K-Nearest Neighbor Estimation of Forest Attributes: Improving Mapping Efficiency

—This paper describes our efforts in refining k-nearest neighbor forest attributes classification using U.S. Department of Agriculture Forest Service Forest Inventory and Analysis plot data and Landsat 7 Enhanced Thematic Mapper Plus imagery. The analysis focuses on FIA-defined forest type classification across St. Louis County in northeastern Minnesota. We outline three steps in the classification process that highlight improvements in mapping efficiency: (1) using transformed divergence for spectral feature selection, (2) applying a mathematical rule for reducing the nearest neighbor search set, and (3) using a database to reduce redundant nearest neighbor searches. Our trials suggest that when combined, these approaches can reduce mapping time by half without significant loss of accuracy. The k-nearest neighbor (kNN) multisource inventory has proved timely, cost-efficient, and accurate in the Nordic countries and initial U.S trials. (Franco-Lopez et al. 2001, Haapanen et al. 2004, McRoberts et al. 2002). This approach for extending field point inventories is ideally suited to the estimation and monitoring needs of Federal agencies, such as the U.S. Department of Agriculture (USDA) Forest Service, that conduct natural and agricultural resource inventories. It provides wall-towall maps of forest attributes, retains the natural data variation found in the field inventory (unlike many parametric algorithms), and provides precise and localized estimates in common metrics across large areas and various ownerships. At a pixel-level classification, the kNN algorithm assigns each unknown (target) pixel the field attributes of the most similar reference pixels for which field data exists. Similarity is defined in terms of the feature space, typically measured as Euclidean or Mahalanobis distance between spectral features. The kNN algorithm is not mathematically complex; however, using multiple image dates and features from each date, along with several thousand field reference observations, makes kNN pixel-based mapping of large areas very inefficient. Specifically, the kNN classification approximates to F·N distance calculations, where F is the number of pixels to classify and N is the number of references. For example, standard kNN mapping of a 1.3 x 106 ha area, with a pixel resolution of 30 m2, and approximately 1,500 FIA field reference observations requires about 22 billion distance calculations and around 16 hours to process on a Pentium 4, single-processor computer. Our study examined using USDA Forest Service Forest Inventory and Analysis (FIA) plot data and Landsat 7 Enhanced Thematic Mapper Plus (ETM+) imagery in kNN classification of FIA-defined forest types. Specific emphasis is placed on improving mapping efficiency by reducing classification feature space, decreasing the number of distance calculations in the nearest neighbor search, and eliminating redundancy in redundant nearest neighbor searches by building a database of feature patterns associated with different forest type classes.