dist_mah

dist_ma

Calculate the Mahalanobis distance between two groups in a high-dimensional space (d &gt; n), using a ridge correction on the covariance matrix to ensure invertibility. The method also supports a single-member cluster and works in low-dimensional settings without a ridge correction.

We provide three distance metrics for measuring the separation between two clusters in high-dimensional spaces. The first metric is the centroid distance, which calculates the Euclidean distance between the centers of the two groups. The second is a ridge Mahalanobis distance, which incorporates a ridge correction constant, alpha, to ensure that the covariance matrix is invertible. The third metric is the maximal data piling distance, which computes the orthogonal distance between the affine spaces spanned by each class. These three distances are asymptotically interconnected and are applicable in tasks such as discrimination, clustering, and outlier detection in high-dimensional settings.

Jung Ae Lee

distanceHD

Distance Metrics for High-Dimensional Clustering

Jeongyoun Ahn

dist_mah function

<dl> <dt>x</dt>
<dd><code>x</code> is n by d matrix</dd> <dt>group</dt>
<dd><code>group</code> is a binary group label with the length of n1 and n2</dd><dt>alpha</dt>
<dd><code>alpha</code> is a positive numeric value representing the ridge correction constant. If not specified, the default value is set to \(\sqrt{\log(d)/n}\).</dd>
 </dl>

Arguments

Jung Ae Lee &lt;jungae.lee@umassmed.edu&gt;

Author

ridge Mahalanobis distance between two groups — dist_mah

<dl>

 <dt>x</dt>
<dd><code>x</code> is n by d matrix</dd>

 <dt>group</dt>
<dd><code>group</code> is a binary group label with the length of n1 and n2</dd>

<dt>alpha</dt>
<dd><code>alpha</code> is a positive numeric value representing the ridge correction constant. If not specified, the default value is set to \(\sqrt{\log(d)/n}\).</dd>
 </dl>

dist_mah: ridge Mahalanobis distance between two groups

Description

Usage

Value

Arguments

Author

Examples