S-Isomap++: Multi manifold learning from streaming data
S-Isomap++: Multi manifold learning from streaming data
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DOI：
10.1109/bigdata.2017.8257987
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发表时间：
2017-10
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影响因子：
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通讯作者：
Suchismit Mahapatra;V. Chandola
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文献类型：
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作者：
Suchismit Mahapatra;V. Chandola
基于流形学习的方法已被广泛用于非线性降维（NLDR）。然而，在许多实际设置中，由于所涉及的高计算复杂性，处理流数据的需要对于这样的方法是一个挑战。此外，大多数方法都假设输入数据是从单个流形中采样的，嵌入在高维空间中。我们提出了一种方法，当观察到的数据是从多个流形或不规则采样从一个单一的流形流NLDR。我们表明，现有的NLDR方法，如Isomap，在这种情况下失败，主要是因为它们依赖于光滑性和连续性的基础流形，这是违反了本文探讨的情况。然而，所提出的算法能够在存在多个且可能相交的流形的情况下有效地学习，同时允许输入数据作为大量流到达。
Manifold learning based methods have been widely used for non-linear dimensionality reduction (NLDR). However, in many practical settings, the need to process streaming data is a challenge for such methods, owing to the high computational complexity involved. Moreover, most methods operate under the assumption that the input data is sampled from a single manifold, embedded in a high dimensional space. We propose a method for streaming NLDR when the observed data is either sampled from multiple manifolds or irregularly sampled from a single manifold. We show that existing NLDR methods, such as Isomap, fail in such situations, primarily because they rely on smoothness and continuity of the underlying manifold, which is violated in the scenarios explored in this paper. However, the proposed algorithm is able to learn effectively in presence of multiple, and potentially intersecting, manifolds, while allowing for the input data to arrive as a massive stream.