Distance metrics and clustering in recurrent neural networks

1. A method comprising:

determining whether topological patterns of activity in a collection of topological patterns occur in a recurrent artificial neural network in response to input of first data into the recurrent artificial neural network;

determining whether the topological patterns of activity in the collection occur in the recurrent artificial neural network in response to input of second data into the recurrent artificial neural network; and

determining a distance between the first data and the second data by comparing the topological patterns of activity that are determined to occur in response to the input of the first data with the topological patterns of activity that are determined to occur in response to the input of the second data.

2. The method of claim 1 , wherein the distance is determined between the first data and either a centroid of a cluster or a cluster boundary of the second data.

3. The method of claim 1 , wherein:

the occurrence of the topological patterns of activity is represented in a collection of binary or multivalued digits that each indicate whether a respective topological pattern occurred or not.

4. The method of claim 1 , wherein the distance is determined using a distance metric that treats a first subset of the topological patterns of activity in the collection differently from a second subset of topological patterns of activity in the collection.

5. The method of claim 4 , wherein the treatment weighs the first subset of the topological patterns as more strongly indicative of distance than the second subset of topological patterns.

6. The method of claim 4 , wherein:

the first data and the second data include multiple classes of input data; and

the first subset of the topological patterns only includes topological patterns that arise in a region of the recurrent artificial neural network that is primarily perturbed by a single class of the input data.

7. The method of claim 6 , wherein:

each of the multiple classes of input data originates from a different sensor; and

the single class of input data originates only from a first of the sensors.

8. The method of claim 4 , wherein:

the recurrent artificial neural network is trained; and

the second subset of the topological patterns only includes topological patterns that arise in a region of the recurrent artificial neural network that reflects the training.

9. The method of claim 4 , wherein a complexity of the topological patterns in the second subset of the topological patterns is higher than a complexity of the topological patterns in the first subset.

10. The method of claim 4 , wherein at least some of the topological patterns in the first subset are included in the topological patterns in the second subset.

11. The method of claim 1 , wherein the recurrent artificial neural network is untrained.

12. The method of claim 1 , further comprising:

repeatedly determining whether the topological patterns of activity in the collection occur in the recurrent artificial neural network in response to input of data into the recurrent artificial neural network; and

clustering the input data based on a distance between the data, wherein the distance is determined by comparing the respective topological patterns of activity that are determined to occur in response to the input of the data.

13. The method of claim 1 , wherein determining whether the topological patterns of activity occur comprises determining whether simplex patterns of activity occur.

14. The method of claim 13 , wherein the simplex patterns enclose cavities.

15. The method of claim 13 , wherein determining whether simplex patterns of activity occur comprises determining whether directed simplex patterns of activity occur.

16. The method of claim 1 , wherein determining whether the topological patterns of activity occur comprises:

determining a timing of activity having a complexity that is distinguishable from other activity that is responsive to the input, and

identifying the topological structures based on the timing of the activity that has the distinguishable complexity.

17. A method comprising:

receiving information identifying occurrences of topological patterns of activity in a recurrent artificial neural network in response to input of a plurality of different elements into the recurrent artificial neural network;

calculating a distance between a first element of the different elements and a second element of the different elements by comparing the topological patterns of activity that are determined to occur in response to the input of the first element with the topological patterns of activity that are determined to occur in response to the input of the second element; and

adjusting one or more characteristics of the recurrent artificial neural network to increase or decrease the distances.

18. The method of claim 17 , wherein the distances are calculated using a distance metric that treats a first subset of the topological patterns of activity in the collection differently from a second subset of topological patterns of activity in the collection.

19. The method of claim 18 , wherein the distance calculation weighs the first subset of the topological patterns as more strongly indicative of distance than the second subset of topological patterns.

20. The method of claim 18 , wherein a complexity of the topological patterns in the second subset of the topological patterns is lower than a complexity of the topological patterns in the first subset.

21. The method of claim 17 , wherein:

the information identifying occurrences of topological patterns of activity comprises a first binary vector for a first element and a second binary vector for a second element;

calculating the distances comprises calculating the distances between the binary vectors.

22. The method of claim 17 , wherein the recurrent artificial neural network is untrained.

23. The method of claim 17 , wherein receiving information identifying the occurrences of the topological patterns of activity in the recurrent artificial neural network comprises receiving information identifying the occurrences of directed simplex patterns of activity in the recurrent artificial neural network.

24. A method comprising:

determining whether topological patterns of activity in a collection of topological patterns occur in a recurrent artificial neural network in response to input of first data into the recurrent artificial neural network; and

determining a distance between the first data and either second data or a reference based on the topological patterns of activity that are determined to occur in response to the input of the first data, wherein the distance is determined using a distance metric that treats a first subset of the topological patterns of activity in the collection differently from a second subset of topological patterns of activity in the collection.

25. A method comprising:

receiving information identifying occurrences of topological patterns of activity in a recurrent artificial neural network in response to input of a plurality of different elements into the recurrent artificial neural network, wherein the information identifying occurrences of topological patterns of activity comprises a first binary vector for a first element and a second binary vector for a second element;

calculating distances between the different elements based on the occurrences of the topological patterns of activity, wherein calculating the distances comprises calculating the distances between the binary vectors; and

adjusting one or more characteristics of the recurrent artificial neural network to increase or decrease the distances.