A simplified implementation of the least squares solution for pairwise comparisons matrices

This is a follow up to "Solution of the least squares method problem of pairwise comparisons matrix" by Bozóki published by this journal in 2008. Familiarity with this paper is essential and assumed. For lower inconsistency and decreased accuracy, our proposed solutions run in seconds instead of days. As such, they may be useful for researchers willing to use the least squares method (LSM) instead of the geometric means (GM) method

Analysis of Crowdsourced Sampling Strategies for HodgeRank with Sparse Random Graphs

Crowdsourcing platforms are now extensively used for conducting subjective pairwise comparison studies. In this setting, a pairwise comparison dataset is typically gathered via random sampling, either \emph{with} or \emph{without} replacement. In this paper, we use tools from random graph theory to analyze these two random sampling methods for the HodgeRank estimator. Using the Fiedler value of the graph as a measurement for estimator stability (informativeness), we provide a new estimate of the Fiedler value for these two random graph models. In the asymptotic limit as the number of vertices tends to infinity, we prove the validity of the estimate. Based on our findings, for a small number of items to be compared, we recommend a two-stage sampling strategy where a greedy sampling method is used initially and random sampling \emph{without} replacement is used in the second stage. When a large number of items is to be compared, we recommend random sampling with replacement as this is computationally inexpensive and trivially parallelizable. Experiments on synthetic and real-world datasets support our analysis

Fast and Robust Rank Aggregation against Model Misspecification

In rank aggregation, preferences from different users are summarized into a total order under the homogeneous data assumption. Thus, model misspecification arises and rank aggregation methods take some noise models into account. However, they all rely on certain noise model assumptions and cannot handle agnostic noises in the real world. In this paper, we propose CoarsenRank, which rectifies the underlying data distribution directly and aligns it to the homogeneous data assumption without involving any noise model. To this end, we define a neighborhood of the data distribution over which Bayesian inference of CoarsenRank is performed, and therefore the resultant posterior enjoys robustness against model misspecification. Further, we derive a tractable closed-form solution for CoarsenRank making it computationally efficient. Experiments on real-world datasets show that CoarsenRank is fast and robust, achieving consistent improvement over baseline methods

A General Framework for Flexible Multi-Cue Photometric Point Cloud Registration

The ability to build maps is a key functionality for the majority of mobile robots. A central ingredient to most mapping systems is the registration or alignment of the recorded sensor data. In this paper, we present a general methodology for photometric registration that can deal with multiple different cues. We provide examples for registering RGBD as well as 3D LIDAR data. In contrast to popular point cloud registration approaches such as ICP our method does not rely on explicit data association and exploits multiple modalities such as raw range and image data streams. Color, depth, and normal information are handled in an uniform manner and the registration is obtained by minimizing the pixel-wise difference between two multi-channel images. We developed a flexible and general framework and implemented our approach inside that framework. We also released our implementation as open source C++ code. The experiments show that our approach allows for an accurate registration of the sensor data without requiring an explicit data association or model-specific adaptations to datasets or sensors. Our approach exploits the different cues in a natural and consistent way and the registration can be done at framerate for a typical range or imaging sensor.Comment: 8 page