## Knowledge Base - Technical Articles

## FAQ: What is the Jenks optimization method?

Article ID: | 26442 |
---|---|

Software: | ArcView GIS 3.0, 3.0a, 3.0b, 3.1, 3.2, 3.2a, 3.3 ArcInfo Workstation 7.0.4, 7.1.1, 7.1.2, 7.2.1, 8.0.1, 8.0.2, 8.1, 8.1.2, 8.2, 8.3, 9.0, 9.1, 9.2, 9.3, 9.3.1, 10 ArcGIS - ArcEditor 8.1, 8.1.2, 8.2, 8.3, 9.0, 9.1, 9.2, 9.3, 9.3.1, 10 ArcGIS - ArcInfo 8.0.1, 8.0.2, 8.1, 8.1.2, 8.2, 8.3, 9.0, 9.1, 9.2, 9.3, 9.3.1, 10 ArcGIS - ArcView 8.1, 8.1.2, 8.2, 8.3, 9.0, 9.1, 9.2, 9.3, 9.3.1, 10 |

Platforms: | N/A |

#### Question

What is the Jenks optimization method?

#### Answer

Some Esri products use the Jenks optimization method to classify features using natural breaks in data values. The Jenks optimization method is also known as the goodness of variance fit (GVF). It is used to minimize the squared deviations of the class means. Optimization is achieved when the quantity GVF is maximized:

1. Calculate the sum of squared deviations between classes (SDBC).

GVF = -------------------

2. Calculate the sum of squared deviations from the array mean (SDAM).

3. Subtract the SDBC from the SDAM (SDAM-SDBC). This equals the sum of the squared deviations from the class means (SDCM).

The method first specifies an arbitrary grouping of the numeric data. SDAM is a constant and does not change unless the data changes. The mean of each class is computed and the SDCM is calculated. Observations are then moved from one class to another in an effort to reduce the sum of SDCM and therefore increase the GVF statistic. This process continues until the GVF value can no longer be increased.

• Jenks, George F. 1967. "The Data Model Concept in Statistical Mapping", International Yearbook of Cartography 7: 186-190.

1. Calculate the sum of squared deviations between classes (SDBC).

GVF = -------------------

2. Calculate the sum of squared deviations from the array mean (SDAM).

3. Subtract the SDBC from the SDAM (SDAM-SDBC). This equals the sum of the squared deviations from the class means (SDCM).

The method first specifies an arbitrary grouping of the numeric data. SDAM is a constant and does not change unless the data changes. The mean of each class is computed and the SDCM is calculated. Observations are then moved from one class to another in an effort to reduce the sum of SDCM and therefore increase the GVF statistic. This process continues until the GVF value can no longer be increased.

**Further Reading**• Jenks, George F. 1967. "The Data Model Concept in Statistical Mapping", International Yearbook of Cartography 7: 186-190.

The steps presented in this article are to provide the concept of involved events and are not be used as a specific solution. For more specific assistance, please call our Technical Support department.

#### Related Information

*Created:* 3/17/2004

*Last Modified:* 2/27/2012