This paper presents a spatio-temporal isomap which is basically an extension to the conventional isomap proposed by tenumbum in 2000. The presented method captures the temporal relationships between the neighborhood that can be propgated globally via a shortest path mechanism. ST Isomaps aim to deal with the proximal disambiguation which means to distinguish between spatially close data in the input space that is structurally different and finding the distal correspondence which means finding the common structure in the space. By finding these measures, one can find the spatio-temporal structure of the data. As epr the paper, proximal disambiguation and distance correspondence are the pair wise concepts and as such the existing pairwise dimension reduction needs to be augmmented to include spatio-temporal relationships.
The approach involves:
1 Windowing of the input data into temporal blocks which basically serves as a history of each data point.
2 Computation of sparse distance matrix D from the local neighborhood using Euclidean distance.
3) Using the Distance matrix obtained in above step to obtain the common temporal neighbors CTN which are either local temporal CTN or K-nearest non-trival neighbors.
4) Above measure is used to reduce the distance between points with common and adjacent temporal relationships.
5) The above metric is then used to obtain the shortest pair distance metric using Dijkstra's.
6) Classical MDS is applied to preserve the spacing .
Step 1,3,4 are the contribution of the paper . These steps introduce the temporal information in the Isomaps.
This paper presents the approach to apply ST isomaps on continuous data where K-nearest non trivial neighbor metric is used to find the best matching neighbor from each individual trajectory and removing any redundancy of selection of neighbor. Where as, Local Segmented common temporal neighbor is used for measuring the distance metric for non continuous data. The Segmented Common Temporal Neighbor hood approach is based on the logic that the pair of points are spatio-temporally similar, if they are spatially similar and the points they are transition to are also spatially similar.
They have applied their method a tele-operated NASA Robot to grasp wrenches placed at various locations, on obtaining the Kinematic motion data from human subjects. They have also given a comparison with PCA and standard Isomaps.They also showed some comparizon with HMMs.
Discussion:
They have added another important dimension to the data that can actually capture the motions that repeat in time and may be structurally similar though temporally they may be different for example a spiral motion . Adding temporal information makes a lot of sense as many dimensionality reduction techniques may give false results as they cannot distinguish between repetition of data as a temporal characteristic but in fact it will take it as redundancy of data which in fact it is not (I mean all data is not redundant).
I can now see that for gestures and motion capture we cannot use PCA if our gesture contains repetition of motion and for such cases ST -Isomaps is the solution to capture the embedded motion which characterizes the gesture
3 comments:
I'm not familiar with the PCA and Isomap algorithms, but I'm getting the impression that Isomap is lightyears better than PCA for haptics. Is it fair to say that a big advantage Isomap has over PCA is that Isomap can handle temporal data? Isomap does seem like a viable technique given the comments I read. A shame we haven't read more papers that have done so.
I think PCA is a perfectly viable solution for haptics if used right. You just treat each frame of data as a point in time and treat the eigenspace-projected frames as a stream of data. Regular segmentation and classification approaches should work here.
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