Reducing Dimensionality

Antoine Guillot explains some of the basic concepts of variable reduction in a data analysis:

Each of these people can be represented as points in a 3 Dimensional space. With a gross approximation, each people is in a 50*50*200 (cm) cube. If we use a resolution of 1cm and three color channels, then can be represented by 1,000,000 variables.
On the other hand, the shadow is only in 2 dimensions and in black and white, so each shadow only needs 50*200=10,000 variables.
The number of variables was divided by 100 ! And if your goal is to detect human vs cat, or even men vs women, the data from the shadow may be enough.

Read on for intuitive discussions of techniques like principal component analysis and linear discriminant analysis.  H/T R-Bloggers

Related Posts

Biases in Tree-Based Models

Nina Zumel looks at tree-based ensembling models like random forest and gradient boost and shows that they can be biased: In our previous article , we showed that generalized linear models are unbiased, or calibrated: they preserve the conditional expectations and rollups of the training data. A calibrated model is important in many applications, particularly when financial data […]

Read More

Comparing Poisson Regression to Regressing Against Logs

Nina Zumel compares a pair of methods for performing regression when income is the dependent variable: Regressing against the log of the outcome will not be calibrated; however it has the advantage that the resulting model will have lower relative error than a Poisson regression against income. Minimizing relative error is appropriate in situations when […]

Read More


August 2017
« Jul Sep »