Traditionally the probabilistic ranking principle is used to rank the search results while the ranking based on expected profits is used for paid placement of ads. These rankings try to maximize the expected utilities based on the user click models. Recent empirical analysis on search engine logs suggests a unified click models for both ranked ads and search results. The segregated view of document and ad rankings does not consider this commonality. Further, the used models consider parameters of (i) probability of the user abandoning browsing results (ii) perceived relevance of result snippets. But how to consider them for improved ranking is unknown currently. In this paper, we propose a generalized ranking function---namely "Click Efficiency (CE)"---for documents and ads based on empirically proven user click models. The ranking considers parameters (i) and (ii) above, optimal and has the same time complexity as sorting. To exploit its generality, we examine the reduced forms of CE ranking under different assumptions enumerating a hierarchy of ranking functions. Some of the rankings in the hierarchy are currently used ad and document ranking functions; while others suggest new rankings. While optimality of ranking is sufficient for document ranking, applying CE ranking to ad auctions requires an appropriate pricing mechanism. We incorporate a second price based pricing mechanism with the proposed ranking. Our analysis proves several desirable properties including revenue dominance over VCG for the same bid vector and existence of a Nash Equilibrium in pure strategies. The equilibrium is socially optimal, and revenue equivalent to the truthful VCG equilibrium. Further, we relax the independence assumption in CE ranking and analyze the diversity ranking problem. We show that optimal diversity ranking is NP-Hard in general, and that a constant time approximation is unlikely.
Diversity ranking has received considerable attention recently @cite_15 @cite_21 . The objective functions used to measure diversity by prior works are known to be NP-Hard @cite_7 .
@cite_15 @cite_21 @cite_7
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When mining a large database, the number of patterns discovered can easily exceed the capabilities of a human user to identify interesting results. To address this problem, various techniques have been suggested to reduce and or order the patterns prior to presenting them to the user. In this paper, our focus is on ranking summaries generated from a single dataset, where attributes can be generalized in many different ways and to many levels of granularity according to taxonomic hierarchies. We theoretically and empirically evaluate thirteen diversity measures used as heuristic measures of interestingness for ranking summaries generated from databases. The thirteen diversity measures have previously been utilized in various disciplines, such as information theory, statistics, ecology, and economics. We describe five principles that any measure must satisfy to be considered useful for ranking summaries. Theoretical results show that only four of the thirteen diversity measures satisfy all of the principles. We then analyze the distribution of the index values generated by each of the thirteen diversity measures. Empirical results, obtained using synthetic data, show that the distribution of index values generated tend to be highly skewed about the mean, median, and middle index values. The objective of this work is to gain some insight into the behaviour that can be expected from each of the measures in practice. Enhancing diversity in ranking on graphs has been identified as an important retrieval and mining task. Nevertheless, many existing diversified ranking algorithms either cannot be scalable to large graphs due to the time or memory requirements, or lack an intuitive and reasonable diversified ranking measure. In this paper, we propose a new diversified ranking measure on large graphs, which captures both relevance and diversity, and formulate the diversified ranking problem as a submodular set function maximization problem. Based on the submodularity of the proposed measure, we develop an efficient greedy algorithm with linear time and space complexity w.r.t. the size of the graph to achieve near-optimal diversified ranking. In addition, we present a generalized diversified ranking measure and give a near-optimal randomized greedy algorithm with linear time and space complexity for optimizing it. We evaluate the proposed methods through extensive experiments on five real data sets. The experimental results demonstrate the effectiveness and efficiency of the proposed algorithms. Diversity among the members of a team of classifiers is deemed to be a key issue in classifier combination. However, measuring diversity is not straightforward because there is no generally accepted formal definition. We have found and studied ten statistics which can measure diversity among binary classifier outputs (correct or incorrect vote for the class label): four averaged pairwise measures (the Q statistic, the correlation, the disagreement and the double fault) and six non-pairwise measures (the entropy of the votes, the difficulty index, the Kohavi-Wolpert variance, the interrater agreement, the generalized diversity, and the coincident failure diversity). Four experiments have been designed to examine the relationship between the accuracy of the team and the measures of diversity, and among the measures themselves. Although there are proven connections between diversity and accuracy in some special cases, our results raise some doubts about the usefulness of diversity measures in building classifier ensembles in real-life pattern recognition problems. Result diversity is a topic of great importance as more facets of queries are discovered and users expect to find their desired facets in the first page of the results. However, the underlying questions of how 'diversity' interplays with 'quality' and when preference should be given to one or both are not well-understood. In this work, we model the problem as expectation maximization and study the challenges of estimating the model parameters and reaching an equilibrium. One model parameter, for example, is correlations between pages which we estimate using textual contents of pages and click data (when available). We conduct experiments on diversifying randomly selected queries from a query log and the queries chosen from the disambiguation topics of Wikipedia. Our algorithm improves upon Google in terms of the diversity of random queries, retrieving 14 to 38 more aspects of queries in top 5, while maintaining a precision very close to Google. On a more selective set of queries that are expected to benefit from diversification, our algorithm improves upon Google in terms of precision and diversity of the results, and significantly outperforms another baseline system for result diversification.