data to obtain more geographically accurate density estimates. We apply this method to a residential burglary data set of the San Fernando Valley using geographic features obtained from satellite images of the region and housing density information.</p>http://asp.eurasipjournals.com/content/2010/265631 |
| spellingShingle | Smith LauraM Keegan MatthewS Wittman Todd Mohler GeorgeO Bertozzi AndreaL Improving Density Estimation by Incorporating Spatial Information EURASIP Journal on Advances in Signal Processing |
| title | Improving Density Estimation by Incorporating Spatial Information |
| title_full | Improving Density Estimation by Incorporating Spatial Information |
| title_fullStr | Improving Density Estimation by Incorporating Spatial Information |
| title_full_unstemmed | Improving Density Estimation by Incorporating Spatial Information |
| title_short | Improving Density Estimation by Incorporating Spatial Information |
| title_sort | improving density estimation by incorporating spatial information |
| url | http://asp.eurasipjournals.com/content/2010/265631 |
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