Luis O. Jimenez

Supervised classification in high-dimensional space: geometrical, statistical, and asymptotical properties of multivariate data

The recent development of more sophisticated remote-sensing systems enables the measurement of radiation in many more spectral intervals than was previously possible. An example of this technology is the AVIRIS system, which collects image data in 220 bands. The increased dimensionality of such hyperspectral data greatly enhances the datas information content, but provides a challenge to the current techniques for analyzing such data. Human experience in 3D space tends to mislead our intuition of geometrical and statistical properties in high-dimensional space, properties which must guide our choices in the data analysis process. Using Euclidean and Cartesian geometry, high-dimensional space properties are investigated in this paper, and their implication for high-dimensional data and its analysis is studied in order to illuminate the differences between conventional spaces and hyperdimensional space.

Hyperspectral data analysis and supervised feature reduction via projection pursuit

As the number of spectral bands of high-spectral resolution data increases, the ability to detect more detailed classes should also increase, and the classification accuracy should increase as well. Often the number of labelled samples used for supervised classification techniques is limited, thus limiting the precision with which class characteristics can be estimated. As the number of spectral bands becomes large, the limitation on performance imposed by the limited number of training samples can become severe. A number of techniques for case-specific feature extraction have been developed to reduce dimensionality without loss of class separability. Most of these techniques require the estimation of statistics at full dimensionality in order to extract relevant features for classification. If the number of training samples is not adequately large, the estimation of parameters in high-dimensional data will not be accurate enough. As a result, the estimated features may not be as effective as they could be. This suggests the need for reducing the dimensionality via a preprocessing method that takes into consideration high-dimensional feature-space properties. Such reduction should enable the estimation of feature-extraction parameters to be more accurate. Using a technique referred to as projection pursuit (PP), such an algorithm has been developed. This technique is able to bypass many of the problems of the limitation of small numbers of training samples by making the computations in a lower-dimensional space, and optimizing a function called the projection index. A current limitation of this method is that, as the number of dimensions increases, it is likely that a local maximum of the projection index will be found that does not enable one to fully exploit hyperspectral-data capabilities.

Classification of hyperdimensional data based on feature and decision fusion approaches using projection pursuit, majority voting, and neural networks

Hyperspectral sensors provide a large amount of data. The inherent characteristics of hyperspectral feature space still require the development of information extraction algorithms with a high degree of accuracy. Data fusion techniques can enable one to analyze high-dimensional data that is provided by hyperspectral sensors. There are two levels of fusion that will be discussed in the present paper: feature fusion and decision fusion. Feature fusion is a projection from one feature vector space (spectral bands) to another. An example of this is multispectral data feature extraction. In decision fusion, a local discrimination is performed at each sensor. Then the set of decisions is combined in a decision fusion center. This center has a set of algorithms to integrate the individual and local decisions of each sensor. The algorithms are based on different techniques such as majority voting, max rule, min rule, average rule and neural network. Experiments show that feature and decision fusion schemes enhance the classification accuracy of hyperspectral data.

Integration of spatial and spectral information by means of unsupervised extraction and classification for homogenous objects applied to multispectral and hyperspectral data

This paper presents a method of unsupervised enhancement of pixels homogeneity in a local neighborhood. This mechanism will enable an unsupervised contextual classification of multispectral data that integrates the spectral and spatial information producing results that are more meaningful to the human analyst. This unsupervised classifier is an unsupervised development of the well-known supervised extraction and classification for homogenous objects (ECHO) classifier. One of its main characteristics is that it simplifies the retrieval process of spatial structures. This development is specially relevant for the new generation of airborne and spaceborne sensors with high spatial resolution.

