Incremental alignment manifold learning
Journal of Computer Science and Technology - Special issue on natural language processing
Distributed knowledge discovery with non linear dimensionality reduction
PAKDD'10 Proceedings of the 14th Pacific-Asia conference on Advances in Knowledge Discovery and Data Mining - Volume Part II
A mixed graph model for community detection
International Journal of Intelligent Information and Database Systems
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Most nonlinear data embedding methods use bottom-up approaches for capturing the underlying structure of data distributed on a manifold in high dimensional space. These methods often share the first step which defines neighbor points of every data point by building a connected neighborhood graph so that all data points can be embedded to a single coordinate system. These methods are required to work incrementally for dimensionality reduction in many applications. Because input data stream may be under-sampled or skewed from time to time, building connected neighborhood graph is crucial to the success of incremental data embedding using these methods. This paper presents algorithms for updating $k$-edge-connected and $k$-connected neighborhood graphs after a new data point is added or an old data point is deleted. It further utilizes a simple algorithm for updating all-pair shortest distances on the neighborhood graph. Together with incremental classical multidimensional scaling using iterative subspace approximation, this paper devises an incremental version of Isomap with enhancements to deal with under-sampled or unevenly distributed data. Experiments on both synthetic and real-world data sets show that the algorithm is efficient and maintains low dimensional configurations of high dimensional data under various data distributions.