Landmark point selection
An exemplary method comprises receiving data points, selecting a first subset of the data points to generate an initial set of landmarks, each data point of the first subset defining a landmark point and for each non-landmark data point: calculating first data point distances between a respective non-landmark data point and each landmark point of the initial set of landmarks, identifying a first shortest data point distance from among the first data point distances between the respective non-landmark data point and each landmark point of the initial set of landmarks, and storing the first shortest data point distance as a first landmark distance for the respective non-landmark data point. The method further comprising identifying a non-landmark data point with a longest first landmark distance in comparison with other first landmark distances and adding the identified non-landmark data point associated as a first landmark point to the initial set of landmarks.
1. A method comprising:
receiving multidimensional data points;
selecting a first subset of the multidimensional data points to generate a set of multidimensional landmark points, each multidimensional data point of the first subset being a multidimensional landmark point and each multidimensional data point that is not in the first subset being a multidimensional non-landmark point;
while a number of multidimensional landmark points in the set of multidimensional landmark points is less than a threshold:
for each multidimensional non-landmark data point:
calculating data point distances between that multidimensional non-landmark data point and each multidimensional landmark point of the set of multidimensional landmark points, wherein the multiple dimensions of the respective multidimensional non-landmark data point and the multiple dimensions of each multidimensional landmark point of the set of landmarks are utilized in calculating the data point distances;
identifying a shortest data point distance from among the data point distances between the respective multidimensional non-landmark data point and each multidimensional landmark point of the initial set of multidimensional landmark points; and
storing the shortest data point distance as a landmark distance for the respective multidimensional non-landmark data point;
identifying a multidimensional non-landmark data point with a longest landmark distance in comparison with other landmark distances of other multidimensional non-landmark data points; and
adding the multidimensional non-landmark data point associated with the longest landmark distance as a multidimensional landmark point to the set of multidimensional landmark points to increase the number of multidimensional landmark points in the set of multidimensional landmarks points.
2. The method of claim 1 wherein the set of multidimensional landmark points that is generated by selecting the first subset of the multidimensional data points is representative of the received multidimensional data points.
3. The method of claim 2 wherein when the number of multidimensional landmark points in the set of multidimensional landmark points is equal to the threshold, the threshold being a predetermined number, the set of multidimensional landmark points being representative of the received multidimensional data points.
4. The method of claim 1 wherein receiving multidimensional data points includes storing the multidimensional data points in a memory system, and further comprising storing the set of multidimensional landmark points in a non-transitory storage system.
5. The method of claim 1 wherein selecting a first subset of the multidimensional data points to generate a set of multidimensional landmark points results in a second subset of the multidimensional data points that is a set of multidimensional non-landmark points, each multidimensional data point of the second subset being a multidimensional non-landmark point, and the method further comprising:
while the number of multidimensional landmark points in the set of multidimensional landmark points is less than the threshold:
removing the multidimensional non-landmark data point associated with the longest landmark distance from the second subset of multidimensional non-landmarks points to decrease the number of multidimensional non-landmark points in the second subset of multidimensional non-landmark points.
6. The method of claim 1 , further comprising mapping each of the set of multidimensional landmark points to a similarity space to a mathematical reference spacing using a similarity matrix s, wherein each of the set of multidimensional landmark points are mapped into the mathematical reference space.
7. The method of claim 6 , further comprising:
generating a cover for the multidimensional landmark points of the set of multidimensional landmark points in the mathematical reference space based on a resolution metric;
clustering the multidimensional landmark points of the set of multidimensional landmark points into subsets using a metric to generate subsets of the multidimensional landmark points of the set of multidimensional landmark points to determine each individual node of a plurality of nodes, each of the nodes of the plurality of nodes comprising members representative of at least one subset of the multidimensional landmark points of the set of multidimensional landmark points; and
generating an interactive visualization comprising nodes and a plurality of edges wherein each of the edges of the plurality of edges connects nodes with shared members.
8. The method of claim 1 wherein selecting the first subset of the multidimensional data points to generate the set of multidimensional landmark points includes randomly or pseudo-randomly selecting the first subset of the multidimensional data points to generate the set of multidimensional landmark points.
9. The method of claim 1 wherein identifying the multidimensional non-landmark data point with a longest landmark distance in comparison with other landmark distances of other multidimensional non-landmark data points and adding the multidimensional non-landmark data point associated with the longest landmark distance as the multidimensional landmark point to the set of multidimensional landmark points comprises:
identifying two or more of the multidimensional non-landmark data point with longest landmark distances in comparison with other landmark distances of other multidimensional non-landmark data points; and
adding the two or more multidimensional non-landmark data point associated with the longest landmark distance to the set of multidimensional landmark points.
