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Linear and Order Statistics Combiners for Pattern Classification

Several researchers have experimentally shown that substantial improvements can be obtained in difficult pattern recognition problems by combining or integrating the outputs of multiple classifiers. This chapter provides an analytical framework to quantify the improvements in classification results due to combining. The results apply to both linear combiners and order statistics combiners. We first show that to a first order approximation, the error rate obtained over and above the Bayes error rate, is directly proportional to the variance of the actual decision boundaries around the Bayes optimum boundary. Combining classifiers in output space reduces this variance, and hence reduces the 'added' error. If N unbiased classifiers are combined by simple averaging. the added error rate can be reduced by a factor of N if the individual errors in approximating the decision boundaries are uncorrelated. Expressions are then derived for linear combiners which are biased or correlated, and the effect of output correlations on ensemble performance is quantified. For order statistics based non-linear combiners, we derive expressions that indicate how much the median, the maximum and in general the i-th order statistic can improve classifier performance. The analysis presented here facilitates the understanding of the relationships among error rates, classifier boundary distributions, and combining in output space. Experimental results on several public domain data sets are provided to illustrate the benefits of combining and to support the analytical results.

Tumer, Kagan↗

Water Across Synthetic Aperture Radar Data (WASARD): SAR Water Body Classification for the Open Data Cube

