## 5 Related work  
The distribution of the PCA has been addressed in the signal processing and information theory communities [4; 37; 38; 39]. These approaches, based on distributed source coding, involve compression techniques related to Slepian-Wolf and Wyner-Ziv coding together with Karhunen-Loeve transform for compressing data in distributed systems. Each component of the system is however assumed to observe several dimensions of the problem, and they require the base station to support the task of defining the coding scheme. The network architectures and communication costs analyses are also left as open research areas. Although these approaches may lead to attractive applications for WSN, they still remain in that respect at an early research stage.  
In the fields of machine learning and data mining, distributed PCA schemes have also been addressed in [40; 41] and [19]. The former approaches aimed at combining the PCA results obtained from different sources that share the same variables (_vertically_ distributed databases). The latter work provided an architecture aimed at network anomaly detection, where the PCA is first computed in a centralized manner, and a subsequent distributed and adaptive feedback mechanism is proposed. Despite the similarity in the choice for the method name, the corresponding work is however clearly different from the approach proposed in this article.  
The distributed computation of eigenvectors of large and sparse matrices has been tackled from several angles in the literature, and good reviews of existing state of the art techniques are for example detailed in [21; 22]. The approach proposed in this article is however assumed to be innovative to the best of authors' knowledge, as it leverages two specific architectural properties of sensor networks. First, a wireless sensor network is an _intrinsically_ distributed system where each component only captures one dimension of the system variations. Second, the communication constraints can be coupled with the local covariance hypothesis.  
Recent work in the domain of link analysis and recommendation systems has led authors in [42] to propose a distributed implementation of the power iteration method, which closely matches the approach proposed in this article. Their algorithm aims at computing the principal eigenvector of the adjacency matrix of a peer-to-peer network, which leads to the ranking of the network components, in a way similar to the _page rank_ algorithm. The underlying hypotheses of the distributed system are interestingly close to ours (each component has only access to one dimension the problem, and can communicate with components whose data is related). The network structure is however different, as no coordinating entity is assumed. This leads authors to rely on the harmonic mean to achieve the normalization step of the power iteration method. The computation of subsequent eigenvectors is also not addressed.  
Related work on the use of basis change for sensor networks has been addressed in [43], where authors proposed the radical position of using random bases to project sensor measurements. The work is analyzed in the context of compressed sensing, an emerging field in signal processing (see also [44]). Their work has however mainly focused on the theoretical ability of random bases to retain the sensor measurements variations.