Feature map

As explained in Machine Learning Algorithms in Depth

A feature map is a function that represents input objects as vectors in a feature space, possibly an infinite-dimensional one.

A feature map represents input objects as vectors in a feature space, which may be infinite-dimensional. In convolutional neural networks, a trainable kernel slides across an input, computes a dot product at each position, and gathers the resulting scalars into a feature-map output. section 10.2 section 6.5

Feature maps serve two related purposes:

• Expose local responses to learned filters while preserving translation-related structure in image, time-series, or volumetric inputs. section 10.2
• Provide a transformed space in which inner products can be replaced by kernel evaluations, avoiding explicit vector construction. section 6.5
• Shrink spatial dimensions through pooling while increasing learned feature channels across stacked convolutional layers. section 10.2.1

LeNet feature maps for MNIST

A LeNet-style classifier applies convolution, ReLU activation, and max pooling repeatedly. It learns more features by increasing the number of filters, reduces feature-map dimensions through pooling, then flattens the final map before a dense softmax classifier. The implementation trains and evaluates the model on MNIST. section 10.2.1

(10.8)

Use the convolution figure to trace how sliding-kernel dot products become a feature-map output. section 10.2

How Machine Learning Algorithms in Depth covers it

How deep it goes

Derives convolutional construction and pooling roles, but leaves infinite-dimensional feature maps implicit rather than explicitly representing them.

Examples

Uses sliding-kernel outputs, LeNet on MNIST, max pooling, and Gaussian-kernel feature spaces as concrete examples.

What it assumes

Assumes familiarity with vectors, dot products, kernels, neural-network layers, and basic supervised learning.

What you can do after

Evaluate how convolution and pooling transform inputs, and understand when kernel evaluations replace explicit feature vectors.

How it connects

Connects feature maps to convolution, pooling, kernel trick, Gaussian process regression, ReLU, and softmax classification.

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Also explained in

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  Deep Learning with R, Third EditionA feature map is a spatial array of activations indicating the presence or strength of a learned visual pattern at different image locations.
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  Grokking Machine LearningA mapping that sends data points from an original input space into another feature space, usually of higher dimension.
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  Grokking AI Algorithms, Second EditionA feature map is a spatially organized array of activation values representing learned features at different locations in an input or intermediate image representation.
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  Math and Architectures of Deep LearningA spatial array of activation values produced by applying a convolution or pooling operation over an input image or prior layer output.
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  Deep Learning with Python, Third EditionA spatial grid of activations produced by a convolutional or pooling layer, where each channel encodes the presence of a learned feature over locations.
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  Sutskever's ListA spatial array of responses produced by applying a convolutional filter to an input.
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  Learn Generative AI with PyTorchAn intermediate activation map in a neural network whose spatial resolution can be increased or preserved by convolutional operations.

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Related concepts

• convolutional layerproduced by · A convolutional layer is a neural-network layer that applies shared learned filters to local regions of structured input to produce feature representations.
• kernel functionproduced by · A kernel function is a mathematical function that measures similarity between pairs of inputs, often representing an inner product in an implicit feature space.
• convolution kernelproduced by · A convolution kernel is a small array or tensor of weights applied across local input regions to compute weighted responses and detect or transform patterns.
• Region Proposal Networkused by · A Region Proposal Network is a neural-network module that generates candidate object regions from image features for a two-stage detector.
• channelhas part · A channel is an independent component or dimension of image or tensor data carrying a distinct color, feature, activation, or value stream.
• max poolingused by · Max pooling is an aggregation operation that replaces each local or grouped region with its maximum value, often to downsample a representation.

This explainer was generated by Manning's knowledge graph from the text of Machine Learning Algorithms in Depth. The section links point to the parts of the book it draws on.