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Rule-Based Classification Systems Using
Classification and Regression Tree (CART) Analysis
R i c k L. L a w r e n c e a n d Andrea W r l g h t
Incorporating ancillary data into image classification can increase classification accuracy and precision. Rule-based classification systems using expert systems or machine learning are a particularly useful means of incorporating ancillary data, but have been difficult to implement. We developed a means for creating a rule-based classification using classification and regression tree analysis (CART), a commonly available statistical method. The CART classifica- tion does not require expert knowledge, automatically selects useful spectral and ancillary data from data supplied by the analyst, and can be used with continuous and categorical ancillary data. We demonstrated the use of the CART classi- fication at three increasingly detailed classification levels for a portion of the Greater Yellowstone Ecosystem. Overall accuracies ranged from 96 percent at level 1 , to 79 percent at level 2, and 65 percent at level 3.
Introduction
Ancillary data, either in addition to or derived from remotely sensed data, has the potential for increasing classification accuracy. Incorporation of ancillary data into classification techniques, however, has been problematic. We developed a straightforward approach for creating a rule-based classifica- tion without expert knowledge by applying a commonly avail- able statistical technique, classification and regression tree (CART) analysis, to multiple spectral and ancillary data layers.
Classiflcation and Regression Tree Analysis-Background CART is an increasingly popular form of statistical analysis available through widely used statistical packages, such as S-Plus (Venables and Ripley, 1997; Mathsoft, 1998; Lawrence and Ripple, 2000). CART operates by recursively splitting the data until ending points, or terminal nodes, are achieved using preset criteria. CART therefore begins by analyzing all explana- tory variables and determining which binary division of a sin- gle explanatory variable best reduces deviance in the response variable (Breiman et al., 1984;Efron and Tibshirani, 1991;Ven- ables and Ripley, 1997). In the case of image classification, explanatory variables consist of spectral and ancillary data, whether continuous or categorical, and the response variable is the land-coverlland-use class list. For each portion of the data resulting from this first split, the process is repeated, continuing until homogeneous termi- nal nodes are reached in a hierarchical tree. In the S-Plus imple- mentation of CART, terminal nodes are defined when either the total number of observations at the node is less than ten or the
R.L. Lawrence is with the Mountain Research Center, Depart- ment of Land Resources and Environmental Sciences, P.O. Box 173490, Montana State University, Bozeman, MT 59717- 3490 (rickl8montana.edu). A. Wright is with the Center for the Environment, Cornell University, Ithaca, NY 14853 (awp98cornell.edu).
deviance at the node is less than 1 percent of the total deviance for the entire tree (Venablesand Ripley, 1997). CART usually will over-fit the model, creating a tree that explains substantially all of the deviance in the original data, but in a manner that is specific to the particular data used to fit the tree. It is necessary, therefore, to prune the tree back to a level where the tree can reasonably be expected to be robust. A common method used for pruning, and a method implemented in S-Plus, involves cross validation (Venables and Ripley, 1997).In this method, the original data are randomly divided into ten equal sets. Trees are generated for nine of the data sets and validated against the tenth, with the minimum average deviance indicating the best size tree. The analyst might select a smaller tree if the cross-validation method indicates that, although additional deviance can be reduced, the amount of reduction does not justify an overly complex tree. The result of the CART analysis is a dichotomous decision or classification tree. Each path through the tree, defined by a series of dichotomous splits, specifies the conditions that lead to a most probable class. The tree, therefore, might be viewed as a series of rules that can be used for unknown observations to predict likely class membership. When used with remotely sensed and ancillary data, this naturally extends to a rule-based classification scheme.
