The classification of large dimensional data sets arising from the merging of remote sensing data with more traditional forms of ancillary data causes a significant computational problem. Decision tree classification is a popular approach to the problem. This type of classifier is characterized by the property that samples are subjected to a sequence of decision rules before they are assigned to a unique class. If a decision tree classifier is well designed, the result in many cases is a classification scheme which is accurate, flexible, and computationally efficient. This correspondence provides an automated technique for effective decision tree design which relies only on a priori statistics. This procedure utilizes canonical transforms and Bayes table look-up decision rules. An optimal design at each node is derived based on the associated decision table. A procedure for computing the global probability of correct classification is also provided. An example is given in which class statistics obtained from an actual Landsat scene are used as input to the program. The resulting decision tree design has an associated probability of correct classification of 0.75 compared to the theoretically optimum 0.79 probability of correct classification associated with a full dimensional Bayes classifier. Recommendations for future research are included.

An Automated Approach to the Design of Decision Tree Classifiers

Morphological image analysis applied to crop field mapping

In this research, feature extraction and classification algorithms for high dimensional data are investigated. Developments with regard to sensors for Earth observation are moving in the direction of providing much higher dimensional multispectral imagery than is now possible.
In analyzing such high dimensional data, processing time becomes an important factor. With large increases in dimensionality and the number of classes, processing time will increase significantly. To address this problem, a multistage classification scheme is proposed which reduces the processing time substantially by eliminating unlikely classes from further consideration at each stage. Several truncation criteria are developed and the relationship between thresholds and the error caused by the truncation is investigated.
Next a novel approach to feature extraction for classification is proposed based directly on the decision boundaries. It is shown that all the features needed for classification can be extracted from decision boundaries. A novel characteristic of the proposed method arises by noting that only a portion of the decision boundary is effective in discriminating between classes, and the concept of the effective decision boundary is introduced. The proposed feature extraction algorithm has several desirable properties: (1) it predicts the minimum number of features necessary to achieve the same classification accuracy as in the original space for a given pattern recognition problem; (2) it finds the necessary feature vectors. The proposed algorithm does not deteriorate under the circumstances of equal means or equal covariances as some previous algorithms do. In addition, the decision boundary feature extraction algorithm can be used both for parametric and non-parametric classifiers.
Finally, we study some problems encountered in analyzing high dimensional data and propose possible solutions. We first recognize the increased importance of the second order statistics in analyzing high dimensional data. By investigating the characteristics of high dimensional data, we suggest the reason why the second order statistics must be taken into account in high dimensional data. Recognizing the importance of the second order statistics, there is a need to represent the second order statistics. We propose a method to visualize statistics using a color code. By representing statistics using color coding, one can easily extract and compare the first and the second statistics.

/pdf/feature-extraction-and-classification-algorithms-for-high-35eoz5denz.pdf

Feature extraction and classification algorithms for high-dimensional data

/pdf/an-automated-approach-to-the-design-of-decision-tree-52imn6efuf.pdf

The potential for using data collected in the first four bands of the proposed thematic mapper for monitoring intertidal salt marsh vegetation is assessed, using ground spectral data collected with a portable multiband radiometer. Results from a field study in Chichester Harbour, Southern England, show that certain species can be separated using transformations of these data. The estimation of above ground biomass from ground spectral data was not possible for Spartina × townsendii agg., due to the combined effects of mixtures of different substrate types and mixtures of live and dead vegetation within the field of view of the radiometer. However, biomass estimation was possible for both Zostera marina L. and Fucus vesiculosus L. The relationships between biomass and bidirectional reflectance for these species followed a similar pattern, despite Fucus vesiculosus having carotenoids rather than chlorophylls as the dominant leaf pigments.

Remote sensing of salt marsh vegetation in the first four proposed Thematic Mapper bands

Directed canonical analysis is presented as an extension of the general form of canonical analysis, which is a method for reducing the dimensionality of multivariate data sets with minimum loss of discriminatory variance. The reduction takes the form of a linear transformation, y = Cx, that condenses the discriminatory variance onto a relatively few, high-variance orthogonal discriminant axes. Canonical analysis is developed as an analog to the one-way MANOVA. The directed extension allows user-specified contrasts to define linear relationships that are known or suspected to exist within the data. The linear transformation C is defined by means of the symmetric canonical form of the matrix eigenproblem. Canonical and principal components transformations and various distance classifiers were applied to 3 representative remotely sensed MSS data sets. Results indicate that use of a piecewise maximum likelihood classifier with the directed canonical discriminant axes will give the best overall combination of classification accuracy and computational efficiency if adequate sample sizes are available to estimate category statistics. For small sample sizes, piecewise Euclidean distance with the general canonical axes is recommended. In canonically transformed space, Euclidean distance is equivalent to the Mahalanobis classifier.

/pdf/directed-canonical-analysis-and-the-performance-of-iu3pfb5jfd.pdf

Directed Canonical Analysis And the Performance of Classifiers under Its Associated Linear Transformation

https://ntrs.nasa.gov/api/citations/19810011965/downloads/19810011965.pdf

ICAP: An Interactive Cluster Analysis Procedure for analyzing remotely sensed data

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Directed Canonical Analysis And the Performance of Classifiers under Its Associated Linear Transformation

ICAP: An Interactive Cluster Analysis Procedure for analyzing remotely sensed data