Decision tree classification of land cover from remotely sensed data

Decision tree classification algorithms have significant potential for land cover mapping problems and have not been tested in detail by the remote sensing community relative to more conventional pattern recognition techniques such as maximum likelihood classification. In this paper, we present several types of decision tree classification algorithms arid evaluate them on three different remote sensing data sets. The decision tree classification algorithms tested include an univariate decision tree, a multivariate decision tree, and a hybrid decision tree capable of including several different types of classification algorithms within a single decision tree structure. Classification accuracies produced by each of these decision tree algorithms are compared with both maximum likelihood and linear discriminant function classifiers. Results from this analysis show that the decision tree algorithms consistently outperform the maximum likelihood and linear discriminant function classifiers in regard to classf — cation accuracy. In particular, the hybrid tree consistently produced the highest classification accuracies for the data sets tested. More generally, the results from this work show that decision trees have several advantages for remote sensing applications by virtue of their relatively simple, explicit, and intuitive classification structure. Further, decision tree algorithms are strictly nonparametric and, therefore, make no assumptions regarding the distribution of input data, and are flexible and robust with respect to nonlinear and noisy relations among input features and class labels.

An Accelerated Chow and Liu Algorithm: Fitting Tree Distributions to High Dimensional Sparse Data

Chow and Liu introduced an algorithm for fitting a multivariate distribution with a tree (i.e. a density model that assumes that there are only pairwise dependencies between variables) and that the graph of these dependencies is a spanning tree. The original algorithm is quadratic in the dimesion of the domain, and linear in the number of data points that define the target distribution $P$. This paper shows that for sparse, discrete data, fitting a tree distribution can be done in time and memory that is jointly subquadratic in the number of variables and the size of the data set. The new algorithm, called the acCL algorithm, takes advantage of the sparsity of the data to accelerate the computation of pairwise marginals and the sorting of the resulting mutual informations, achieving speed ups of up to 2-3 orders of magnitude in the experiments.