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Abstract: Traditional nonlinear manifold learning methods have achieved great success in dimensionality reduction and feature extraction, most of which are batch modes. However, if new samples are observed, the batch methods need to be calculated repeatedly, which is computationally intensive, especially when the number or dimension of the input samples are large. This paper presents incremental learning algorithms for Laplacian eigenmaps, which computes the low-dimensional representation of data set by optimally preserving local neighborhood information in a certain sense. Sub-manifold analysis algorithm together with an alternative formulation of linear incremental method is proposed to learn the new samples incrementally. The locally linear reconstruction mechanism is introduced to update the existing samples’ embedding results. The algorithms are easy to be implemented and the computation procedure is simple. Simulation results testify the efficiency and accuracy of the proposed algorithms. [Copyright &y& Elsevier]

Abstract: In real world situations, explanations for the same observations may be different depending on perceptions or contexts. They may change with time especially when concept drift occurs. This phenomenon incurs ambiguities. It is useful if an algorithm can learn to reflect ambiguities and select the best decision according to context or situation. Based on this viewpoint, we study the problem of deriving ambiguous decision trees from data streams to cope with concept drift. CVFDT (Concept-adapting Very Fast Decision Tree) is one of the most well-known streaming data mining methods that can learn decision trees incrementally. In this paper, we establish a method called ambiguous CVFDT (aCVFDT), which integrates ambiguities into CVFDT by exploring multiple options at each node whenever a node is to be split. When aCVFDT is used to make class predictions, it is guaranteed that the best and newest knowledge is used. When old concepts recur, aCVFDT can immediately relearn them by using the corresponding options recorded at each node. Furthermore, CVFDT does not automatically detect occurrences of concept drift and only scans trees periodically, whereas an automatic concept drift detecting mechanism is used in aCVFDT. In our experiments, hyperplane problem and two benchmark problems from the UCI KDD Archive, namely Network Intrusion and Forest CoverType, are used to validate the performance of aCVFDT. The experimental results show that aCVFDT obtains significantly improved results over traditional CVFDT. [Copyright &y& Elsevier]