Optimization Models
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1. Introduction
1.1. Overview
1.2. Optimization Models
2. Linear Algebra
2.1. Vectors
2.2. Matrices
2.3. Linear Equations
2.4.  Least-Squares
2.5. Eigenvalues
2.6  Singular Values
3. Convex Models
3.1. Convexity
3.2. LP and QP
3.3. SOCP
3.4. Robust LP
3.5. GP
3.6. SDP
3.7. Non-Convex Models
4. Duality
4.1. Weak Duality
4.2. Strong Duality
4.3.  Applications
5. Case Studies
5.1. Senate Voting
5.2. Antenna Arrays
5.3. Localization
5.4. Circuit Design

Senate Voting Analysis and Visualization

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In this case study, we take data from the votes on bills in the US Senate (2004-2006), shown as a table on the left, and explore how we can visualize the data by projecting it, first on a line then on a plane. We investigate how we can choose the line or plane in a way that maximizes the variance in the result, via a principal component analysis method. Finally we examine how a variation on PCA that encourages sparsity of the projection directions allows to understand which bills are most responsible for the variance in the data.

Source: VoteWorld.