Where does kernel collide?

The part of an operating system that runs in privileged mode and mediates between the hardware and the programs above it, controlling processes, memory, and access to devices. In On Micro-Kernel Construction Liedtke argued in 1995 that a concept belongs in the kernel only if moving it out would stop the system working, and the long argument between monolithic kernels (Unix, Linux) and microkernels is about how much to place inside this privileged core. The referent is a piece of running software; the unit is a body of code with a defined boundary of privilege, and it differs from every other meaning here because nothing in it is a function or a set: it is something that executes.[1]

Unit

A privileged body of operating-system code

Recovery means

Not applicable

Measured by

Read from a system's design: which code runs in privileged mode and mediates access to hardware

In kernel methods a kernel is a function that returns the inner product of two inputs after they are mapped into a higher-dimensional feature space, so it reports their similarity without ever computing that mapping. Boser, Guyon, and Vapnik used this trick in 1992 to build the support vector machine, replacing dot products with a kernel and so fitting a linear separator in a space that can be very large or even infinite; the idea traces to Aizerman, Braverman, and Rozonoer's potential-function method of 1964. The referent is a bivariate function on pairs of data points; the unit is a positive-definite kernel, and it differs from the operating-system meaning because nothing runs, and from the mathematical meaning because it maps a pair to a number, not to zero.[2]

Unit

A positive-definite similarity function on pairs of points

Recovery means

Not applicable

Measured by

Set by the modeller: a chosen kernel function evaluated on pairs of inputs

The kernel of a linear map, or of a group or ring homomorphism, is the set of elements the map sends to the zero element or identity, and its size records how far the map is from being one-to-one: the map is injective exactly when its kernel is trivial. Axler treats this in Linear Algebra Done Right, where the kernel, also called the null space, is a subspace of the domain. The referent is a subset of an algebraic structure; the unit is a subspace or normal subgroup, and it differs from the statistical and machine-learning meanings because it names a set of inputs rather than a weighting or a similarity, and it shares nothing with the operating-system meaning at all.[3]

Unit

A subspace or normal subgroup of the domain

Recovery means

Not applicable

Measured by

Derived by proof: the elements a given map sends to zero

In kernel density estimation a kernel is a weighting function, usually a symmetric probability density, placed over each observed point and summed to produce a smooth estimate of the underlying distribution. Rosenblatt introduced the idea in 1956, and Parzen generalised it in 1962 in On Estimation of a Probability Density Function and Mode, fixing the estimator's shape together with a bandwidth that sets how much it smooths. The referent is a fixed weighting function chosen by the analyst; the unit is a normalised kernel that integrates to one, and it shares only the word with the machine-learning kernel: here the function spreads weight over space around one point rather than measuring similarity between two.[4][5]

Unit

A normalised weighting function that integrates to one

Recovery means

Not applicable

Measured by

Chosen by the analyst: a weighting function summed over the observed points, with a bandwidth