The detection of inland water bodies from Synthetic Aperture Radar (SAR) data provides a great advantage over water detection with optical data, since SAR imaging is not impeded by cloud cover. Traditional methods of detecting water from SAR data involves using thresholding methods that can be labor intensive and imprecise. This paper describes Water Across Synthetic Aperture Radar Data (WASARD): a method of water detection from SAR data which automates and simplifies the thresholding process using machine learning on training data created from Geoscience Australia’s WOFS algorithm. Of the machine learning models tested, the Linear Support Vector Machine was determined to be optimal, with the option of training using solely the VH polarization or a combination of the VH and VV polarizations. WASARD was able to identify water in the target area with a correlation of 97% with WOFS. Sentinel-1, Open Data Cube, Earth Observations, Machine Learning, Water Detection 1. INTRODUCTION Water classification is an important function of Earth imaging satellites, as accurate remote classification of land and water can assist in land use analysis, flood prediction, climate change research, as well as a variety of agricultural applications [2]. The ability to identify bodies of water remotely via satellite is immensely cheaper than contracting surveys of the areas in question, meaning that an application that can accurately use satellite data towards this function can make valuable information available to nations which would not be able to afford it otherwise. Highly reliable applications for the remote detection of water currently exist for use with optical satellite data such as that provided by LANDSAT. One such application, Geoscience Australia’s Water Observations from Space (WOFS) has already been ported for use with the Open Data Cube [6]. However, water detection using optical data from Landsat is constrained by its relatively long revisit cycle of 16 days [5], and water detection using any optical data is constrained in that it lacks the ability to make accurate classifications through cloud cover [2]. The alternative solution which solves these problems is water detection using SAR data, which images the Earth using cloud-penetrating microwaves. Because of its advantages over optical data, much research has been done into water detection using SAR data. Traditionally, this has been done using the thresholding method, which involves picking a polarization band and labeling all pixels for which this band’s value is below a certain threshold as containing water. The thresholding method works since water tends to return a much lower backscatter value to the satellite than land [1]. However, this method can be flawed since estimating the proper threshold is often imprecise, complicated, and labor intensive for the end user. Thresholding also tends to use data from only one SAR polarization, when a combination of polarizations can provide insight into whether water is present. [2] In order to alleviate these problems, this paper presents an application for the Open Data Cube to detect water from SAR data using support vector machine (SVM) classification. 2. PLATFORM WASARD is an application for the Open Data Cube, a mechanism which provides a simple yet efficient means of ingesting, storing, and retrieving remote sensing data. Data can be ingested and made analysis ready according to whatever specifications the researcher chooses, and easily resampled to artificially alter a scene’s resolution. Currently WASARD supports water detection on scenes from ESA’s Sentinel-1 and JAXA’s ALOS. When testing WASARD, Sentinel-1 was most commonly used due to its relatively high spatial resolution and its rapid 6 day revisit cycle [5]. With minor alterations to the application's code, however, it could support data from other satellites. 3. METHODOLOGY Using supervised classification, WASARD compares SAR data to a dataset pre-classified by WOFS in order to train an SVM classifier. This classifier is then used to detect water in other SAR scenes outside the training set. Accuracy was measured according to the following metrics:  Precision: a measure of what percentage of the points WASARD labels as water are truly water  Recall: a measure of what percentage of the total water cover WASARD was able to identify.  F1 Score: a harmonic average of the precision and recall scores Both precision and recall are calculated at the end of the training phase, when the trained classifier is compared to a testing dataset. Because the WOFS algorithm’s classifications are used as the truth values when training a WASARD classifier, when precision and recall are mentioned in this paper, they are always with respect to the values produced by WOFS on a similar scene of Landsat data, which themselves have a classification accuracy of 97% [6]. Visual representations of water identified by WASARD in this paper were produced using the function wasard_plot(), which is included in WASARD. 3.1 Algorithm Selection The machine learning model used by WASARD is the Linear Support Vector Machine (SVM). This model uses a supervised learning algorithm to develop a classifier, meaning it creates a vector which can be multiplied by the vector formed by the relevant data bands to determine whether a pixel in a SAR scene contains water. This classifier is trained by comparing data points from selected bands in a SAR scene to their respective labels, which in this case are “water” or “not water” as given by the WOFS algorithm. The SVM was selected over the Random Forest model, which outperformed the SVM in training speed, but had a greater classification time and lower accuracy, and the Multilayer Perceptron Artificial Neural Network, which had a slightly higher average accuracy than the SVM, but much greater training and classification times. Figure 1: Visual representation of the SVM Classifier. Each white point represents a pixel in a SAR scene. In Figure 1, the diagonal line separating pixels determined to be water from those determined not to be water represents the actual classification vector produced by the SVM. It is worth noting that once the model has been trained, classification of pixels is done in a similar manner as in the thresholding method. This is especially true if only one band was used to train the model. 3.1 Feature Selection Sentinel-1 collects data from two bands: the Vertical/Vertical polarization (VV) and the Vertical/Horizontal polarization (VH). When 100 SVM classifiers were created for each polarization individually, and for the combination of the two, the following results were achieved: Figure 2: Accuracy of classifiers trained using different polarization bands. Precision and Recall were measured with respect to the values produced by WOFS. Figure 2 demonstrates that using both the VV and VH bands trades slightly lower recall for significantly greater precision when compared with the VH band alone, and that using the VV band alone is inferior in both metrics. WASARD therefore defaults to using both the VV and VH bands, and includes the option to use solely the VH band. The VV polarization’s lower precision compared to the VH polarization is in contrast to results from previous research and may merit further analysis [4]. 3.2 Training a Classifier The steps in training a classifier with WASARD are 1. Selecting two scenes (one SAR, one optical) with the same spatial extents, and acquired close to each other in time, with a preference that the scenes are taken on the same day. 2. Using the WOFS algorithm to produce an array of the detected water in the scene of optical data, to be used as the labels during supervised learning 3. Data points from the selected bands from the SAR acquisition are bundled together into an array with the corresponding labels gathered from WOFS. A random sample with an equal number of points labeled “Water” and “Not Water” is selected to be partitioned into a training and a testing dataset 4. Using Scikit-Learn’s LinearSVC object, the training dataset is used to produce a classifier, which is then tested against the testing dataset to determine its precision and recall The result is a wasard_classifier object, which has the following attributes: 1. f1, recall, and precision: 3 metrics used to determine the classifier’s accuracy 2. Coefficient: Vector which the SVM uses to make its predictions. The classifier detects water when the dot product of the coefficient and the vector formed by the SAR bands is positive 3. Save(): allows a user to save a classifier to the disk in order to use it without retraining 4. wasard_classify(): Classifies an entire xarray of SAR data using the SVM classifier All of the above steps are performed automatically when the user creates a wasard_classifier object. 3.3 Classifying a Dataset Once the classifier has been created, it can be used to detect water in an xarray of SAR data using wasard_classify(). By taking the dot product of the classifier’s coefficients and the vector formed by the selected bands of SAR data, an array of predictions is constructed. A classifier can effectively be used on the same spatial extents as the ones where it was trained, or on any area with a similar landscape. While

Kreiser, Zachary↗

Directional-cosine and related pre-processing techniques - Possibilities and problems in earth-resources surveys

The possibilities of using various pre-processing techniques (directional-cosine, ratios and ratio/sum) have been investigated in relation to an urban land-use problem in Marion County, Indiana (USA) and for geologic applications in the San Juan Mountains of Colorado. For Marion County, it proved possible to classify directional-cosine data from September 1972 into different land uses by applying statistics developed with data from a May 1973 ERTS frame, thereby demonstrating the possibilities of using this type of data for signature-extension purposes. In the Silverton (Colorado) area pre-processed data proved superior to original data when extracting useful information in mountainous areas without corresponding ground observations. This approach allowed meaningful classification and interpretation of the data. The main problems encountered as a result of atmospheric effects, mixing of different surface materials, and the performance characteristics of ERTS are elucidated.

