Objective
- Notice the image below. See how a 'sector' has been cut off from the canvas? That is the data not available for training. We will be training on various conditions and see the model performance visually.
- As for the overall data, see how the color is constant across the angles as long as the distance from the center is the same
- There are two ways of representing this data, Cartesian and Polar
- In the Cartesian coordinate system, we have the Abscissa and the Ordinate,
- In the Polar coordinate system we have \(r\) and \(\theta\)
- The color is the output variable we need to predict
- And given that the color is varying across \(r\) and constant with respect to \(\theta\), for this case, it is better to have the data in polar coordinates.
- However, in real life machine learning use cases, we are often not sure about the relationship between the input and the output variables to foresee the best transformation of the \(x\) variables.
- And we generally pick the best model based on the best performance.
- The objective of this exercise is to observe how a given representation of the data can be beneficial for model training and complexity
Scenarios
Model Types and variations. Overall, we have 4 scenarios.
- Linear Regressor Single Layer
- Cartesian type data
- Polar type data
- Linear Regressor Multi Layer
- Cartesian type data
- Polar type data
Note that with Polar type data, it is theoretically easier to perform the training and get a better performance. Cartesian on the other hand should need a complex model or longer training to get reasonable performance. We will however, do not dwell into the model performance metrics in the traditional sense. We will use purely visual information for this study. The grey portion right hand side plot below is the one that will be used as the test dataset.
Comparison of the 4 scenarios
- [TOP LEFT] Linear Regressor Single Layer with Cartesian type data
- Trains Slowly and overall result at the end of the 20th epoch is poor
- [TOP RIGHT] Linear Regressor Single Layer with Polar type data
- The overall result is better than the one with polar coordinates
- [BOTTOM LEFT] Linear Regressor Multi Layer with Cartesian type data
- Trains better than its single layer counterpart and the end result does not look bad at all
- [BOTTOM RIGHT] Linear Regressor Multi Layer with Polar type data
- Trains fastest in terms of number of epochs