High dimensional feature reduction via projection pursuit

The recent development of more sophisticated remote sensing systems enables the measurement of radiation in many more spectral intervals than previously possible. An example of that technology is the AVIRIS system, which collects image data in 220 bands. As a result of this, new algorithms must be developed in order to analyze the more complex data effectively. Data in a high dimensional space presents a substantial challenge, since intuitive concepts valid in a 2-3 dimensional space do not necessarily apply in higher dimensional spaces. For example, high dimensional space is mostly empty. This results from the concentration of data in the corners of hypercubes. Other examples may be cited. Such observations suggest the need to project data to a subspace of a much lower dimension on a problem specific basis in such a manner that information is not lost. Projection pursuit is a technique that will accomplish such a goal. Since it processes data in lower dimensions, it should avoid many of the difficulties of high dimensional spaces. The authors investigate some of the properties of projection pursuit.<<ETX>>

Subset selection analysis for the reduction of hyperspectral imagery

Presents the formulation of the dimension reduction problem using subset selection as a matrix approximation problem. A heuristic algorithm to solve this problem is presented. Numerical results using LANDSAT and AVIRIS images show that the selected bands are contained in a space that is almost aligned with the first few principal components.

Projection pursuit in high dimensional data reduction: initial conditions, feature selection and the assumption of normality

Supervised classification techniques use labeled samples to train the classifier. Often the number of such samples is limited, thus limiting the precision with which class characteristics can be estimated. As the number of spectral bands becomes large, the limitation on performance imposed by the limited number of training samples can become severe. Such consequences suggest the value of reducing the dimensionality by a pre-processing method that takes advantage of the asymptotic normality of projected data. Using a technique called projection pursuit, a pre-processing dimensional reduction method has been developed based on the optimization of a projection index. A method to estimate an initial value that can more quickly lead to the global maximum is presented for projection pursuit using the Bhattacharyya distance as the projection index.

Social, Ethical and Global Issues in Engineering

The College of Engineering of the University of Puerto Rico-Mayaguez (UPRM) adopted an ethics across the curriculum (EAC) strategy in 2005. EAC is based on the combination of faculty development workshops, a stand-alone course in ethics, and ethics learning modules integrated at various levels of the engineering curriculum. In 2006 the EAC strategy was expanded to include social and global issues in engineering. A Coordinator for Social, Ethical and Global Issues (SEGI) in Engineering was appointed in the College of Engineering to coordinate and support activities related to these areas at all engineering departments. Such a position is valuable in demonstrating the commitment to educating integral engineers that are both technically capable and socially responsible. This SEGI work presents a more integrated curriculum to students through activities that link liberal arts courses and topics to engineering. The position also serves as a liaison with other Colleges in these matters, and supports the achievement of eight of the learning outcomes from ABETpsilas criterion 3. This paper describes the various activities of the coordination of the SEGI work, and its relationship to the general education component of engineering curricula.

Projection pursuit for high dimensional feature reduction: parallel and sequential approaches

Supervised classification techniques use labeled samples in order to train the classifier. Usually the number of such samples is limited, and as the number of bands available increases, this limitation becomes more severe, and can become dominate over the projected added value of having the additional bands available. This suggests the need for reducing the dimensionality via a preprocessing method. Such reduction should enable the estimation of feature extraction parameters to be more accurate. Using a technique referred to as projection pursuit, two parametric projection pursuit algorithms have been developed: parallel parametric projection pursuit and sequential parametric projection pursuit. In the present paper both methods are presented, and an iterative procedure of the sequential approach that mitigates the computation time problem is shown.

Creating ethical awareness in electrical and computer engineering students: a learning module on ethics

The complex interaction between engineering, technology, social needs and values challenges engineering education programs to prepare new professionals to respond to real engineering problems with more than technical skills. The goal of the Electrical and Computer Engineering (ECE) Department at the University of Puerto Rico-Mayaguez is to develop a full-scale program of Ethics Across the Engineering Curriculum. As a first step we have developed an Ethics Module for ECE students. Ethics workshops were given to students of Pattern Recognition and Power Engineering. Instruments were developed to assess student learning and perception about the ethical and social implications in engineering. At the end of each workshop, participants completed the assessment instrument. The assessment instruments were used to evaluate the impact of the Ethics Module in two aspects: the learning process of the students and their perception, and the impact on their ethical conduct