Quiel, F.↗

Active Learning with Irrelevant Examples

Active learning algorithms attempt to accelerate the learning process by requesting labels for the most informative items first. In real-world problems, however, there may exist unlabeled items that are irrelevant to the user's classification goals. Queries about these points slow down learning because they provide no information about the problem of interest. We have observed that when irrelevant items are present, active learning can perform worse than random selection, requiring more time (queries) to achieve the same level of accuracy. Therefore, we propose a novel approach, Relevance Bias, in which the active learner combines its default selection heuristic with the output of a simultaneously trained relevance classifier to favor items that are likely to be both informative and relevant. In our experiments on a real-world problem and two benchmark datasets, the Relevance Bias approach significantly improved the learning rate of three different active learning approaches.

machine learning↗

Enhancing and Archiving the APS Catalog of the POSS I

We have worked on two different projects: 1) Archiving the APS Catalog of the POSS I for distribution to NASA's NED at IPAC, SIMBAD in France, and individual astronomers and 2) The automated morphological classification of galaxies. We have completed archiving the Catalog into easily readable binary files. The database together with the software to read it has been distributed on DVD's to the national and international data centers and to individual astronomers. The archived Catalog contains more than 89 million objects in 632 fields in the first epoch Palomar Observatory Sky Survey. Additional image parameters not available in the original on-line version are also included in the archived version. The archived Catalog is also available and can be queried at the APS web site (URL: http://aps.umn.edu) which has been improved with a much faster and more efficient querying system. The Catalog can be downloaded as binary datafiles with the source code for reading it. It is also being integrated into the SkyQuery system which includes the Sloan Digital Sky Survey, 2MASS, and the FIRST radio sky survey. We experimented with different classification algorithms to automate the morphological classification of galaxies. This is an especially difficult problem because there are not only a large number of attributes or parameters and measurement uncertainties, but also the added complication of human disagreement about the adopted types. To solve this problem we used 837 galaxy images from nine POSS I fields at the North Galactic Pole classified by two independent astronomers for which they agree on the morphological types. The initial goal was to separate the galaxies into the three broad classes relevant to issues of large scale structure and galaxy formation and evolution: early (ellipticals and lenticulars), spirals, and late (irregulars) with an accuracy or success rate that rivals the best astronomer classifiers. We also needed to identify a set of parameters derived from the digitized images that separate the galaxies by type. The human eye can easily recognize complicated patterns in images such as spiral arms which can be spotty, blotchy affairs that are difficult for automated techniques. A galaxy image can potentially be described by hundreds of parameters, all of which may have some relation to the morphological type. In the set of initial experiments we used 624 such parameters, in two colors, blue and red. These parameters include the surface brightness and color measured at different radii, ratios of these parameters at different radii, concentration indices, Fourier transforms and wavelet decomposition coefficients. We experimented with three different classes of classification algorithms; decision trees, k-nearest neighbors, and support vector machines (SVM). A range of experiments were conducted and we eventually narrowed the parameters to 23 selected parameters. SVM consistently outperformed the other algorithms with both sets of features. By combining the results from the different algorithms in a weighted scheme we achieved an overall classification success of 86%.

Humphreys, Roberta M.↗

Maneuver Classification for Aircraft Fault Detection

Automated fault detection is an increasingly important problem in aircraft maintenance and operation. Standard methods of fault detection assume the availability of either data produced during all possible faulty operation modes or a clearly-defined means to determine whether the data provide a reasonable match to known examples of proper operation. In the domain of fault detection in aircraft, identifying all possible faulty and proper operating modes is clearly impossible. We envision a system for online fault detection in aircraft, one part of which is a classifier that predicts the maneuver being performed by the aircraft as a function of vibration data and other available data. To develop such a system, we use flight data collected under a controlled test environment, subject to many sources of variability. We explain where our classifier fits into the envisioned fault detection system as well as experiments showing the promise of this classification subsystem.

Oza, Nikunj C.↗

Application of LANDSAT data to monitor land reclamation progress in Belmont County, Ohio

Strip and contour mining techniques are reviewed as well as some studies conducted to determine the applicability of LANDSAT and associated digital image processing techniques to the surficial problems associated with mining operations. A nontraditional unsupervised classification approach to multispectral data is considered which renders increased classification separability in land cover analysis of surface mined areas. The approach also reduces the dimensionality of the data and requires only minimal analytical skills in digital data processing.

