You get a bonus - 1 coin for daily activity. Now you have 1 coin

Sequential recognition procedures

Lecture



If, in the previously considered recognition methods, the decision on whether an object was in one form or another was carried out immediately along the entire set of features, then in this section we will discuss the case of their consistent measurement and use.

Let be   Sequential recognition procedures . First, the object is measured   Sequential recognition procedures and on the basis of this information, the question of attributing this object to one of the images is decided. If this can be done with a sufficient degree of confidence, then other signs are not measured and the recognition procedure ends. If there is no such certainty, then the sign is measured.   Sequential recognition procedures and the decision is made in two ways:   Sequential recognition procedures and   Sequential recognition procedures . Further, the procedure is either terminated or the sign is measured.   Sequential recognition procedures and so on until either a decision is made to classify the object to any image, or all   Sequential recognition procedures signs.

Such procedures are extremely important in cases where the measurement of each of the signs requires a significant expenditure of resources (material, temporary, etc.).

Let be   Sequential recognition procedures and known   Sequential recognition procedures   Sequential recognition procedures Where   Sequential recognition procedures Note that if the distribution is known   Sequential recognition procedures then all distributions of smaller dimension are known (the so-called marginal distributions). For example,

  Sequential recognition procedures   Sequential recognition procedures

Let measured   Sequential recognition procedures   Sequential recognition procedures signs. Build likelihood ratio   Sequential recognition procedures If a   Sequential recognition procedures then the object is attributed to the image   Sequential recognition procedures , if a   Sequential recognition procedures then to the image   Sequential recognition procedures . If   Sequential recognition procedures then the sign is measured   Sequential recognition procedures and calculate the likelihood ratio   Sequential recognition procedures etc.

It is clear that the thresholds   Sequential recognition procedures and   Sequential recognition procedures associated with the permissible probability of recognition errors. Achieving inequality   Sequential recognition procedures we strive to ensure that the probability of correctly assigning the object of the first image to   Sequential recognition procedures Was in   Sequential recognition procedures times more than the erroneous assignment of the object of the second image to   Sequential recognition procedures , i.e   Sequential recognition procedures or   Sequential recognition procedures . Insofar as   Sequential recognition procedures then   Sequential recognition procedures (upper threshold). Similar reasoning is carried out to determine   Sequential recognition procedures . Achieving inequality   Sequential recognition procedures we strive to ensure that the probability of correctly assigning the object of the second image to   Sequential recognition procedures Was in   Sequential recognition procedures times more than the incorrect assignment of the object of the first image to   Sequential recognition procedures , i.e

  Sequential recognition procedures ,

  Sequential recognition procedures ,

  Sequential recognition procedures (lower threshold).

In a consistent procedure for measuring signs, a very useful property of these signs is their statistical independence. Then   Sequential recognition procedures and there is no need to store (and most importantly, build) multidimensional distributions. In addition, it is possible to optimize the sequence of the measured signs. If they are ranked in descending order of classification informativity (the amount of discriminating information) and a consistent procedure is organized in accordance with this ranking, the number of measured signs can be reduced on average.

We have reviewed the case of   Sequential recognition procedures (two images). If a   Sequential recognition procedures , then likelihood relationships can be built   Sequential recognition procedures , for example of this type:   Sequential recognition procedures Stopping boundary (threshold) for   Sequential recognition procedures th image is chosen equal   Sequential recognition procedures If a   Sequential recognition procedures then   Sequential recognition procedures th image is discarded and built   Sequential recognition procedures likelihood ratios and thresholds   Sequential recognition procedures . The procedure continues until only one image remains unreleased or all of them have been exhausted.   Sequential recognition procedures signs. If in the latter case more than one image remained unreleased, the decision is made in favor of the one for which the likelihood ratio   Sequential recognition procedures as much as possible.

If there are two images (   Sequential recognition procedures ) and the number of signs is not limited, then a sequential procedure with probability 1 ends in a finite number of steps. It is also proved that given   Sequential recognition procedures and   Sequential recognition procedures considered procedure with the same informativeness of various signs will give a minimum of the average number of steps. For   Sequential recognition procedures Vald introduced a sequential procedure and called it a successive criterion for the ratio of probabilities (c.to.v.).

For   Sequential recognition procedures optimal procedure is not proven.

With known prior probabilities, you can implement a Bayesian sequential procedure, and if you know the costs of character measurements and the matrix of penalties for incorrect recognition, then the sequential procedure can be stopped to minimize the average risk. The point here is to compare the losses caused by recognition errors when the procedure is terminated, and the expected losses after the next measurement plus the cost of this measurement. Such a problem is solved by the dynamic programming method if successive measurements are statistically independent. More detailed information on the optimization of the Bayes sequential procedure can be found in the recommended literature [8].


Comments


To leave a comment
If you have any suggestion, idea, thanks or comment, feel free to write. We really value feedback and are glad to hear your opinion.
To reply

Pattern recognition

Terms: Pattern recognition