Papers › THE EFFECTIVE RANK: A MEASURE OF EFFECTIVE DIMENSIONALITY
THE EFFECTIVE RANK: A MEASURE OF EFFECTIVE DIMENSIONALITY
Olivier Roy, Martin Vetterli
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.
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