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This paper proposes an active learning algorithm and models which can gradually learn individual’s preference through pairwise comparisons. The active learning scheme aims at finding individual’s most preferred choice (e.g. an airline itinerary) with minimized number of pairwise comparisons. The pairwise comparisons are encoded into probabilistic models based on assumptions of choice models and deep Gaussian processes. More specifically, this paper develops two novel probabilistic models assuming correlated Gumbel noises and latent utility functions. One is based on shallow Gaussian priors and the other assumes deep Gaussian priors. In the active learning algorithm, the next-to-compare decision is determined by an original acquisition function. The proposed algorithm and models have been benchmarked using functions with multiple local optima and one public airline itinerary dataset. In both experiments, nests are designed to capture correlated Gumbel noises. The experiments indicate the effectiveness of our active learning algorithm and models. The deep Gaussian models are proven to find the best choice with a lower number of pairwise comparisons than the shallow one. In both experiments, deep Gaussian models outperform the shallow model. The shallow model is recommended when the choice set is large and less computational time is required (e.g. in one experiment, deep Gaussian models require approximately 60%-70% more time on average). [ABSTRACT FROM AUTHOR]

We present an algorithm for L1-norm kernel PCA and provide a convergence analysis for it. While an optimal solution of L2-norm kernel PCA can be obtained through matrix decomposition, finding that of L1-norm kernel PCA is not trivial due to its non-convexity and non-smoothness. We provide a novel reformulation through which an equivalent, geometrically interpretable problem is obtained. Based on the geometric interpretation of the reformulated problem, we present a “fixed-point” type algorithm that iteratively computes a binary weight for each observation. As the algorithm requires only inner products of data vectors, it is computationally efficient and the kernel trick is applicable. In the convergence analysis, we show that the algorithm converges to a local optimal solution in a finite number of steps. Moreover, we provide a rate of convergence analysis, which has been never done for any L1-norm PCA algorithm, proving that the sequence of objective values converges at a linear rate. In numerical experiments, we show that the algorithm is robust in the presence of entry-wise perturbations and computationally scalable, especially in a large-scale setting. Lastly, we introduce an application to outlier detection where the model based on the proposed algorithm outperforms the benchmark algorithms. [ABSTRACT FROM AUTHOR]

We introduce a semi-supervised discrete choice model with algorithmic approaches to estimate choice models when relatively few requests have actual preferences but the majority only have the choice sets. Two classic semi-supervised learning algorithms, the expectation maximization algorithm and the cluster-and-label algorithm, have been adapted to our choice modeling problem setting. We also develop two new algorithms based on the cluster-and-label algorithm. The new algorithms use the Bayesian Information Criterion to evaluate a clustering setting to automatically generate new clusters out of existing clusters and adjust the number of clusters. Two computational studies focusing on travel demand forecasting (i.e., a hotel booking case and a large-scale airline itinerary shopping case) are presented to evaluate the prediction accuracy and computational effort of the proposed algorithms. Algorithmic recommendations are rendered under various scenarios based on the hotel booking case while economic insights are derived based on the itinerary shopping case. [ABSTRACT FROM AUTHOR]

Massive Radio Frequency Identification (RFID) data sets are expected to become commonplace in supply chain management systems. Warehousing and mining this data is an essential problem with great potential benefits for inventory management, object tracking, and product procurement processes. Since RFID tags can be used to identify each individual item, enormous amounts of location-tracking data are generated. With such data, object movements can be modeled by movement graphs, where nodes correspond to locations and edges record the history of item transitions between locations. In this study, we develop a movement graph model as a compact representation of RFID data sets. Since spatiotemporal as well as item information can be associated with the objects in such a model, the movement graph can be huge, complex, and multidimensional in nature. We show that such a graph can be better organized around gateway nodes, which serve as bridges connecting different regions of the movement graph. A graph-based object movement cube can be constructed by merging and collapsing nodes and edges according to an application-oriented topological structure. Moreover, we propose an efficient cubing algorithm that performs simultaneous aggregation of both spatiotemporal and item dimensions on a partitioned movement graph, guided by such a topological structure. [ABSTRACT FROM AUTHOR]