1 / 9

Kernel Nearest Means in Feature Space for Euclidean Distances

Learn about the efficient computation of distances to means in feature space using the Kernel Nearest Means algorithm, allowing for Euclidean distance calculations in different feature spaces. Transform your data effortlessly!

sammyt
Download Presentation

Kernel Nearest Means in Feature Space for Euclidean Distances

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Kernel nearest means Usman Roshan

  2. Feature space transformation • Let Φ(x) be a feature space transformation. • For example if we are in a two-dimensional vector space and x=(x1, x2) then

  3. Computing Euclidean distances in a different feature space • The advantage of kernels is that we can compute Euclidean and other distances in different features spaces without explicitly doing the feature space conversion.

  4. Computing Euclidean distances in a different feature space • First note that the Euclidean distance between two vectors can be written as • In feature space we have where K is the kernel matrix.

  5. Computing distance to mean in feature space • Recall that the mean of a class (say C1) is given by • In feature space the mean Φm would be

  6. Computing distance to mean in feature space

  7. Computing distance to mean in feature space

  8. Computing distance to mean in feature space • Replace K(m,m) and K(m,x) with calculations from previous slides

  9. Kernel nearest means algorithm • Compute kernel • Let xi (i=0..n-1) be the training datapoints and yi (i=0..n’-1) the test. • For each mean mi compute K(mi,mi) • For each datapoint yi in the test set do • For each mean mj do • dj = K(mj,mj) + K(yi,yi) - 2K(mi,yj) • Assign yi to the class with the minimum dj

More Related