Mining Posets from Linear Orders

There has been much research on the combinatorial problem of generating the linear extensions of a given poset. This paper focuses on the reverse of that problem, where the input is a set of linear orders, and the goal is to construct a poset or set of posets that generates the input. Such a problem finds applications in computational neuroscience, systems biology, paleontology, and physical plant engineering. In this paper, several algorithms are presented for efficiently finding a single poset that generates the input set of linear orders. The variation of the problem where a minimum set of posets that cover the input is also explored. It is found that the problem is polynomially solvable for one class of simple posets (kite(2) posets) but NP-complete for a related class (hammock(2,2,2) posets)

Extensión del concepto de utopía para el problema de la agregación de rankings sin empates

The use of rankings and how to aggregate or summarize them has received increasing attention in various fields: bibliometrics, web search, data mining, statistics, educational quality, and computational biology. For the Optimal Bucket Order Problem, the concept of Utopian Matrix was recently introduced: an ideal and not necessarily feasible solution with an unsurpassed quality for the feasible solutions of the problem. This work proposes an extension of the notion of Utopian Matrix to the Rank Aggregation Problem in which ties are not allowed between elements in the output ranking. Beyond the extension that is direct, the work focuses on studying its usefulness as an idealization or super optimal solution. As the Rank Aggregation Problem can be solved exactly based on its definition as an Integer Linear Programming Problem, an experimental study is presented where it is analyzed the relationship that exists between utopian (and anti utopian) values and the optimal solution in several instances solved by using the open source software SCIP. Among the 47 instances analyzed, in 19 the Utopian Value turned out to be equal to the optimal value (40.43 % feasibility) and in 18 the Anti Utopian Value also turned out to be feasible (38.00 %). This experimental study demonstrates the usefulness of utopian and anti utopian values to be considered as extreme values in the Rank Aggregation Problem, thus being able to find higher and lower bounds for optimization very quickly.El uso de los rankings y la forma de agregarlos o resumirlos ha recibido una atención creciente en diversos campos: bibliometría, búsquedas web, minería de datos, estadística, calidad educativa y biología computacional. Para el Problema de Ordenamiento Óptimo con empates fue introducido recientemente el concepto de Matriz Utópica: una solución ideal y no necesariamente factible con una calidad insuperable para las soluciones factibles del problema. Este trabajo propone una extensión de la noción de Matriz Utópica para el Problema de Agregación de Rankings en que no se permiten empates entre elementos en el ranking de salida. Más allá de la extensión que es directa, el trabajo se centra en estudiar su valor como idealización o solución súper óptima. Como el Problema de Agregación de Rankings puede resolverse de forma exacta a partir de su definición como Problema de Programación Lineal Entera, se presenta un estudio experimental donde se analiza la relación que existe entre los valores utópicos (y anti utópicos) y la solución óptima en instancias resueltas con la ayuda del software de código abierto SCIP. Entre las 47 instancias analizadas, en 19 el Valor Utópico resultó ser igual al valor óptimo (40,43 % de factibilidad) y en 18 el Valor Anti Utópico también resultó ser factible (38,00 %). Este estudio experimental demuestra la utilidad de los valores utópicos y anti utópicos para ser considerados como valores extremos en el Problema de Agregación de Rankings, pudiendo así encontrase muy rápidamente cotas superiores e inferiores para la optimización

Computational Techniques to Identify Rare Events in Spatio-temporal Data

University of Minnesota Ph.D. dissertation.May 2018. Major: Computer Science. Advisor: Vipin Kumar. 1 computer file (PDF); xi, 96 pages.Recent attention on the potential impacts of land cover changes to the environment as well as long-term climate change has increased the focus on automated tools for global-scale land surface monitoring. Advancements in remote sensing and data collection technologies have produced large earth science data sets that can now be used to build such tools. However, new data mining methods are needed to address the unique characteristics of earth science data and problems. In this dissertation, we explore two of these interesting problems, which are (1) build predictive models to identify rare classes when high quality annotated training samples are not available, and (2) classification enhancement of existing imperfect classification maps using physics-guided constraints. We study the problem of identifying land cover changes such as forest fires as a supervised binary classification task with the following characteristics: (i) instead of true labels only imperfect labels are available for training samples. These imperfect labels can be quite poor approximation of the true labels and thus may have little utility in practice. (ii) the imperfect labels are available for all instances (not just the training samples). (iii) the target class is a very small fraction of the total number of samples (traditionally referred to as the rare class problem). In our approach, we focus on leveraging imperfect labels and show how they, in conjunction with attributes associated with instances, open up exciting opportunities for performing rare class prediction. We applied this approach to identify burned areas using data from earth observing satellites, and have produced a database, which is more reliable and comprehensive (three times more burned area in tropical forests) compared to the state-of-art NASA product. We explore approaches to reduce errors in remote sensing based classification products, which are common due to poor data quality (eg., instrument failure, atmospheric interference) as well as limitations of the classification models. We present classification enhancement approaches, which aim to improve the input (imperfect) classification by using some implicit physics-based constraints related to the phenomena under consideration. Specifically, our approach can be applied in domains where (i) physical properties can be used to correct the imperfections in the initial classification products, and (ii) if clean labels are available, they can be used to construct the physical properties