Using visual distortion to emphasize targeted regions of data visualizations according to geodesic curves

A computer system, comprising:

• one or more processors;
• memory;
• a display;
• and
• one or more programs stored in the memory and configured for execution by the one or more processors, the one or more programs comprising instructions for:
• visualizing on the display a set of data according to a first data space having a first number of dimensions;
• receiving user selection of a focus point in the first data space;
• constructing a set of geodesics using the focus point as a starting point, each geodesic configured to connect the focus point to a respective data point in the first data space, wherein a vector field formed by the geodesics defines a matrix;
• computing a second number of primary eigenvectors for the matrix, wherein the second number is less than the first number;
• for each data point, determining a respective second number of projection values, each of which is associated with a distinct one of the primary eigenvectors, wherein the projection values form a second data space having the second number of dimensions;
• and
• re-visualizing the set of data in the second data space using the respective second number of projection values of each data point in the set of data, thereby facilitating subsequent analysis of the set of data visualized in the second data space, which has fewer dimensions than the first data space, with a focus on the focus point.

A non-transitory computer readable storage medium storing one or more programs configured for execution by a computer system having one or more processors, memory, and a display, the one or more programs comprising instructions for:

• visualizing on the display a set of data according to a first data space having a first number of dimensions;
• receiving user selection of a focus point in the first data space;
• constructing a set of geodesics using the focus point as a starting point, each geodesic configured to connect the focus point to a respective data point in the first data space, wherein a vector field formed by the geodesics defines a matrix;
• computing a second number of primary eigenvectors for the matrix, wherein the second number is less than the first number;
• for each data point, determining a respective second number of projection values, each of which is associated with a distinct one of the primary eigenvectors, wherein the projection values form a second data space having the second number of dimensions;
• and
• re-visualizing the set of data in the second data space using the respective second number of projection values of each data point in the set of data, thereby facilitating subsequent analysis of the set of data visualized in the second data space, which has fewer dimensions than the first data space, with a focus on the focus point.