Abstract
String kernels are attractive data analysis tools for analyzing string data.Among them, alignment kernels are known for their high prediction accuracies in string classifications when tested in combination with SVM in various applications. However, alignment kernels have a crucial drawback in that they scale poorly due to their quadratic computation complexity in the number of input strings, which limits large-scale applications in practice. We address this need by presenting the first approximation for string alignment kernels, which we call space-efficient feature maps for edit distance with moves (SFMEDM), by leveraging a metric embedding named edit-sensitive parsing and feature maps (FMs) of random Fourier features (RFFs) for large-scale string analyses.The original FMs for RFFs consume a huge amount of memory proportional to the dimension d of input vectors and the dimension D of output vectors, which prohibits its large-scale applications.We present novel space-efficient feature maps (SFMs) of RFFs for a space reduction from O(dD) of the original FMs to O(d) of SFMs with a theoretical guarantee with respect to concentration bounds. We experimentally test SFMEDM on its ability to learn SVM for large-scale string classifications with various massive string data, and we demonstrate the superior performance of SFMEDM with respect to prediction accuracy, scalability and computation efficiency.
Highlights
Massive string data are ubiquitous throughout research and industry, in areas such as biology, chemistry, natural language processing and data science
Our SFMEDM has the following desirable properties: (1) Scalability SFMEDM is applicable to massive string data
280 Memory for building RFFs (MB) and 80 MB of memory were consumed by SFMEDM for D = 16,384 for “Sports” and “Compound,” respectively. These results suggest that compared with FMEDM, SFMEDM dramatically reduces the amount of required memory
Summary
Massive string data are ubiquitous throughout research and industry, in areas such as biology, chemistry, natural language processing and data science. It is known that kernel methods achieve high prediction accuracy for various tasks such as classification and regression, they scale poorly due to a quadratic complexity in the number of training data [9, 13]. In this study, we present space-efficient FMs (SFMs) that require only O(d) memory to solve this problem and can be used for approximating any shift-invariant kernel such as a Laplacian kernel. This is an essential property which is required for approximating alignment kernels and has not been taken into account by previous research. We experimentally test the ability of SFMEDM to train SVM with various massive string data and demonstrate that SFMEDM has superior performance in terms of prediction accuracy, scalability and computational efficiency
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