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Winner Determination of Combinatorial Auction Using the Knapsack Problem
http://doi.org/10.5626/JOK.2020.47.7.629
In combinatorial auctions, bidders can make bids on a set of items. When the items show complementarities in values, combinatorial auctions make it possible to express the values more accurately and enhance the market’s efficiency. The winner determination problem is an NP-complete problem. To address this difficult and important problem, we can attempt to solve the special subproblem that can be solved efficiently or develop approximate solutions. In this paper, we reformulated the WDP into a knapsack problem. By using Markov chain Monte Carlo method, we achieved a desired stationary solution with a large objective function. The solution is comparable to that of integer programming.
Infinite Latent Topic Models for Document Analysis
http://doi.org/10.5626/JOK.2018.45.7.701
Since the concept of the topic is highly abstract, the characterization of the topics of a text is not clearly defined. Depending on the problem’s context or needs, various levels of detail may be provided, which could make it difficult to automatically analyze documents. This paper presents infinite topic extensions to the well-known model of Latent Dirichlet Allocation (LDA) i.e., the infinite Latent Dirichlet Topic model and the infinite Latent Markov Topic model. The first model simply relaxes the constraint of fixed known number of topics in LDA using the method of the Dirichlet process. The second model further extends it by including Markov dynamics that captures the sequential evolution of topics in a text. Both models are theoretically rigorous and structurally flexible, as well as being capable of capturing document organizations at a desired level of topics. A set of experiments show interesting results and a more intuitive topic characterization and local stationarity properties than related models with Gibbs sampling and variational inferences.
Parallel Gaussian Processes for Gait and Phase Analysis
This paper proposes a sequential state estimation model consisting of continuous and discrete variables, as a way of generalizing all discrete-state factorial HMM, and gives a design of gait motion model based on the idea. The discrete state variable implements a Markov chain that models the gait dynamics, and for each state of the Markov chain, we created a Gaussian process over the space of the continuous variable. The Markov chain controls the switching among Gaussian processes, each of which models the rotation or various views of a gait state. Then a particle filter-based algorithm is presented to give an approximate filtering solution. Given an input vector sequence presented over time, this finds a trajectory that follows a Gaussian process and occasionally switches to another dynamically. Experimental results show that the proposed model can provide a very intuitive interpretation of video-based gait into a sequence of poses and a sequence of posture states.
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