Ancillary Data Incorporation In Classification-Background Traditional methods of land-uselland-cover classification using satellite imagery have relied solely on the spectral infor- mation present in the images. With purely spectral approaches, the spectral and spatial resolutions of the imagery are the pri- mary determinants of the level of classification detail that can be achieved. For example, given the spectral and spatial reso- lution of Landsat Thematic Mapper (TM) imagery, such images have generally been considered adequate for mapping uSGS level I1 (Jensen and Cowen, 1999). By using ancillary data in addition to spectral responses, however, it might be possible to achieve either greater classification detail or greater classifica- tion accuracy for a given combination of spectral and spatial resolutions. Classification techniques using ancillary data in addition to spectral data have demonstrated that, in many cases, the proper addition of ancillary data to spectral data can lead to greater class distinctions (e.g., Strahler et al., 1978;Hutchen- son, 1982; Trotter, 1991; Jensen, 1996). Ancillary data generally is derived from GIS layers, such as digital elevation models, but might also include information derived from the imagery, such as texture information or multi-date composites. Initially,
Photogrammetric Engineering & Remote Sensing Vol. 67, No. 10, October 2001, pp. 1137-1142. 0099-lllZ/01/6710-1137$3.00/ O 2001 American Society for Photogrammetry and Remote Sensing
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methods incorporating ancillary data included pre-classifica- tion stratification, logical channel addition, and post-classifi- cation sorting (Jensen, 1996) and have met with considerable success. Each of these approaches builds on conventional supervised or unsupervised classification methods. Using ancillary data for pre-classification stratification or post-classification sorting does not incorporate additional data into the actual classification algorithm, but might increase accuracy by segregating otherwise confused classes using such information as elevation or landscape position (Vogelmann et al., 1998;Ricchetti, 2000). While these methods have been suc- cessful in increasing classification accuracies, failure to incor- porate ancillary data into the classification algorithm might fail to fully exploit the range of information available. When ancillary data have been incorporated into traditional classifi- cation algorithms as logical channels (combining the ancillary data as an additional data layer with the spectral bands), the full range of information available in the ancillary data was
used (e.g., Strahler et al., 1978;Elumnoh and Shrestha, 2000;
Ricchetti, 2000). With logical channel addition, ancillarv data are given equal weight tisingle spectral bands unless weights are assigned in a maximum-likelihood classifier. This im~licit weightLg of ancillary data might not be appropriate or Lpti- mal, but proper weighting is usually unknown or must be sought out by trial and error. In addition, logical channel addi- tion is not appropriate for categorical, as opposed to continu- ous, ancillary data. More recently, ancillary data have been incorporated into modern classification methods such as expert systems (Goodenough et al., 1987)and neural networks (Bruzzone et al., 1997;Skidmore et al., 1997).These approaches incorporate the ancillary data directly into the classification algorithms and are usually not dependent on a priori weights. Attempts to de- velop expert systems, however, are often hampered by the lack of requisite expert knowledge or difficulties in developing rules from such knowledge (Kontoes et al., 1993; Huang and Jensen, 1997).For example, it might be known that certain tree species only exist above certain elevations, but spectral distinc- tions among tree species within an image generally are not known prior to the analysis. Neural network approaches are still largely in the developmental stage, are not easily imple- mented (Bruzzone et al., 1997),and have had unpredictable results (Skidmore et al., 1997). Machine-learning approaches have been used to establish rule-based classification systems where expert knowledge was inadequate (Huang and Jensen, 1997).These methods use train- ing data and machine-learning algorithms to develop a series of rules to define each class. Although machine-learning approaches overcome many of the limitations of other approaches to incorporating ancillary data, they have required sophisticated programming skills and have not been readily available to the wider remote sensing community. Our approach using CART has similarities to machine learning approaches, but the tools we used are readily available and eas- ily implemented with commercially available software.
