The Effective Rank: A Measure of Effective Dimensionality

Many signal processing algorithms include numerical problems where the solution is obtained by adjusting the value of parameters such that a specific matrix exhibits rank deficiency. Since rank minimization is generally not practicable owing to its integer nature, we propose a real-valued extension that we term effective rank. After proving some of its properties, the effective rank is provided with an operational meaning using a result on the coefficient rate of a stationary random process. Finally, the proposed measure is assessed in a practical scenario and other potential applications are suggested.


Published in:
European Signal Processing Conference (EUSIPCO), 606-610
Presented at:
European Signal Processing Conference (EUSIPCO), Poznan, Poland, September 3-7, 2007
Year:
2007
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 Record created 2007-08-19, last modified 2018-03-17

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