Coordinate change

As explained in Deep Learning with Python, Third Edition

A transformation that converts data points into a different coordinate system to obtain a more useful representation.

A coordinate change converts data into a new representation where the task becomes easier. Instead of separating points with a complicated rule, choose coordinates that expose a simple boundary. section 1.4

Separating black and white points

Suppose points are labeled black or white in an (x, y) system. A hand-designed coordinate change can make the classes separable by one threshold: black points have x > 0, while white points have x < 0. The transformation supplies the useful representation; the threshold supplies the simple rule. section 1.4

Reading a clock

Extract the tips of the clock hands as Cartesian coordinates, then change those coordinates to polar form around the image center. The resulting hand angles can make time recognition simple enough for rounding and dictionary lookup, without machine learning. section 5.4.2

Use these practical rules:

• Designing a useful coordinate change by hand requires understanding the problem; digit-image rules based on loops or pixel histograms can be effective but brittle. section 1.4
• Treat coordinate changes as feature engineering: organize the data so its underlying structure becomes smoother, simpler, and easier to learn. section 5.4.2

Figure 1.4 Coordinate change

Use the coordinate-change figure to compare the original point arrangement with its more useful representation. section 1.4

How Deep Learning with Python, Third Edition covers it

How deep it goes

Defines the transformation through point classification and clock recognition, but stops short of formal derivations.

Examples

Uses separated black-and-white points, handwritten-digit features, and Cartesian-to-polar clock-hand coordinates.

What it assumes

Assumes basic coordinates and classification, while motivating why useful representations are difficult to design for complex data.

What you can do after

Apply via feature engineering to express data in coordinates that support simpler rules or reduce the need for learning.

How it connects

Links coordinate change to feature engineering, data representation, machine learning, and convolutional neural networks.

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Also explained in

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  Deep Learning with R, Third EditionA coordinate change is a transformation that expresses points using a different coordinate system.

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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 Python, Third Edition. The section links point to the parts of the book it draws on.