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# Communication Efficient Distributed Kernel Principal Component Analysis

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### Abstract

Kernel Principal Component Analysis (KPCA) is a key machine learning algorithm for extracting nonlinear features from data. In the presence of a large volume of high dimensional data collected in a distributed fashion, it becomes very costly to communicate all of this data to a single data center and then perform kernel PCA. Can we perform kernel PCA on the entire dataset in a distributed and communication efficient fashion while maintaining provable and strong guarantees in solution quality? In this paper, we give an affirmative answer to the question by developing a communication efficient algorithm to perform kernel PCA in the distributed setting. The algorithm is a clever combination of subspace embedding and adaptive sampling techniques, and we show that the algorithm can take as input an arbitrary configuration of distributed datasets, and compute a set of global kernel principal components with relative error guarantees independent of the dimension of the feature space or the total number of data points. In particular, computing $$k$$ principal components with relative error $$\epsilon$$ over $$s$$ workers has communication cost $$\tilde{O}(s \rho k/\epsilon+s k^2/\epsilon^3)$$ words, where $$\rho$$ is the average number of nonzero entries in each data point. Furthermore, we experimented the algorithm with large-scale real world datasets and showed that the algorithm produces a high quality kernel PCA solution while using significantly less communication than alternative approaches.

### Author and article information

###### Journal
2015-03-23
2016-02-13
1503.06858