Bloemer, H. H. L.↗

Uncertainty methodology for in-flight thrust determination

A methodology is proposed for the evaluation of uncertainty in the in-flight determination of aircraft thrust, which provides error traceability to a national standards laboratory, and is independent of the procedure used to calculate or measure thrust in flight, thereby yielding a consistent means for the evaluation of measurement capabilities. Attention is given to the factors of measurement error, precision, bias, uncertainty, error estimation and classification, error propagation, ground testing, and the related problems of model bias error, model precision error, and the uncertainty limit.

Adams, G. R.↗

Information extraction and transmission techniques for spaceborne synthetic aperture radar images

Information extraction and transmission techniques for synthetic aperture radar (SAR) imagery were investigated. Four interrelated problems were addressed. An optimal tonal SAR image classification algorithm was developed and evaluated. A data compression technique was developed for SAR imagery which is simple and provides a 5:1 compression with acceptable image quality. An optimal textural edge detector was developed. Several SAR image enhancement algorithms have been proposed. The effectiveness of each algorithm was compared quantitatively.

Frost, V. S.↗

Uncertainty management by relaxation of conflicting constraints in production process scheduling

Mathematical-analytical methods as used in Operations Research approaches are often insufficient for scheduling problems. This is due to three reasons: the combinatorial complexity of the search space, conflicting objectives for production optimization, and the uncertainty in the production process. Knowledge-based techniques, especially approximate reasoning and constraint relaxation, are promising ways to overcome these problems. A case study from an industrial CIM environment, namely high-grade steel production, is presented to demonstrate how knowledge-based scheduling with the desired capabilities could work. By using fuzzy set theory, the applied knowledge representation technique covers the uncertainty inherent in the problem domain. Based on this knowledge representation, a classification of jobs according to their importance is defined which is then used for the straightforward generation of a schedule. A control strategy which comprises organizational, spatial, temporal, and chemical constraints is introduced. The strategy supports the dynamic relaxation of conflicting constraints in order to improve tentative schedules.

Dorn, Juergen↗

Multivariate statistical analysis software technologies for astrophysical research involving large data bases

The existing and forthcoming data bases from NASA missions contain an abundance of information whose complexity cannot be efficiently tapped with simple statistical techniques. Powerful multivariate statistical methods already exist which can be used to harness much of the richness of these data. Automatic classification techniques have been developed to solve the problem of identifying known types of objects in multi parameter data sets, in addition to leading to the discovery of new physical phenomena and classes of objects. We propose an exploratory study and integration of promising techniques in the development of a general and modular classification/analysis system for very large data bases, which would enhance and optimize data management and the use of human research resources.

Djorgovski, Stanislav↗

Multivariate statistical analysis software technologies for astrophysical research involving large data bases

The existing and forthcoming data bases from NASA missions contain an abundance of information whose complexity cannot be efficiently tapped with simple statistical techniques. Powerful multivariate statistical methods already exist which can be used to harness much of the richness of these data. Automatic classification techniques have been developed to solve the problem of identifying known types of objects in multiparameter data sets, in addition to leading to the discovery of new physical phenomena and classes of objects. We propose an exploratory study and integration of promising techniques in the development of a general and modular classification/analysis system for very large data bases, which would enhance and optimize data management and the use of human research resource.

Djorgovski, George↗

Using machine learning techniques to automate sky survey catalog generation

We describe the application of machine classification techniques to the development of an automated tool for the reduction of a large scientific data set. The 2nd Palomar Observatory Sky Survey provides comprehensive photographic coverage of the northern celestial hemisphere. The photographic plates are being digitized into images containing on the order of 10(exp 7) galaxies and 10(exp 8) stars. Since the size of this data set precludes manual analysis and classification of objects, our approach is to develop a software system which integrates independently developed techniques for image processing and data classification. Image processing routines are applied to identify and measure features of sky objects. Selected features are used to determine the classification of each object. GID3* and O-BTree, two inductive learning techniques, are used to automatically learn classification decision trees from examples. We describe the techniques used, the details of our specific application, and the initial encouraging results which indicate that our approach is well-suited to the problem. The benefits of the approach are increased data reduction throughput, consistency of classification, and the automated derivation of classification rules that will form an objective, examinable basis for classifying sky objects. Furthermore, astronomers will be freed from the tedium of an intensely visual task to pursue more challenging analysis and interpretation problems given automatically cataloged data.

Fayyad, Usama M.↗

Generalized superposition.

