Weighted Heuristic Ensemble of Filters

Feature selection has become increasingly important in data mining in recent years due to the rapid increase in the dimensionality of big data. However, the reliability and consistency of feature selection methods (filters) vary considerably on different data and no single filter performs consistently well under various conditions. Therefore, feature selection ensemble has been investigated recently to provide more reliable and effective results than any individual one but all the existing feature selection ensemble treat the feature selection methods equally regardless of their performance. In this paper, we present a novel framework which applies weighted feature selection ensemble through proposing a systemic way of adding different weights to the feature selection methods-filters. Also, we investigate how to determine the appropriate weight for each filter in an ensemble. Experiments based on ten benchmark datasets show that theoretically and intuitively adding more weight to ‘good filters’ should lead to better results but in reality it is very uncertain. This assumption was found to be correct for some examples in our experiment. However, for other situations, filters which had been assumed to perform well showed bad performance leading to even worse results. Therefore adding weight to filters might not achieve much in accuracy terms, in addition to increasing complexity, time consumption and clearly decreasing the stability

Using interval weights in MADM problems

The choice of weights vectors in multiple attribute decision making (MADM) problems has generated an important literature, and a large number of methods have been proposed for this task. In some situations the decision maker (DM) may not be willing or able to provide exact values of the weights, but this difficulty can be avoided by allowing the DM to give some variability in the weights. In this paper we propose a model where the weights are not fixed, but can take any value from certain intervals, so the score of each alternative is the maximum value that the weighted mean can reach when the weights belong to those intervals. We provide a closed-form expression for the scores achieved by the alternatives so that they can be ranked them without solving the proposed model, and apply this new method to an MADM problem taken from the literature.Este trabajo forma parte del proyecto de investigación: MEC-FEDER Grant ECO2016-77900-P

Rank Centrality: Ranking from Pair-wise Comparisons

The question of aggregating pair-wise comparisons to obtain a global ranking over a collection of objects has been of interest for a very long time: be it ranking of online gamers (e.g. MSR's TrueSkill system) and chess players, aggregating social opinions, or deciding which product to sell based on transactions. In most settings, in addition to obtaining a ranking, finding `scores' for each object (e.g. player's rating) is of interest for understanding the intensity of the preferences. In this paper, we propose Rank Centrality, an iterative rank aggregation algorithm for discovering scores for objects (or items) from pair-wise comparisons. The algorithm has a natural random walk interpretation over the graph of objects with an edge present between a pair of objects if they are compared; the score, which we call Rank Centrality, of an object turns out to be its stationary probability under this random walk. To study the efficacy of the algorithm, we consider the popular Bradley-Terry-Luce (BTL) model (equivalent to the Multinomial Logit (MNL) for pair-wise comparisons) in which each object has an associated score which determines the probabilistic outcomes of pair-wise comparisons between objects. In terms of the pair-wise marginal probabilities, which is the main subject of this paper, the MNL model and the BTL model are identical. We bound the finite sample error rates between the scores assumed by the BTL model and those estimated by our algorithm. In particular, the number of samples required to learn the score well with high probability depends on the structure of the comparison graph. When the Laplacian of the comparison graph has a strictly positive spectral gap, e.g. each item is compared to a subset of randomly chosen items, this leads to dependence on the number of samples that is nearly order-optimal.Comment: 45 pages, 3 figure

Aggregating preference rankings using an optimistic-pessimistic approach: Closed-form expressions

Producción CientíficaThere exist in the literature several models to tackle the problem of aggregating preferences rankings where each alternative is evaluated with the most favorable scoring vector for it (which can be considered as an optimistic approach). Recently, Khodabakhshi and Aryavash (2015) have suggested a new model where both the optimistic and the pessimistic approaches are taken into account. In this paper we provide closed-form expressions for the scores of alternatives when the model proposed by these authors is used. The expressions obtained allow us to analyze the model and suggest some small modifications.Ministerio español de Economía y Competitividad (Project ECO2016-77900-P) and FEDERJunta de Castilla y León (Consejería de Educación, Project VA066U13

Multidimensional Indices of Achievements and Poverty: What Do We Gain and What Do We

Poverty and wellbeing are multi-dimensional. Nobody questions that deprivations and achievements go beyond income. There is, however, sharp disagreement on whether the various dimensions of poverty and wellbeing can be aggregated into a single, multi-dimensional index in a meaningful way. Is aggregating dimensions of poverty and wellbeing useful? Is it sensible? Here I summarize and contrast three key papers that respond these questions in strikingly different ways. The papers are: The HDI 2010: New Controversies, Old Critiques by Jeni Klugman, Francisco Rodríguez and Hyung-Jin Choi; Understandings and Misunderstandings of Multidimensional Poverty Measurement by Sabina Alkire and James Foster; and, On Multidimensional Indices of Poverty by Martin Ravallion.poverty measurement, multidimensional poverty, deprivation, axioms, Human Development Index, capabilities, substitutability, trade-offs, welfare, country classifications

Multidimensional indices of achievements and poverty: What do we gain and what do we lose?

Poverty and wellbeing are multi-dimensional. Nobody questions that deprivations and achievements go beyond income. There is, however, sharp disagreement on whether the various dimensions of poverty and wellbeing can be aggregated into a single, multi-dimensional index in a meaningful way. Is aggregating dimensions of poverty and wellbeing useful? Is it sensible? Here I summarize and contrast three key papers that respond these questions in strikingly different ways. The papers are: The HDI 2010: New Controversies, Old Critiques by Jeni Klugman, Francisco Rodríguez and Hyung-Jin Choi; Understandings and Misunderstandings of Multidimensional Poverty Measurement by Sabina Alkire and James Foster; and, On Multidimensional Indices of Poverty by Martin Ravallion.poverty measurement, multidimensional poverty, deprivation, axioms, Human Development Index, capabilities, substitutability, trade-offs, welfare, country classifications