Random Projection (RP) technique has been widely applied in many scenarios because it can reduce high-dimensional features into low-dimensional space within short time and meet the need of real-time analysis of massive data. There is an urgent need of dimensionality reduction with fast increase of big genomics data. However, the performance of RP is usually lower. We attempt to improve classification accuracy of RP through combining other reduction dimension methods such as Principle Component Analysis (PCA), Linear Discriminant Analysis (LDA), and Feature Selection (FS). We compared classification accuracy and running time of different combination methods on three microarray datasets and a simulation dataset. Experimental results show a remarkable improvement of 14.77 in classification accuracy of FS followed by RP compared to RP on BC-TCGA dataset. LDA followed by RP also helps RP to yield a more discriminative subspace with an increase of 13.65 on classification accuracy on the same dataset. FS followed by RP outperforms other combination methods in classification accuracy on most of the datasets.
In @cite_3 and @cite_0 , RP has been proposed to address the burdensome computation time in dimensionality reduction. In RP, transformation matrix @math is randomly generated. Experiment results @cite_3 @cite_6 have reveals that RP is computationally less expensive with a little distortion of original data. On the other hand, RP may not capture intrinsic structure underlying original data because @math is generated without considering the structure of data.
@cite_0 @cite_6 @cite_3
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We present a novel approach to learning heuristic functions for AI planning domains. Given a state, we view a relaxed plan (RP) found from that state as a relational database, which includes the current state and goal facts, the actions in the RP, and the actions' add and delete lists. We represent heuristic functions as linear combinations of generic features of the database, selecting features and weights using training data from solved problems in the target planning domain. Many recent competitive planners use RP-based heuristics, but focus exclusively on the length of the RP, ignoring other RP features. Since RP construction ignores delete lists, for many domains, RP length dramatically under-estimates the distance to a goal, providing poor guidance. By using features that depend on deleted facts and other RP properties, our learned heuristics can potentially capture patterns that describe where such under-estimation occurs. Experiments in the STRIPS domains of IPC 3 and 4 show that best-first search using the learned heuristic can outperform FF (Hoffmann & Nebel 2001), which provided our training data, and frequently outperforms the top performances in IPC 4. In this paper, we elaborate over the well-known interpretability issue in echo-state networks (ESNs). The idea is to investigate the dynamics of reservoir neurons with time-series analysis techniques developed in complex systems research. Notably, we analyze time series of neuron activations with recurrence plots (RPs) and recurrence quantification analysis (RQA), which permit to visualize and characterize high-dimensional dynamical systems. We show that this approach is useful in a number of ways. First, the 2-D representation offered by RPs provides a visualization of the high-dimensional reservoir dynamics. Our results suggest that, if the network is stable, reservoir and input generate similar line patterns in the respective RPs. Conversely, as the ESN becomes unstable, the patterns in the RP of the reservoir change. As a second result, we show that an RQA measure, called @math , is highly correlated with the well-established maximal local Lyapunov exponent. This suggests that complexity measures based on RP diagonal lines distribution can quantify network stability. Finally, our analysis shows that all RQA measures fluctuate on the proximity of the so-called edge of stability, where an ESN typically achieves maximum computational capability. We leverage on this property to determine the edge of stability and show that our criterion is more accurate than two well-known counterparts, both based on the Jacobian matrix of the reservoir. Therefore, we claim that RPs and RQA-based analyses are valuable tools to design an ESN, given a specific problem. The @math -means clustering algorithm is a ubiquitous tool in data mining and machine learning that shows promising performance. However, its high computational cost has hindered its applications in broad domains. Researchers have successfully addressed these obstacles with dimensionality reduction methods. Recently, [1] develop a state-of-the-art random projection (RP) method for faster @math -means clustering. Their method delivers many improvements over other dimensionality reduction methods. For example, compared to the advanced singular value decomposition based feature extraction approach, [1] reduce the running time by a factor of @math for data matrix @math with @math data points and @math features, while losing only a factor of one in approximation accuracy. Unfortunately, they still require @math for matrix multiplication and this cost will be prohibitive for large values of @math and @math . To break this bottleneck, we carefully build a sparse embedded @math -means clustering algorithm which requires @math ( @math denotes the number of non-zeros in @math ) for fast matrix multiplication. Moreover, our proposed algorithm improves on [1]'s results for approximation accuracy by a factor of one. Our empirical studies corroborate our theoretical findings, and demonstrate that our approach is able to significantly accelerate @math -means clustering, while achieving satisfactory clustering performance.