Generalization of superposition principle for linear systems applied to classification of nonlinear systems and solution of nonlinear filtering problems

Oppenheim, A. V.↗

LANDSAT data for state planning

The results of an effort to generate and apply automated classification of LANDSAT digital data to state of Georgia problems are presented. This phase centers on an analysis of the usefulness of LANDSAT digital data to provide land-use data for transportation planning. Hall County, Georgia was chosen as a test site because it is part of a seventeen county area for which the Georgia Department of Transportation is currently designing a Transportation Planning Land-Use Simulation Model. The land-cover information derived from this study was compared to several other existing sources of land-use data for Hall County and input into this simulation. The results indicate that there is difficulty comparing LANDSAT derived land-cover information with previous land-use information since the LANDSAT data are acquired on an acre by acre grid basis while all previous land-use surveys for Hall County used land-use data on a parcel basis.

Faust, N. L.↗

The luminosity structure and objective classification of galaxies

The luminosity structure of spiral galaxies is studied using the technique of principal component analysis. It is found that approximately 94% of the variation in the luminosity distribution of galaxies can be accounted for by just two principal components. The principal luminosity components may contain valuable information about star formation history or whatever luminosity-regulating process occurs in galaxies. Practically, these principal components provide a new approach for the investigation of the luminosity structures of galaxies and their dependence on other properties. They also serve as an excellent objective classification system for galaxies. We introduce in this paper such a classification scheme and explore its various properties. The new system shows a number of very impressive characteristics. Most important, it can well segregate virtually all the important galactic properties we tested and does so much better than the conventional morphological classification systems. Of particular interest is that some distance-dependent parameters can also be determined to a surprisingly good accuracy; for example, absolute magnitude may be determined to an accuracy of approximately 0.6 mag (yet further improvement is believed to be highly possible). Second, the system is objective, and the classification procedure can be automated to a large degree; also the new system can apply to much smaller and fainter images than do eye-based clasification systems. These properties make the new system suitable for practical application, especially on very large (and deeper) digital image catalogs. Third, the classification is expressed in dimensionless numbers, yet the simple notation bears significant and easily understandable meaning, making it easy and convenient to use. Finally, the new system has another extremely useful feature: it provides a very powerful and convenient platform not only for classification, but also for easily recording, examining, and studying the variations and correlations of galaxy properties-all these may be carried out graphically by using the C-vectors and the C-diagrams introduced in the paper. We wil also give an example to demonstrate the use of the classification system for the study of the internal extinction problem in spiral galaxies.

Han, Mingshen↗

Fast Solution in Sparse LDA for Binary Classification

An algorithm that performs sparse linear discriminant analysis (Sparse-LDA) finds near-optimal solutions in far less time than the prior art when specialized to binary classification (of 2 classes). Sparse-LDA is a type of feature- or variable- selection problem with numerous applications in statistics, machine learning, computer vision, computational finance, operations research, and bio-informatics. Because of its combinatorial nature, feature- or variable-selection problems are NP-hard or computationally intractable in cases involving more than 30 variables or features. Therefore, one typically seeks approximate solutions by means of greedy search algorithms. The prior Sparse-LDA algorithm was a greedy algorithm that considered the best variable or feature to add/ delete to/ from its subsets in order to maximally discriminate between multiple classes of data. The present algorithm is designed for the special but prevalent case of 2-class or binary classification (e.g. 1 vs. 0, functioning vs. malfunctioning, or change versus no change). The present algorithm provides near-optimal solutions on large real-world datasets having hundreds or even thousands of variables or features (e.g. selecting the fewest wavelength bands in a hyperspectral sensor to do terrain classification) and does so in typical computation times of minutes as compared to days or weeks as taken by the prior art. Sparse LDA requires solving generalized eigenvalue problems for a large number of variable subsets (represented by the submatrices of the input within-class and between-class covariance matrices). In the general (fullrank) case, the amount of computation scales at least cubically with the number of variables and thus the size of the problems that can be solved is limited accordingly. However, in binary classification, the principal eigenvalues can be found using a special analytic formula, without resorting to costly iterative techniques. The present algorithm exploits this analytic form along with the inherent sequential nature of greedy search itself. Together this enables the use of highly-efficient partitioned-matrix-inverse techniques that result in large speedups of computation in both the forward-selection and backward-elimination stages of greedy algorithms in general.

Moghaddam, Baback↗

Vorticity-dilatation boundary conditions for viscous compressible flows

The theoretical generalization, synthesis, and classification of various relevant formulations of the vorticity-dilatation conditioning problem is presented. Kinematic and dynamic conditions as well as differential and integral forms are considered. The possibility of using various variables that relate directly to vorticity and dilatation to construct the desired boundary conditions is examined. Some new formulations are given and previously proposed ones are located properly in the classification, and their interrelations are clarified.

Wu, J. Z.↗