Study Area
The study area consisted of the northwest portion of the Greater Yellowstone Ecosystem (GYE). Covering approximately 20,
km2, the portion of the GYE included in this study spans two TM
scenes, path 39, rows 28 and 29, and includes parts of Idaho, Montana, and Wyoming in the Rocky Mountain physiographic province. Most of the private land within the study area is found in broad valleys drained by active rivers (including the Gallatin, Madison, and Jefferson)and is surrounded by pub- licly owned, forested mountain ranges. The southeastern part of the study area contains the western-most boundary of Yel- lowstone National Park and the town of West Yellowstone, Montana. Remnants of the 1988 Yellowstone fires and large-
scale clearcut logging are dominant disturbances in the south- east. The northern and western portions of the study area lie mainly within the Gallatin and Targhee National Forests and include the Gallatin Valley and the town of Bozeman, Mon- tana, which is the largest urban center in the GYE. Vegetation in the study area consists of mixed species conifer forests, gener- ally above 2000 m, intermixed with natural shrublands and grasslands. Less than 2 percent of the study area consists of exposed rock outcrops above treeline. At lower elevations, a mix of sagebrush, grasslands, and agricultural lands dominates the landscape. Hardwoods are mixed throughout the land- scape, generally in linear patches following rivers (cotton- wood and willow) and at the lower interfaces of forest and grassland (aspen). Water was excluded £rom the study area by thresholding TM band 5, and the limited areas of urban develop- ment were delineated by manual digitizing.
Two pairs of TM scenes were acquired for the study area from 28 June and 15 August 1994. These dates were chosen to encom- pass the growing season in the region and were the most cloud- free scenes available. The scenes were georeferenced, and paired scenes for each date were mosaicked. Radiometric cor- rection between scenes was performed through dark-body sub- traction to minimize artificial brightness and haze (Chavez, 1998). In addition to using TM bands 1-7 from each date, we performed a Tasseled Cap transformation (Crist and Cicone, 1984)for each date and used the first three components from the transformation (brightness, greenness, and wetness) for the analysis. Finally, for each of the three Tasseled Cap bands, we computed difference images between the two dates. In addition to the data from the TM scenes, we used a 30-m USGS digital elevation model (DEM)to extract elevation, slope, and aspect for the study area. A cosine transformation was applied to the aspect layer to provide a continuous variable measuring angle from due north (Beers et al., 1966),and the results were rescaled from 0 to 2000. Reference data were collected through aerial photo inter- pretation using either 1:15,840-or 1:24,000-scalephotos from the 1990s, as available. Within the study area, seven transects were located covering the known range of cover types (from U.S. Forest Service stand maps) and elevation (from the DEM). For each cover type, 30 to 100 sample sites were collected using a stratified random sampling design, with stratification by elevation, aspect, and cover type. A total of 500 reference sites were interpreted using this method and were evenly divided into training and accuracy assessment (verification) sites. An additional 129 training sites were interpreted to increase the sample sizes for underrepresented classes, result- ing in 379 sites for classification training. In order to positively locate and interpret sample sites on the aerial photos, sample sites were designated as 2.25-ha areas, which was the smallest mapping unit practically