Unsupervised Few-shot Learning via Deep Laplacian Eigenmaps

Learning a new task from a handful of examples remains an open challenge in machine learning. Despite the recent progress in few-shot learning, most methods rely on supervised pretraining or meta-learning on labeled meta-training data and cannot be applied to the case where the pretraining data is unlabeled. In this study, we present an unsupervised few-shot learning method via deep Laplacian eigenmaps. Our method learns representation from unlabeled data by grouping similar samples together and can be intuitively interpreted by random walks on augmented training data. We analytically show how deep Laplacian eigenmaps avoid collapsed representation in unsupervised learning without explicit comparison between positive and negative samples. The proposed method significantly closes the performance gap between supervised and unsupervised few-shot learning. Our method also achieves comparable performance to current state-of-the-art self-supervised learning methods under linear evaluation protocol

Vehicle routing and inventory control for in -bound logistics.

This dissertation is concerned with operational optimization of an in-bound logistics network with multiple suppliers and one manufacturing facility. A fleet having an unlimited number of capacitated trucks is responsible for transporting parts from suppliers to the manufacturing facility in order to support a scheduled production over a finite planning horizon. Assuming more than one truck can pick up parts at the same suppliers, i.e., split pick-ups are allowed, the problem is called the inventory routing problem with split pick-ups (IRPSP). The objective is to minimize the sum of inventory and transportation costs. The split pick-ups assumption allows more flexibility but it also introduces more complexity to the solution procedures. The multiple vehicle routing problem with split pick-ups (mVRPSP) is a sub-problem of the IRPSP and has been solved optimally using dynamic programming. In spite of potentially significant savings due to the allowance of split pick-ups, the mVRPSP has received less attention than has the conventional VRP. The research reported in this dissertation initially formulates the mVRPSP as an infinite state dynamic program and then reduces it to a finite state, finite action dynamic program. The reduced dynamic program is solved using a shortest path heuristic search which guarantees solution optimality. This approach significantly outperforms the mathematical programming-based approaches. We have applied an annealing-based heuristic to the IRPSP, where the problem decomposes into two sub-problems: inventory optimization and transportation problems. The inventory optimization problem for a given set of routes is solved using a linear program, and the transportation problem is solved by perturbing the current routes utilizing the information provided by the optimal solution to the linear program. Numerical studies suggest that the heuristic algorithm performs well in terms of solution quality and computational efficiency. We also investigated a structural characteristic of optimal solutions to the IRPSP. Independent of the unit inventory carrying cost, transportation cost dominates inventory cost in optimal solutions to the IRPSP. Numerical examples show that this property holds for the IRPSP with a finite planning horizon, dynamic demand, and routing among multiple suppliers. The property is proved for the IRPSP with an infinite horizon, stationary demand, and dedicated trips.Ph.D.Applied SciencesIndustrial engineeringOperations researchUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/127944/2/3029367.pd