10. A non-transitory computer readable medium comprising instructions executable by a processor to perform a method, the method comprising:
receiving multidimensional data points;
selecting a first subset of the multidimensional data points to generate a set of multidimensional landmark points, each multidimensional data point of the first subset being a multidimensional landmark point and each multidimensional data point that is not in the first subset being a multidimensional non-landmark point;
while a number of multidimensional landmark points in the set of multidimensional landmark points is less than a threshold:
for each multidimensional non-landmark data point,
calculating data point distances between that multidimensional non-landmark data point and each multidimensional landmark point of the set of multidimensional landmark points, wherein the multiple dimensions of the respective multidimensional non-landmark data point and the multiple dimensions of each multidimensional landmark point of the set of landmarks are utilized in calculating the data point distances;
identifying a shortest data point distance from among the data point distances between the respective multidimensional non-landmark data point and each multidimensional landmark point of the initial set of multidimensional landmark points; and
storing the shortest data point distance as a landmark distance for the respective multidimensional non-landmark data point;
identifying a multidimensional non-landmark data point with a longest landmark distance in comparison with other landmark distances of other multidimensional non-landmark data points; and
adding the multidimensional non-landmark data point associated with the longest landmark distance as a multidimensional landmark point to the set of multidimensional landmark points to increase the number of multidimensional landmark points in the set of multidimensional landmarks points.
11. The non-transitory computer readable medium of claim 10 wherein the set of multidimensional landmark points that is generated by selecting the first subset of the multidimensional data points is representative of the received multidimensional data points.
12. The non-transitory computer readable medium of claim 11 wherein when the number of multidimensional landmark points in the set of multidimensional landmark points is equal to the threshold, the threshold being a predetermined number, the set of multidimensional landmark points being representative of the received multidimensional data points.
13. The non-transitory computer readable medium of claim 10 wherein receiving multidimensional data points includes storing the multidimensional data points in a memory system, and the method further comprises storing the set of multidimensional landmark points in a non-transitory storage system.
14. The non-transitory computer readable medium of claim 10 wherein selecting a first subset of the multidimensional data points to generate a set of multidimensional landmark points results in a second subset of the multidimensional data points that is a set of multidimensional non-landmark points, each multidimensional data point of the second subset being a multidimensional non-landmark point, and the method further comprises:
while the number of multidimensional landmark points in the set of multidimensional landmark points is less than the threshold:
removing the multidimensional non-landmark data point associated with the longest landmark distance from the second subset of multidimensional non-landmarks points to decrease the number of multidimensional non-landmark points in the second subset of multidimensional non-landmark points.
15. The non-transitory computer readable medium of claim 10 wherein the method further comprises:
mapping each of the set of multidimensional landmark points to a similarity space to a mathematical reference spacing using a similarity matrix s, wherein each of the set of multidimensional landmark points are mapped into the mathematical reference space.
16. The non-transitory computer readable medium of claim 15 wherein the method further comprises:
generating a cover for the multidimensional landmark points of the set of multidimensional landmark points in the mathematical reference space based on a resolution metric;
clustering the multidimensional landmark points of the set of multidimensional landmark points into subsets using a metric to generate subsets of the multidimensional landmark points of the set of multidimensional landmark points to determine each individual node of a plurality of nodes, each of the nodes of the plurality of nodes comprising members representative of at least one subset of the multidimensional landmark points of the set of multidimensional landmark points; and
generating an interactive visualization comprising nodes and a plurality of edges wherein each of the edges of the plurality of edges connects nodes with shared members.
17. The non-transitory computer readable medium of claim 10 wherein selecting the first subset of the multidimensional data points to generate the set of multidimensional landmark points includes randomly or pseudo-randomly selecting the first subset of the multidimensional data points to generate the set of multidimensional landmark points.
18. The non-transitory computer readable medium of claim 10 wherein identifying the multidimensional non-landmark data point with a longest landmark distance in comparison with other landmark distances of other multidimensional non-landmark data points and adding the multidimensional non-landmark data point associated with the longest landmark distance as the multidimensional landmark point to the set of multidimensional landmark points comprises:
identifying two or more of the multidimensional non-landmark data point with longest landmark distances in comparison with other landmark distances of other multidimensional non-landmark data points; and
adding the two or more multidimensional non-landmark data point associated with the longest landmark distance to the set of multidimensional landmark points.
19. A system comprising:
one or more processors;
memory;
an input module configured to receive multidimensional data points;
a random landmark selection module configured to select a first subset of the multidimensional data points to generate a set of multidimensional landmark points, each multidimensional data point of the first subset being a multidimensional landmark point and each multidimensional data point that is not in the first subset being a multidimensional non-landmark point;
a distance calculation module configured to, while a number of multidimensional landmark points in the set of multidimensional landmark points is less than a threshold:
for each multidimensional non-landmark data point,
calculate data point distances between that multidimensional non- landmark data point and each multidimensional landmark point of the set of multidimensional landmark points, wherein the multiple dimensions of the respective multidimensional non-landmark data point and the multiple dimensions of each multidimensional landmark point of the set of landmarks are utilized in calculating the data point distances; and
identify a shortest data point distance from among the data point distances between the respective multidimensional non-landmark data point and each multidimensional landmark point of the initial set of multidimensional landmark points;
a landmark distance comparison module configured to identify a multidimensional non-landmark data point with a longest landmark distance in comparison with other landmark distances of other multidimensional non-landmark data points; and
a landmark assignment module configured to add the multidimensional non-landmark data point associated with the longest landmark distance as a multidimensional landmark point to the set of multidimensional landmark points to increase the number of multidimensional landmark points in the set of multidimensional landmarks points.