LoCA was performed on several data sets. The summary images show the 16 basis vectors minimizing the reconstruction error, where each vector is represented by an object/graph pair. The object represents the average item of the data set, and the arrows indicate the degree that the object changes as the corresponding shape parameter is varied.
The graphs plot the magnitude of basis vector's effect on a point against the point's distance to the vector's "center point". The center point of the region is defined as the point that minimizes our cost function.
The example on the right corresponds to the animation above. One can see that PCA generates a global deformation, bending the corpus callosum in half. In contrast, LoCA generates a localized deformation that expands the genu and leaves everything else alone.
The accompanying movies show how the shape parameters alter objects in the space. Each parameter is controlled by a slider, and is initially set to 0. The ends of each slider are capped at 4 standard deviations away from 0. Each slider doubles as a histogram showing how many objects from the original data set have a particular value for the corresponding parameter.
55 2D tracings of corpora callosa were used, each consisting of 103 points.
Principal Components Analysis7/54 vectors required to get 90% variation 
Localized Components AnalysisParameters set so 26/54 vectors required to get 90% variation 

First basis vectors (Large image) (Movie) 
First basis vectors (Large image) (Movie) 
Principal Components Analysis26/135 vectors required to get 90% variation 
Localized Components AnalysisParameters set so that 82/135 vectors were required to get 90% variation 

Front view of the first vectors (Large image) (Movie) 
Front view of the first vectors (Large image) (Movie) 
Side view of the first vectors (Large image) (Movie) 
Side view of the first vectors (Large image) (Movie) 
Symmetric Localized Components Analysis
In addition to distance, symmetry is taken into account to determine compatibility. Parameters were set so that 64/135 vectors were required for 90% variation 

First basis vectors (front view) (Large image) (Movie) 
First 16 basis vectors (side view) (Large image) (Movie) 
First 16 basis vectors (under) (Large image) (Movie) 
Principal Components Analysis17/54 vectors required to get 90% variation 
Symmetric Localized Components AnalysisParameters set so that 31/54 vectors were required to get 90% variation 