sampled on the photos. Reference data were recorded at three levels of classification (Table 1). Spectral and topographic data were extracted for each ref- erence site. The ERDAS Imagine "Convert pixels to ASCII" utility was used to extract the data for each reference site from each data layer to a text file. Data extracted for each reference site were the mean value for a 5- by 5-pixel area to correspond to the size of the reference sites. The ASCII text file, which included three levels of land- coverlland-use classification and 26 possible explanatory vari- ables for each training site, was imported as an S-Plus data frame. CART analysis was performed to develop classification rules for the level 1 classification. Data classified as natural veg- etation was subset and CART analysis was performed on this subset to develop classification rules for the level 2 classifica- tion. For the level 3 classification, four CART analyses were con- ducted, with the hardwood, herbaceous, agriculture, and
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TABLE4. (^) DICHOTOMOUSCLASS~FICAT~ONTREEFOR LML 2 CLASSIFICAT~ON BASEDON CART ANALYSIS
TAELE 6. DICHOTOMOUSCLASSIFICATIONTREES FOR LEVEL 3 CLASSIFICATIONS
BASEDON CART ANALYSES
1. August Tasseled Cap wetness < -17. 1.1. June Tasseled Cap greenness < -4. 1. 1. 1. June TM band 4 < 53.5, THEN Burned 1.1.2. June TM band 4 > 53. 1.1.2.1. June Tasseled Cap brightness < 133.24, THEN Herbaceous 1.1.2.2. June Tasseled Cap brightness > 133.24, THEN Burned 1.2. June Tasseled Cap greenness > -4. 1.2.1. Tasseled Cap greenness difference < -13. 1.2.1.1. June TM band 3 < 28.5, THEN Herbaceous 1.2.1.2. June TM band 3 > 28.5,THEN Herbaceous 1.2.2. Tasseled Cap greenness difference > -13.5, THEN Coniferl herbaceous mix 2. August Tasseled Cap wetness > -17. 2.1. June Tasseled Cap brightness < 122. 2.1.1. Tasseled Cap brightness difference < -2. 2.1.1.1. Tasseled Cap wetness difference < 8.54, THEN Conifer 2.1.1.2. Tasseled Cap wetness difference > 8.54, THEN Conifer 2.1.2. Tasseled Cap brightness difference > 122.5, THEN Coniferl herbaceous mix 2.2. June Tasseled Cap brightness > 122. 2.2.1. August TM band 6 < 140. 2.2.1.1. Tasseled Cap wetness difference < -3. 2.2.1.1.1. June TM band 2 < 26.5, THEN Hardwood 2.2.1.1.2. June TM band 2 > 26.5, THEN Hardwoodlherba- ceous mix 2.2.1.2. Tasseled Cap wetness difference > -3.5, THEN Hardwood 2.2.2. August TM band 6 > 140.5, THEN Conifer
occurred with (1)conifer/herbaceous mix (defined as a mix of conifer and herbaceous with less than 70 percent conifer), which was primarily confused with the related classes of coni- fer and herbaceous, and (2) hardwood/herbaceous mix (defined as a mix of hardwood and herbaceous with less than 70 percent hardwood), which was primarily confused with the related class hardwood, as well as with agriculture. When coniferlher- baceous mix was combined with conifer, and hardwoodlherba- ceous mix was combined with hardwood, overall accuracy increased to 85 percent (Kappa statistic was 0.81) and individ- ual class accuracies ranged from 62 percent to 100 percent. The level 3 CART classification created four rules to subdi- vide hardwood classes into aspen, willow, and cottonwood; three rules to subdivide herbaceous classes in to sage-grassland and grassland; six rules to subdivide agriculture classes into perennial and annual agriculture; and four rules to subdivide conifer classes into mixed conifer species and Douglas-fir (Table 6). For hardwood classes, slope and band 1 (blue) from each of the June and August TM images were used to make class distinctions. Amen was distinguished from other hardwood classes by occu&ing on steepe~slopes,which was explained by the other hardwood classes-willow and cottonwood-
