Star Coordinate Dimension Arrangement using Euclidean Distance and Pearson Correlation

On Clustering Time Series Using Euclidean Distance and Pearson Correlation

For time series comparisons, it has often been observed that z-score normalized Euclidean distances far outperform the unnormalized variant. In this paper we show that a z-score normalized, squared Euclidean Distance is, in fact, equal to a distance based on Pearson Correlation. This has profound impact on many distance-based classification or clustering methods. In addition to this theoretical...

Coordinate Shadows of Semidefinite and Euclidean Distance Matrices

We consider the projected semi-definite and Euclidean distance cones onto a subset of the matrix entries. These two sets are precisely the input data defining feasible semi-definite and Euclidean distance completion problems. We classify when these sets are closed, and use the boundary structure of these two sets to elucidate the Krislock-Wolkowicz facial reduction algorithm. In particular, we ...

Euclidean distance matrix analysis: a coordinate-free approach for comparing biological shapes using landmark data.

For problems of classification and comparison in biological research, the primary focus is on the similarity of forms. A biological form can be conveniently defined as consisting of size and shape. Several approaches for comparing biological shapes using landmark data are available. Lele (1991a) critically discusses these approaches and proposes a new method based on the Euclidean distance matr...

Complex networks embedded in space: Dimension and scaling relations between mass, topological distance and Euclidean distance

Thorsten Emmerich,1 Armin Bunde,1 Shlomo Havlin,2 Guanliang Li,3 and Daqing Li4 1Institut für Theoretische Physik, Justus-Liebig-Universität Giessen, 35392 Giessen, Germany 2Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel 3Center for Polymer Studies, Department of Physics, Boston University, Boston, Massachusetts 02215, USA 4School of Reliability and Systems Engineering, Bei...

Pearson Product-Moment Correlation