l1-norm penalized orthogonal forward regression

A l1-norm penalized orthogonal forward regression (l1-POFR) algorithm is proposed based on the concept of leave-one-out mean square error (LOOMSE), by defining a new l1-norm penalized cost function in the constructed orthogonal space and associating each orthogonal basis with an individually tunable regularization parameter. Due to orthogonality, the LOOMSE can be analytically computed without actually splitting the data set, and moreover a closed form of the optimal regularization parameter is derived by greedily minimizing the LOOMSE incrementally. We also propose a simple formula for adaptively detecting and removing regressors to an inactive set so that the computational cost of the algorithm is significantly reduced. Examples are included to demonstrate the effectiveness of this new l1-POFR approach

Uncovering the popularity mechanisms for Facebook applications

Understanding the popularity dynamics of online application(App) is significant for the online social systems. In this paper, by dividing the Facebook Apps into different groups in terms of their popularities, we empirically investigate the popularity dynamics for different kinds of Facebook Apps. Then, taking into account the influence of cumulative and recent popularities on the user choice, we present a model to regenerate the growth of popularity for different App groups. The experimental results of 917 Facebook Apps show that as the popularities of Facebook Apps increase, the recent popularity plays more important role. Specifically, the recent popularity plays more important role in regenerating the popularity dynamics for more popular Apps, and the cumulative popularity plays more important role for unpopular Apps. We also conduct temporal analysis on the growth characteristic of individual App by comparing the increment at each time with the average of historical records. The results show that the growth of more popular App tends to fluctuate more greatly. Our work may shed some lights for deeply understanding the popularity mechanism for online applications