Generalized Low-Rank Approximations

We study the frequent problem of approximating a target matrix with a matrix of lower rank. We provide a simple and efficient (EM) algorithm for solving {\\em weighted} low rank approximation problems, which, unlike simple matrix factorization problems, do not admit a closed form solution in general. We analyze, in addition, the nature of locally optimal solutions that arise in this context, demonstrate the utility of accommodating the weights in reconstructing the underlying low rank representation, and extend the formulation to non-Gaussian noise models such as classification (collaborative filtering).

Applying the Lessons of “Lean Now” to Transform the US Aerospace Enterprise

Lean is common sense and good business sense. As organizations grow and become more successful, they begin to lose insight into the basic truths of what made them successful. Organizations have to deal with more and more issues that may not have anything to do with directly providing products or services to their customers. Lean is a holistic management approach that brings the focus of the organization back to providing value to the customer. In August 2002, Mrs. Darleen Druyun, the Principal Deputy to the Assistant Secretary of the Air Force for Acquisition and government co-chairperson of the Lean Aerospace Initiative (LAI), decided it was time for Air Force acquisitions to embrace the concepts of lean. At her request, the LAI Executive Board developed a concept and methodology to employ lean into the Air Force’s acquisition culture and processes. This was the birth of the “Lean Now” initiative. An enterprise-wide approach was used, involving Air Force System Program Offices (SPOs), aerospace industry, and several Department of Defense agencies. The aim of Lean Now was to focus on the process interfaces between these “enterprise” stakeholders to eliminate barriers that impede progress. Any best practices developed would be institutionalized throughout the Air Force and the Department of Defense (DoD). The industry members of LAI agreed to help accelerate the government-industry transformation by donating lean Subject Matter Experts (SMEs) to mentor, train, and facilitate the lean events of each enterprise. Currently, the industry SMEs and the Massachusetts Institute of Technology are working together to help the Air Force develop its own lean infrastructure of training courses and Air Force lean SMEs. The first Lean Now programs were the F/A-22, Global Hawk, and F-16. Each program focused on specific acquisition processes. The F/A-22 focused on the Test and Evaluation process; the Global Hawk focused on Evolutionary Acquisitions; and the F-16 focused on improving the Contract Closeout process. Through lean, each enterprise made many significant improvements. The F/A-22 was able to reduce its Operational Flight Plan (OFP) Preparation and Load process time of 2 to 3 months down to 7 hours. The Global Hawk developed a new production plan that increases the annual production of its Integrated Sensor Suite from 3 per year to 6 per year. The F-16 enterprise generated and is working 12 initiatives that could result in a contract closeout cycle time reduction of 3 to 7 years. Each enterprise continues to generate more lean initiatives that focus on other areas and processes within their respective enterprises.