While robots are more and more deployed among people in public spaces, the impact of cyber-security attacks is significantly increasing. Most of consumer and professional robotic systems are affected by multiple vulnerabilities and the research in this field is just started. This paper addresses the problem of automatic detection of anomalous behaviors possibly coming from cyber-security attacks.
We consider the problem of approximating a given matrix by a low-rank matrix so as to minimize the entry-wise ?p-approximation error, for any P ? 1; the case p = 2 is the classical SVD problem. We obtain the first provably good approximation algorithms for this version of low-rank approximation that work for every value of p ? 1, including p = ?. Our algorithms are simple, easy to implement, work well in practice, and illustrate interesting tradeoffs between the approximation quality, the running time, and the rank of the approximating matrix.
Portable Document Format, more commonly known as PDF, has become, in the last 20 years, a standard for document exchange and dissemination due its portable nature and widespread adoption. The flexibility and power of this format are not only leveraged by benign users, but from hackers as well who have been working to exploit various types of vulnerabilities, overcome security restrictions, and then transform the PDF format in one among the leading malicious code spread vectors.
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