Binarized support vector machines

The widely used Support Vector Machine (SVM) method has shown to yield very good results in Supervised Classification problems. Other methods such as Classification Trees have become more popular among practitioners than SVM thanks to their interpretability, which is an important issue in Data Mining. In this work, we propose an SVM-based method that automatically detects the most important predictor variables, and the role they play in the classifier. In particular, the proposed method is able to detect those values and intervals which are critical for the classification. The method involves the optimization of a Linear Programming problem, with a large number of decision variables. The numerical experience reported shows that a rather direct use of the standard Column-Generation strategy leads to a classification method which, in terms of classification ability, is competitive against the standard linear SVM and Classification Trees. Moreover, the proposed method is robust, i.e., it is stable in the presence of outliers and invariant to change of scale or measurement units of the predictor variables. When the complexity of the classifier is an important issue, a wrapper feature selection method is applied, yielding simpler, still competitive, classifiers

The Influence of Organizational Speed on Organizational Mishaps: The Moderating Role of Dynamism

Previous studies have shown the importance of organizational speed for firms’ competitive advantage and financial performance. However, more recent studies have also demonstrated that speed can be detrimental for companies. Drawing on the managerial cognitive perspective, we argue that organizational speed can contribute to organizational mishaps. We focus on organizational speed in relation to firms’ mergers and acquisitions and strategic alliances. Based on a sample of 331 companies in the United States over the period 2003-2009, our findings suggest that organizational speed has a positive influence on firms’ mishaps. Furthermore, we found that this effect is stronger when firms operate in dynamic environments.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Bivariate trinomials over finite fields

We study the number of points in the family of plane curves defined by a trinomial $$\mathcal{C}(\alpha,\beta)= \{(x,y)\in\mathbb{F}_q^2\,:\,\alpha x^{a_{11}}y^{a_{12}}+\beta x^{a_{21}}y^{a_{22}}=x^{a_{31}}y^{a_{32}}\}$$ with fixed exponents (not collinear) and varying coefficients over finite fields. We prove that each of these curves has an almost predictable number of points, given by a closed formula that depends on the coefficients, exponents, and the field, with a small error term $N(\alpha,\beta)$ that is bounded in absolute value by $2\tilde{g}q^{1/2}$, where $\tilde{g}$ is a constant that depends only on the exponents and the field. A formula for $\tilde{g}$ is provided, as well as a comparison of $\tilde{g}$ with the genus $g$ of the projective closure of the curve over $\overline{\mathbb{F}_q}$. We also give several linear and quadratic identities for the numbers $N(\alpha,\beta)$ that are strong enough to prove the estimate above, and in some cases, to characterize them completely.Comment: 11 page