1. Hardwood Classifications
1.1. Slope gradient < 5"
1.1.1. August TM band 1 < 59.66, THEN Willow 1.1.2. August TM band 1 > 59.
1.1.2.1. June TM band 1 < 62.5, THEN Cottonwood
1.1.2.2. June TM band 1 > 62.5, THEN Cottonwood
1. 2. Slope gradient > 5", THEN Aspen
2. Herbaceous Classifications 2.1. June Tasseled Cap brightness < 156. 2.1.1. Tasseled Cap wetness difference < -3.58, THEN Sage- grassland 2.1.2. Tasseled Cap wetness difference > -3.58, THEN Grassland 2.2. June Tasseled Cap brightness 3 156.34, THEN Grassland 3. Agriculture Classifications 3.1. Tasseled Cap brightness difference < 40. 3.1.1. Tasseled Cap greenness difference < -13. 3.1.1.1. Aspect < 1878.5, THEN Perennial agriculture 3.1.1.2. Aspect > 1878.5, THEN Perennial agriculture 3.1.2. Tasseled Cap greenness difference > -13.9, THEN Annual agriculture 3.2. Tasseled Cap brightness difference > 40. 3.2.1. June Tasseled Cap wetness < -28. 3.2.1.1. June Tasseled Cap greenness < 6.22, THEN Annual agriculture 3.2.1.2. June Tasseled Cap greenness > 6.22, THEN Perennial agriculture 3. 2. 2. June Tasseled Cap wetness > -28.38, THEN Annual agriculture 4. Conifer Classifications 4.1. June Tasseled Cap greenness < 8.06, THEN Mixed conifer 4.2. June Tasseled Cap greenness > 8. 4.2.1. August TM band 6 < 133.34, THEN Douglas-fir
4.2.2. August TM band 6 > 133.
4. 2. 2. 1. Elevation < 1823.5 m, THEN Mixed conifer 4.2.2.2. Elevation > 1823 m, THEN Mixed conifer
occurring within stream bottoms. Willow was distinguished from cottonwood by lower reflectance in blue in the August TM image. Within the herbaceous classes, sage-grassland was dis- tinguished from grassland by lower values in the Tasseled Cap wetness difference image, which resulted from August senes- cence of the grasses. Tasseled Cap brightness and wetness dif- ference images, Tasseled Cap greenness and wetness from the June TM image, and aspect were used to distinguish annual from perennial agriculture. At lower values of brightness dif- ference, annual agriculture had higher greenness difference values than did perennial agriculture. At higher values of brightness difference, perennial agriculture was distinguished by having higher greenness values in the June image. Finally, between conifer classes, Douglas-fir was distinguished from mixed conifer by having lower values in band 6 (thermal) of the August TEA image, probably as a result of denser canopies in the Douglas-fir forests.
TABLE5. ACCURACYASSESSMENT FOR LEVEL 2 CLASSIFICATION.COLUMNSREPRESENT REFERENCEDATAAND ROWS REPRESENT CLASSI!=ICATIONDATA Conifer1 Hardwood Urban Burned Agriculture Conifer Hardwood Herbaceous herbaceous mix herbaceous mix
Urban (^19 0 0 0 0 0 0 ) Burned (^0 31 0 0 0 0 0 ) Agriculture (^0 0 51 0 1 2 0 ) Conifer (^1 2 1 63 9 2 4 ) Hardwood (^0 0 0 0 17 0 2 ) Herbaceous (^0 4 0 0 3 18 4 ) Coniferlherbaceous mix (^0 0 0 5 1 2 6 ) Hardwoodlherbaceous mix (^0 0 0 0 3 0 0 ) Producer's accuracy 79% 84% 98% 93% (^) 50% 75% 38% 25% User's accuracy 100% 100% 85% 76% 77% (^) 62% 43% 40%
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TABLE7. ACCURACYASSESSMENTFOR^ LEVEL^3 CLASSIFICATION.COLUMNSREPRESENT^ REFERENCEDATAA N 0^ ROWS REPRESENT^ CLASS~FICAT~ONDATA Annual Perennial Mixed Urban Burned agriculture agriculture conifer Douglas-fir Aspen Cottonwood Willow Sage-grassland Grass
Urban 19 0 0 0 0 0 0 0 0 0 0 Burned 0 31 0 0 0 0 0 0 0 0 0 Annual agriculture 0 0 3 6 0 0 0 0 0 0 0 Perennial agriculture 4 0 33 9 0 0 0 0 1 1 1 Mixed conifer 1 2 0 1 57 6 5 1 1 1 2 Douglas-fir 0 0 0 0 3 2 3 0 0 0 1 Aspen 0 0 0 0 0 0 15 0 0 0 0 Cottonwood 0 0 0 0 0 0 0 8 1 0 0 Willow 0 0 0 0 0 0 0 0 7 0 0 Sage-grassland 0 0 0 0 0 0 3 0 0 5 7 Grass 0 4 0 0 0 0 0 0 0 0 7 Producer's accuracy 79% 84% 8% 56% 95% 25%^ 58% 89% 70% 71% 41% User's accuracy 100% 100% 33% (^) 18% 74% 22% 100% 89% 100% 36% (^) 64%
Overall accuracy of the level 3 classification was 65 per- cent and the Kappa statistic was 0.58. Individual class accura- cies were highly variable, ranging from 8 percent to 100 percent (Table 7 ). Particular problems were encountered with distin- guishing (1)annual from perennial agriculture, (2) Douglas-fir from other conifer forests, (3) aspen from conifer classes, and (4) sage-grassland from other grasslands without sage.
