Searching methods for biometric identification systems: Fundamental limits

Abstract

cation rate. This extends a result of Willems et al. [8] showing that the maximum identification rate of a biometrical system is equal to the mutual information between the enrollment and identification observations, see also [4]. A crucial observation to obtain this result is that a set of biometric enrollment vectors can be regarded as a random channel code.In the current manuscript we focus on speeding up the search process, as in [9]. We are not interested in compressing the database as in [5], [6]. We will show that in an informationtheoretical setting quantization methods are optimal.To demonstrate what we mean by quantization, suppose that the system upon observing an individual, first detects to which cluster the individual belongs, and after that decides about the individual itself (two-stage identification). If there are M individuals, an ideal systems will have v'iJ clusters each containing v'iJ individuals. To determine the cluster index v'iJ candidate-clusters can be checked, and then to determine the individual within the cluster, v'iJ refinement-checks are needed. This results in 2v'iJ checks in total, considerably less than the M checks that are required for exhaustive search. In general however individuals can be in more than one cluster, see Fig. 1, and then the number of cluster-checks times the number of refinement-checks exceeds the number of individuals. Here we investigate the fundamental trade-off between cluster-check rate and refinement-check rate.An important point is what we mean by a cluster-check. In principle a cluster-check could correspond to v'iJ subchecks, one for each individual within the cluster. To prevent this, we require the device that makes the cluster-decision to be "ignorant" of the biometric enrollment vectors. Under this assumption an optimal system contains an ignorant device that acts as a vector quantizer.In the next section we present our model of a biometrical identification system based on two-stage identification and we

Fundamental limits of identification: Identification rate, search and memory complexity trade-off

“…that coincides to the results shown by Willems [9]. It should be noted that under this Markov condition R 3 = 0, which means that only a single u N is sent to the second decoder.…”

“…2, one can conclude that the proposed scheme in this context can achieve a new search-complexity region with less search-memory complexity compared to the scheme proposed in [9]. Search−complexity exponent Memory−complexity exponent Fig.…”

“…Where the system upon observing a query, first detects to which cluster the related item belongs, and after that decides about the item itself (two-stage identification). The main differences between the current manuscript and [9] are: (a) generalization of cluster representative points, considered as auxiliary random variables, based on statistics of both entries of the database and queries, while in [9] the cluster representative points have been generated only based on statistics of queries; (b) estimation of a list of clusters versus unique estimation in [9], upon observing a query at the first stage of decoding; (c) the memory complexity was not addressed directly in [9], for the analysis of the triple tradeoff; (d) a new result on search-memory complexity region of capacity achieving identification systems.…”

“…On the other hand, Fig. 2 (blue ×' s) shows the exponent of the search-memory complexity under Markov chain X ↔ Y ↔ U condition similarly to [9].…”

“…However, it should be noted that this scheme is efficient only for low degradations between queries and enrolled data. This paper is a generalization of the scheme introduced by Willems in [9] to speed up the search process by means of clustering. Where the system upon observing a query, first detects to which cluster the related item belongs, and after that decides about the item itself (two-stage identification).…”