Winner-relaxing and winner-enhancing Kohonen maps: Maximal mutual information from enhancing the winner

The magnification behaviour of a generalized family of self-organizing feature maps, the Winner Relaxing and Winner Enhancing Kohonen algorithms is analyzed by the magnification law in the one-dimensional case, which can be obtained analytically. The Winner-Enhancing case allows to acheive a magnification exponent of one and therefore provides optimal mapping in the sense of information theory. A numerical verification of the magnification law is included, and the ordering behaviour is analyzed. Compared to the original Self-Organizing Map and some other approaches, the generalized Winner Enforcing Algorithm requires minimal extra computations per learning step and is conveniently easy to implement.Comment: 6 pages, 5 figures. For an extended version refer to cond-mat/0208414 (Neural Computation 17, 996-1009

Magnification Control in Winner Relaxing Neural Gas

An important goal in neural map learning, which can conveniently be accomplished by magnification control, is to achieve information optimal coding in the sense of information theory. In the present contribution we consider the winner relaxing approach for the neural gas network. Originally, winner relaxing learning is a slight modification of the self-organizing map learning rule that allows for adjustment of the magnification behavior by an a priori chosen control parameter. We transfer this approach to the neural gas algorithm. The magnification exponent can be calculated analytically for arbitrary dimension from a continuum theory, and the entropy of the resulting map is studied numerically conf irming the theoretical prediction. The influence of a diagonal term, which can be added without impacting the magnification, is studied numerically. This approach to maps of maximal mutual information is interesting for applications as the winner relaxing term only adds computational cost of same order and is easy to implement. In particular, it is not necessary to estimate the generally unknown data probability density as in other magnification control approaches.Comment: 14pages, 2 figure

Backward Compatibility to Sustain Market Dominance – Evidence from the US Handheld Video Game Industry

The introduction of a new product generation forces incumbents in network industries to rebuild their installed base to maintain an advantage over potential entrants. We study if backward compatibility can help moderate this process of rebuilding an installed base. Using a structural model of the US market for handheld game consoles, we show that backward compatibility lets incumbents transfer network effects from the old generation to the new to some extent but that it also reduces supply of new software. We also find that backward compatibility matters most shortly after the introduction of a new generation. Finally, we examine the tradeoff between technological progress and backward compatibility and find that backward compatibility matters less if there is a large technological leap between two generations. We subsequently use our results to assess the role of backward compatibility as a strategy to sustain a dominant market position

The Strength of Direct Ties: Evidence from the Electronic Game Industry

We analyze the economic effects of a developer’s connectedness in the electronic game industry. Knowledge spillovers between developers should be of special relevance in this knowledge-based industry. We calculate measures for a developer’s connectedness to other developers at multiple points in time. In a regression with developer, developing firm, publishing firm, and time fixed effects, we find that the number of a developer’s direct ties, i.e., common past experience, has a strong effect on both a game’s revenues and critics’ scores. The intensity of indirect ties makes no additional contribution to the game’s success

Incentives for Quality over Time – The Case of Facebook Applications

We study the market for applications on Facebook, the dominant platform for social networking and make use of a rule change by Facebook by which high-quality applications were rewarded with further opportunities to engage users. We find that the change led to quality being a more important driver of usage while sheer network size became less important. Further, we find that update frequency helps applications maintain higher usage, while generally usage of Facebook applications declines less rapidly with age