Properties of Support Vector Machines

Support Vector Machines (SVMs) perform pattern recognition between two point classes by finding a decision surface determined by certain points of the training set, termed Support Vectors (SV). This surface, which in some feature space of possibly infinite dimension can be regarded as a hyperplane, is obtained from the solution of a problem of quadratic programming that depends on a regularization parameter. In this paper we study some mathematical properties of support vectors and show that the decision surface can be written as the sum of two orthogonal terms, the first depending only on the margin vectors (which are SVs lying on the margin), the second proportional to the regularization parameter. For almost all values of the parameter, this enables us to predict how the decision surface varies for small parameter changes. In the special but important case of feature space of finite dimension m, we also show that there are at most m+1 margin vectors and observe that m+1 SVs are usually sufficient to fully determine the decision surface. For relatively small m this latter result leads to a consistent reduction of the SV number.

Measuring Value in Product Development

“What is value in product development?” is the key question of this paper. The answer is critical to the creation of lean in product development. By knowing how much value is added by product development (PD) activities, decisions can be more rationally made about how to allocate resources, such as time and money.

Measuring Value in Product Development

“What is value in product development?” is the key question of this paper. The answer is critical to the creation of lean in product development. By knowing how much value is added by product development (PD) activities, decisions can be more rationally made about how to allocate resources, such as time and money. In order to apply the principles of Lean Thinking and remove waste from the product development system, value must be precisely defined. Unfortunately, value is a complex entity that is composed of many dimensions and has thus far eluded definition on a local level. For this reason, research has been initiated on “Measuring Value in Product Development.” This paper serves as an introduction to this research. It presents the current understanding of value in PD, the critical questions involved, and a specific research design to guide the development of a methodology for measuring value. Work in PD value currently focuses on either high-level perspectives on value, or detailed looks at the attributes that value might have locally in the PD process. Models that attempt to capture value in PD are reviewed. These methods, however, do not capture the depth necessary to allow for application. A methodology is needed to evaluate activities on a local level to determine the amount of value they add and their sensitivity with respect to performance, cost, time, and risk. Two conceptual tools are proposed. The first is a conceptual framework for value creation in PD, referred to here as the Value Creation Model. The second tool is the Value-Activity Map, which shows the relationships between specific activities and value attributes. These maps will allow a better understanding of the development of value in PD, will facilitate comparison of value development between separate projects, and will provide the information necessary to adapt process analysis tools (such as DSM) to consider value. The key questions that this research entails are: · What are the primary attributes of lifecycle value within PD? · How can one model the creation of value in a specific PD process? · Can a useful methodology be developed to quantify value in PD processes? · What are the tools necessary for application? · What PD metrics will be integrated with the necessary tools? The research milestones are: · Collection of value attributes and activities (September, 200) · Development of methodology of value-activity association (October, 2000) · Testing and refinement of the methodology (January, 2001) · Tool Development (March, 2001) · Present findings at July INCOSE conference (April, 2001) · Deliver thesis that captures a formalized methodology for defining value in PD (including LEM data sheets) (June, 2001) The research design aims for the development of two primary deliverables: a methodology to guide the incorporation of value, and a product development tool that will allow direct application.