Guillermo Sánchez-Díaz

On the relation between rough set reducts and typical testors

This paper studies the relations between rough set reducts and typical testors from the so-called logical combinatorial approach to pattern recognition. Definitions, comments and observations are formally introduced and supported by illustrative examples. Furthermore, some theorems expressing theoretical relations between reducts and typical testors are enunciated and proved. We also discuss several practical applications of these relations that can mutually enrich the development of research and applications in both areas. Although we focus on the relation between the classical concepts of testor and reduct, our study can be expanded to include other types of testors and reducts.

Mapping aboveground biomass by integrating geospatial and forest inventory data through a k -nearest neighbor strategy in North Central Mexico

As climate change negotiations progress, monitoring biomass and carbon stocks is becoming an important part of the current forest research. Therefore, national governments are interested in developing forest-monitoring strategies using geospatial technology. Among statistical methods for mapping biomass, there is a nonparametric approach called k-nearest neighbor (kNN). We compared four variations of distance metrics of the kNN for the spatially-explicit estimation of aboveground biomass in a portion of the Mexican north border of the intertropical zone. Satellite derived, climatic, and topographic predictor variables were combined with the Mexican National Forest Inventory (NFI) data to accomplish the purpose. Performance of distance metrics applied into the kNN algorithm was evaluated using a cross validation leave-one-out technique. The results indicate that the Most Similar Neighbor (MSN) approach maximizes the correlation between predictor and response variables (r=0.9). Our results are in agreement with those reported in the literature. These findings confirm the predictive potential of the MSN approach for mapping forest variables at pixel level under the policy of Reducing Emission from Deforestation and Forest Degradation (REDD+).

Typical testors generation based on an evolutionary algorithm

Typical testors are useful for both feature selection and feature relevance determination in supervised classification problems. However, reported algorithms that address the problem of finding the set of all typical testors have exponential complexity. In this paper, we propose to adapt an evolutionary method, the Hill-Climbing algorithm, with an acceleration operator in mutation process, to address this problem in polinomial time. Experimental results with the method proposed are presented and compared, in efficiency, with other methods, namely, Genetic Algorithms (GA) and Univariate Marginal Distribution Algorithm (UMDA).

Building fast decision trees from large training sets

Decision trees are commonly used in supervised classification. Currently, supervised classification problems with large training sets are very common, however many supervised classifiers cannot handle this amount of data. There are some decision tree induction algorithms that are capable to process large training sets, however almost all of them have memory restrictions because they need to keep in main memory the whole training set, or a big amount of it. Moreover, algorithms that do not have memory restrictions have to choose a subset of the training set, needing extra time for this selection; or they require to specify the values for some parameters that could be very difficult to determine by the user. In this paper, we present a new fast heuristic for building decision trees from large training sets, which overcomes some of the restrictions of the state of the art algorithms, using all the instances of the training set without storing all of them in main memory. Experimental results show that our algorithm is faster than the most recent algorithms for building decision trees from large training sets.

A Fast Implementation for the Typical Testor Property Identification Based on an Accumulative Binary Tuple

Abstract In this paper, we introduce a fast implementation of the CT EXT algorithm for testor property identification, that is based on an accumulative binary tuple. The fast implementation of the CT EXT algorithm (one of the fastest algorithms reported), is designed to generate all the typical testors from a training matrix, requiring a reduced number of operations. Experimental results using this fast implementation and the comparison with other state-of-the-art algorithms that generate typical testors are presented.

An evolutionary algorithm with acceleration operator to generate a subset of typical testors

The proposed Hill-Climbing algorithm incorporates an acceleration operator.The acceleration operator improves the exploration capability of the algorithm.Local search is more adequate than global search for generating typical testors.The proposed algorithm has better performance than other heuristics reported. This paper is focused on introducing a Hill-Climbing algorithm as a way to solve the problem of generating typical testors - or non-reducible descriptors - from a training matrix. All the algorithms reported in the state-of-the-art have exponential complexity. However, there are problems for which there is no need to generate the whole set of typical testors, but it suffices to find only a subset of them. For this reason, we introduce a Hill-Climbing algorithm that incorporates an acceleration operation at the mutation step, providing a more efficient exploration of the search space. The experiments have shown that, under the same circumstances, the proposed algorithm performs better than other related algorithms reported so far.

Forest Cover Mapping in North-Central Mexico: A Comparison of Digital Image Processing Methods

Vegetation type is an environmental attribute that varies across the landscape and over time. Its continuous assessment is important for monitoring land use changes and forest degradation. There are advanced methods that can estimate the fractional cover of vegetation types within each pixel. This paper compares some methods for subpixel mapping of forest cover in the state of San Luis Potosí, Mexico, using Moderate Resolution Imaging Spectroradiometer (MODIS)-derived spectral data (MCD43A4). Three methods were tested: (1) Bayesian posterior probability, (2) the Fuzzy k nearest neighbor (FkNN), and (3) linear spectral mixture analysis (LSMA). While the Bayesian approach gave the poorest correlations, FkNN (r = 0.78) and LSMA (r = 0.81) estimations were successfully validated with information obtained from a Landsat image. This paper represents an interesting attempt to compare rarely reported FkNN with traditional approaches such as LSMA and the Bayesian one.

A parallel hill-climbing algorithm to generate a subset of irreducible testors

The generation of irreducible testors from a training matrix is an expensive computational process: all the algorithms reported have exponential complexity. However, for some problems there is no need to generate the entire set of irreducible testors, but only a subset of them. Several approaches have been developed for this purpose, ranging from Univariate Marginal Distribution to Genetic Algorithms. This paper introduces a parallel version of a Hill-Climbing Algorithm useful to find a subset of irreducible testors from a training matrix. This algorithm was selected because it has been one of the fastest algorithms reported in the state-of-the-art on irreducible testors. In order to efficiently store every different irreducible testor found, the algorithm incorporates a digital-search tree. Several experiments with synthetic and real data are presented in this work.

An image resizing algorithm for binary maps

Loss of connectivity property is a common problem presented in binary map resizing operation. There are several algorithms to make the enlargement or reduction of digital images. However, when these techniques are applied in a binary geographic map image, in order to obtain a scaled map, these algorithms do not preserve the connectivity property. When a filled algorithm is required for coloring each item of a geographic map (e.g. its political division), the connectivity property is fundamental. In This work, we propose a resizing algorithm for processing binary geographic maps. The proposed algorithm preserves the connectivity property in the maps when an enlargement or reduction operation is applied.

Determination of Similarity Threshold in Clustering Problems for Large Data Sets

A new automatic method based on an intra-cluster criterion, to obtain a similarity threshold that generates a well-defined clustering (or near to it) for large data sets, is proposed. This method uses the connected component criterion, and it neither calculates nor stores the similarity matrix of the objects in main memory. The proposed method is focused on unsupervised Logical Combinatorial Pattern Recognition approach. In addition, some experimentations of the new method with large data sets are presented.