## Pade¶

Replaces a continuous class with a derivative or a MQC by one or more continuous attributes.

### Signals¶

- Inputs:
- Classified Examples (ExampleTableWithClass)
Input data set.

- Outputs:
- Classified Examples (ExampleTableWithClass)
Output data set.

### Description¶

This widget implements several techniques for assessing partial derivatives of the class variable for the given set of examples. The derivative is appended to the example table as a new class attribute. The widget can compute either quantitative derivative by a chosen continuous attribute or a qualitative derivative by one or more attributes.

The widget is implemented to cache some data. After, for instance, computing
the derivatives by `x` and `y` separately, the widget has already
stored all the data to produce the derivatives by both in a moment.

The `Attributes` box lists all continuous attributes and lets the user
select the attribute by which she wants to compute the qualitative derivative.
The selection is important only when the widget actually outputs a qualitative
derivative (this depends on other settings, described below). Buttons
`All` and `None` select the entire list and nothing.

Derivatives by more than one attribute are mathematically questionable, and computing by many attributes can be slow and messy. Methods that are based on triangulation will include all attributes in the triangulation, regardless of the selection, but then compute only the selected derivatives.

Box `Method` determines the used method and its settings. Available
methods are `First triangle`, `Star Regression`,
`Univariate Star Regression` and `Tube Regression`. First triangle is
unsuitable for data with non-negligible noise. Star regression seems to perform
rather poor; the quantitative derivatives it computes are even theoretically
wrong. Univariate Star Regression will handle noise well, but also work well
for very complex functions (like sin(x)sin(y) across several periods). Tube
regression is very noise resistant, which can lead it to oversimplify the
model, yet it is the only method that does not use the triangulation and is
thus capable of handling discrete attributes, unknown values and large number
of dimensions. It may be slow when the number of examples is very large.
Detailed description of these methods can be found in Zabkar and Demsar’s
papers.

`Ignore differences below` lets the user set a threshold for qualitative
derivatives.

The widget can also put some data in meta attributes: the
`Qualitative constraint`, as described above,
`Derivatives of selected attributes` and the
`Original class attribute`.

The changes take effect and the widget start processing when `Apply`
is hit.