Reverse Engineering

What are Parametric and Non-parametric Modeling

In the past, designers resorted to the physical measurement of the product to redraw its geometry. Today, designers use 3D scanners to capture measurements. The scanned data is then imported to CAD, where the design can be analyzed, processed, manipulated, and refined. Two key aspects that fall in place when focusing on the reverse engineering process are:

Parametric Model/Modeling

A parametric model captures all its information about the data within its parameters. All you need to know to predict a future data value from the model's current state is its parameters. The parameters are usually finite in dimensions. Knowing the parameters for a parametric model to predict new data is enough. A parametric model is one where we assume the 'shape' of the data and, therefore, only have to estimate the coefficients of the model. A significant advantage of parametric modeling is that it compactly describes the underlying process, making further data processing more accessible. However, most work in parametric system identification relies on the assumption of time-invariance of the system and stationarity of the observed signal. But this assumption is not valid for all signals. In these cases, a heuristic approach often determines the optimal reduced model.

Parametric models keep a history of the parameters that determine a model's geometry. As a result, they allow the user to explore different design options while minimizing edit time. Similarly, parametric models can be visualized in 3D drawing programs. It means that they can more closely simulate the actual behavior of the original project.

Non-parametric Model/Modeling

A non-parametric model can capture more subtle aspects of the data. It allows more information to pass from the current set of data attached to the model at the current state to predict future data. The parameters are usually said to be infinite in dimensions. Hence, it can express the characteristics in the data much better than parametric models. For a non-parametric model, predicting future data is based not just on the parameters but also on the observed data state. A non-parametric model is one where we do not assume the 'shape' of the data, and we have to estimate the most suitable form of the model, along with the coefficients.

Parametric models require a fixed number of parameters, while non-parametric ones don't. The former is better for models with well-defined and predictable input data. Non-parametric models can be trained with a more significant number of data. However, the disadvantages of a parametric model are greater training time. While both models effectively predict the future, the latter tends to produce better results. The former requires less training data but is faster than non-parametric methods. Non-parametric models have the disadvantage of overfitting because they need many observations to approximate f. Non-parametric models have a much lower precision rate but can produce better-fitting models.

As for the disadvantages of both models, parametric models are generally easier to understand and use. Besides requiring less training data, parametric models tend to produce poorer results. It is why they are more popular. However, the benefits of non-parametric algorithms are far outweighed by their disadvantages. The latter is often better for data that are not linear or have many missing values. Parametric models use different methods to estimate model parameters.

Parametric modeling is based on mathematical functions, while non-parametric models are based on data. The difference between the two is a big one and can make the difference between success and failure in the field of statistics.

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