Feature Selection in k-Median Clustering

An e ective method for selecting features in clustering unlabeled data is proposed based on changing the objective function of the standard k-median clustering algorithm. The change consists of perturbing the objective function by a term that drives the medians of each of the k clusters toward the (shifted) global median of zero for the entire dataset. As the perturbation parameter is increased, more and more features are driven automatically toward the global zero median and are eliminated from the problem until one last feature remains. An error curve for unlabeled data clustering as a function of the number of features used gives reducedfeature clustering error relative to the \gold standard" of the full-feature clustering. This clustering error curve parallels a classi cation error curve based on real data labels. This justi es the utility of the former error curve for unlabeled data as a means of choosing an appropriate number of reduced features in order to achieve a correctness comparable to that obtained by the full set of original features. For example, on the 3-class Wine dataset, clustering with 4 selected input space features is comparable to within 4% to clustering using the original 13 features of the problem

Germany and the world of yesterday

In the past six decades, the four pillars of Germany’s post-World War II security model were built and expanded: NATO, the European Union, trans-Atlanticism and free trade. This gave Germans their longest period of peace, making them fantastically rich as the world’s fourth biggest economy. Can Germany’s view of itself as a ‘big Switzerland’ be sustained? Leon Mangasarian argues not. The Biden presidency is providing Germans with a false sense of security, one which means that Germany will fail to build the appropriate policies and NATO alliances Germany desperately needs in order to build a grand strategy of its place in Europe. If that debate is not led by the chancellery then it needs to come from the Bundestag, from the country’s expanding think tank community, the universities and citizen fora

Exact Penalty Functions for Mathematical Programs with Linear Complementarity Constraints

We establish a new general exact penalty function result for a constrained optimization problem and apply this result to a mathematical program with linear complementarity constraints

A theoretical framework for supervised learning from regions

Supervised learning is investigated, when the data are represented not only by labeled points but also labeled regions of the input space. In the limit case, such regions degenerate to single points and the proposed approach changes back to the classical learning context. The adopted framework entails the minimization of a functional obtained by introducing a loss function that involves such regions. An additive regularization term is expressed via differential operators that model the smoothness properties of the desired input/output relationship. Representer theorems are given, proving that the optimization problem associated to learning from labeled regions has a unique solution, which takes on the form of a linear combination of kernel functions determined by the differential operators together with the regions themselves. As a relevant situation, the case of regions given by multi-dimensional intervals (i.e., “boxes”) is investigated, which models prior knowledge expressed by logical propositions

Meta-stable memory in an artificial immune network

Abstract. This paper describes an artificial immune system algorithm which implements a fairly close analogue of the memory mechanism proposed by Jerne(1) (usually known as the Immune Network Theory). The algorithm demonstrates the ability of these types of network to produce meta-stable structures representing populated regions of the antigen space. The networks produced retain their structure indefinitely and capture inherent structure within the sets of antigens used to train them. Results from running the algorithm on a variety of data sets are presented and shown to be stable over long time periods and wide ranges of parameters. The potential of the algorithm as a tool for multivariate data analysis is also explored.

Clones in Graphs

Finding structural similarities in graph data, like social networks, is a far-ranging task in data mining and knowledge discovery. A (conceptually) simple reduction would be to compute the automorphism group of a graph. However, this approach is ineffective in data mining since real world data does not exhibit enough structural regularity. Here we step in with a novel approach based on mappings that preserve the maximal cliques. For this we exploit the well known correspondence between bipartite graphs and the data structure formal context $(G,M,I)$ from Formal Concept Analysis. From there we utilize the notion of clone items. The investigation of these is still an open problem to which we add new insights with this work. Furthermore, we produce a substantial experimental investigation of real world data. We conclude with demonstrating the generalization of clone items to permutations.Comment: 11 pages, 2 figures, 1 tabl

Independence or dependence? The arms industries in Israel, South Africa and Yugoslavia during the Cold War.

This dissertation examines the development of armaments production in Israel, South Africa and Yugoslavia and the implications thereof regarding military import dependency, arms exports, and defence production cooperation among developing arms producers. The dissertation concentrates on strategic and political issues of Third world arms production and does not deal with questions of arms industries and development. The dissertation makes three broad arguments: First, that truly indigenous arms production hardly exists in the three case study countries. I illustrate this by showing the heavy dependence of Israel, South Africa and Yugoslavia on foreign technology, licences, foreign components and foreign capital for all major -- and many minor -- weapons manufacturing projects undertaken since the 1960s. Second, that despite billions of dollars invested in building up respective defence industry sectors, all three states (or successor states in the case of Yugoslavia) remained dependent on imports of most of the same major weapons systems at the end of the Cold War as they were 30 years earlier. Embargo of systems such as fighter aircraft, ships and tanks by the old arms supplier oligopoly was the key reason for the initiation of arms production in all three countries. But the cancellation or failure of key arms manufacturing projects in all three countries, such as the Israeli Lavi fighter, means that far from achieving weapons supply independence, this dependency is set to continue into the next century Third, that despite the above two points, Israel, South Africa, Yugoslavia and other Third World arms producers have played an expanding and important role the world arms trade and proliferation of military technology since the 1970s. This seeming paradox will be illustrated by contrasting Israel's growing dependency on the United States for advanced weapons, capital and technology from 1970 to 1990, with the Israeli role as the single most important UN arms sanctions buster to South Africa from 1977 to the early 1990s; as an arms supplier to Argentina during the 1982 Falklands/Malvinas War, to Iran during the Iran-Iraq War and to Guatemala after the 1977 U.S. arms cut-off. The dissertation concludes that while some arms production is bound to continue in all three states (or successor states), major weapons manufacturing projects are a thing of the past and will be initiated -- if at all -- with the cooperation of arms industries from the very industrialised powers which Israel, South Africa and Yugoslavia sought total independence from through indigenous arms production during the Cold War