Discussion A wide variety of classification options are available for image processing, and no single classification solution will always perform best. Incorporating ancillary data into rule-based clas- sifications, however, has been shown to be an effective approach in certain circumstances. We developed and demon- strated a method for creating and executing such a classifica- tion system without extensive a priori expert knowledge. This method, based on CART analysis, was easily implemented using commonly available image processing and statistical software. Overall and individual class accuracies at level 1 were excellent. While many classes were well classified at levels 2 and 3, certain class accuracies were clearly unacceptable. Pri- mary reasons for unacceptable results might have included (1) inadequate spatial resolution for the desired level of classifica- tion, especially with respect to level 3 (Jensen and Cowen, 1999), and (2) irresolvable class overlap with the spectral and GIS layers available. Attempts to distinguish problem classes with other classification algorithms were not successful. One of the strongest advantages of using CART to create classification rules was that a large array of potentially useful data could be entered into the analysis and CART automatically selected which layers were useful and which were not. This selection process distinguished CART from logical channel addition, expert systems, and neural networks. With logical channel addition, additional data must be selected before clas-
sification. With expert systems, a priori knowledge is neces-
sary to select ancillary data. With neural networks, only useful layers will be used, but the selection might be hidden from the analyst, hindering interpretation of the results and application to other classification problems. The automatic selection of useful data by CART should not be interpreted as a license to add layers to the analysis indis-
criminately. As with any statistical analysis, the uncritical
addition of potential explanatory variables increases the possi- bility of chance agreement between some explanatory variables and the response. Thus, an analyst should only include those data layers that are reasonably believed to have the potential to distinguish classes. CART is sensitive to large discrepancies in the size (number of observations) of training samples among individual classes.
PHOTOGRAMMETRIC ENGINEERING 81 REMOTE SENSING
Distinctions within the CART analysis are made based on min- imizing total misclassifications for the entire training set. Thus, a class with a larger number of training pixels might have greater weight in the analysis because it potentially contri- butes a larger number of misclassified pixels. Reasonable efforts, therefore, should be taken to keep the number of train- ing pixels per class roughly equivalent so that within class vari- ations do not overwhelm the among class distinctions that are the primary interest of classification. Furthermore, in selecting training sites, the caveats that apply to all supervised classifi- cation methods apply to CART as well. For example, training sites should be taken from relatively homogeneous locations, include all class types known to be present within the area to be classified, and cover the range of conditions present for each class Uensen, 1996). In addition to providing predicted classes at terminal nodes, CART analysis reports for each terminal node the proba- bility of misclassification and the probability of membership for each other class. This information can be used to assess the quality of the classification, assign fuzzy class memberships, or conduct Bayesian probability analysis. Supervised classification with CART analysis is an effective and easily implemented means for creating a ruled-based clas- sification when expert knowledge is insufficient. Applied in appropriate circumstances, it provides an alternative tool for the image analyst wishing to take advantage of ancillary data for classification.
Acknowledgments
The authors wish to thank Dr. Andrew Hansen, Ecology Depart- ment, Montana State University, for his advice and support throughout this research. This research was supported by NASA Land Cover Land Use Change Program.
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