Coordinate change

As explained in Deep Learning with R, Third Edition

A coordinate change is a transformation that expresses points using a different coordinate system.

A coordinate change transforms points into a different coordinate system so that the underlying task becomes easier. For black-and-white point classification, a suitable change can turn a complicated boundary into the simple rule “black points have x > 0” and “white points have x < 0.” section 1.4

Reading a clock

Suppose an image contains a clock face. First, extract the (x, y) coordinates of each clock hand’s tip. Then change those Cartesian coordinates into polar coordinates centered on the clock. The resulting angles make the problem simple enough for rounding and dictionary lookup to recover the approximate time, without machine learning. section 5.4.2

Coordinate changes are a form of feature engineering: they express data in a simpler, better-organized form. They can make a classical machine-learning problem easy, but designing useful transformations requires understanding the problem. Modern neural networks can often learn useful representations automatically, reducing the need for manual transformations. section 5.4.2 section 1.4

Figure 1.4 Coordinate change

Visualizes how the same points become easier to separate after changing coordinates. section 1.4

Figure 5.17 Feature engineering for reading the time on a clock

Illustrates coordinate change as a feature-engineering step for recognizing clock times. section 5.4.2

How Deep Learning with R, Third Edition covers it

How deep it goes

Explains hand-designed point separation and Cartesian-to-polar conversion, but does not develop formal coordinate mathematics.

Examples

Uses black-and-white point classification and clock-hand angles as concrete transformation examples.

What it assumes

Assumes basic point coordinates and problem understanding, while introducing representation design through concrete examples.

What you can do after

Apply it by redesigning input features so a simple rule or machine-learning algorithm can solve the task.

How it connects

Connects coordinate change with feature engineering, classification, polar coordinates, and automatic feature extraction by neural networks.

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Also explained in

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  Deep Learning with Python, Third EditionA transformation that converts data points into a different coordinate system to obtain a more useful representation.

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Related concepts

• feature engineeringused by · Feature engineering is the creation, transformation, or selection of input features from data to provide useful representations for analysis or modeling.
• getBoundingClientRectuses · getBoundingClientRect is a DOM method that returns an element's size and position relative to the viewport.
• polar coordinateproduces · A polar coordinate specifies a point in two-dimensional space by its distance from an origin and its angle relative to a reference direction.
• coordinateuses · A coordinate is a numerical value or ordered set of values specifying a position relative to a coordinate system.
• rotationuses · A rotation is a geometric transformation that turns points or objects about a fixed center, origin, or axis through an angle while preserving distances and angles.

This explainer was generated by Manning's knowledge graph from the text of Deep Learning with R, Third Edition. The section links point to the parts of the book it draws on.