01921nas a2200169   4500008004100000245003800041210003800079260002400117520140400141100001901545700001901564700002101583700002001604700002101624700002501645856008101670       2015                        eng d00aQuantification in Social Networks0 aQuantification in Social Networks  aParis, FrancebIEEE3 aIn many real-world applications there is a need to monitor the distribution of a population across different classes, and to track changes in this distribution over time. As an example, an important task is to monitor the percentage of unemployed adults in a given region. When the membership of an individual in a class cannot be established deterministically, a typical solution is the classification task. However, in the above applications the final goal is not determining which class the individuals belong to, but estimating the prevalence of each class in the unlabeled data. This task is called quantification. Most of the work in the literature addressed the quantification problem considering data presented in conventional attribute format. Since the ever-growing availability of web and social media we have a flourish of network data representing a new important source of information and by using quantification network techniques we could quantify collective behavior, i.e., the number of users that are involved in certain type of activities, preferences, or behaviors. In this paper we exploit the homophily effect observed in many social networks in order to construct a quantifier for networked data. Our experiments show the effectiveness of the proposed approaches and the comparison with the existing state-of-the-art quantification methods shows that they are more accurate. 1 aMilli, Letizia1 aMonreale, Anna1 aRossetti, Giulio1 aPedreschi, Dino1 aGiannotti, Fosca1 aSebastiani, Fabrizio  uhttp://www.giuliorossetti.net/about/wp-content/uploads/2015/12/main_DSAA.pdf02131nas a2200169   4500008003900000245002500039210002500064300001400089520168900103100001901792700001901811700002101830700002101851700002001872700002501892856004401917       2013                          d00aQuantification Trees0 aQuantification Trees  a528–5363 aIn many applications there is a need to monitor how a population is distributed across different classes, and to track the changes in this distribution that derive from varying circumstances, an example such application is monitoring the percentage (or "prevalence") of unemployed people in a given region, or in a given age range, or at different time periods. When the membership of an individual in a class cannot be established deterministically, this monitoring activity requires classification. However, in the above applications the final goal is not determining which class each individual belongs to, but simply estimating the prevalence of each class in the unlabeled data. This task is called quantification. In a supervised learning framework we may estimate the distribution across the classes in a test set from a training set of labeled individuals. However, this may be sub optimal, since the distribution in the test set may be substantially different from that in the training set (a phenomenon called distribution drift). So far, quantification has mostly been addressed by learning a classifier optimized for individual classification and later adjusting the distribution it computes to compensate for its tendency to either under-or over-estimate the prevalence of the class. In this paper we propose instead to use a type of decision trees (quantification trees) optimized not for individual classification, but directly for quantification. Our experiments show that quantification trees are more accurate than existing state-of-the-art quantification methods, while retaining at the same time the simplicity and understandability of the decision tree framework.1 aMilli, Letizia1 aMonreale, Anna1 aRossetti, Giulio1 aGiannotti, Fosca1 aPedreschi, Dino1 aSebastiani, Fabrizio  uhttp://dx.doi.org/10.1109/ICDM.2013.122