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Study of geometric measures of proximity of objects and classes in recognition systems

Lecture



The task:

1. Develop a decision-making algorithm in a deterministic recognition system based on the use of known geometric measures of proximity.

2. Run the software implementation of the developed algorithm, debug the program.

3. Run control recognition of unknown objects by their feature vectors.

4. To compare the efficiency of making decisions on the assignment of unknown objects to given classes for various methods of calculating the distance between an object and a class. Determine the best combination of the proposed.

Stages of sequential work:

1. Determine the values ​​of signs of five standards for each of the four classes.

2. Display on the graph certain standards of all classes, instances of each class in the form of a point of a certain shape and color.

3. Implement the sequential interactive introduction of feature vectors of unknown objects that need to be recognized and assigned to one of four classes (feature values ​​can be determined by pressing the mouse button, asking the user or setting fixed values ​​in the code).

4. Implement the functions for calculating the degree of proximity between an unknown object and a given object of a particular class (methods for calculating the degree of proximity between two objects are different).

5. Implement the function of calculating the distance from each unknown object with a given class (methods for calculating the distance between an object and a class are different).

6. Implement the ability to select combinations of methods for calculating the degree of proximity and distance between objects.

7. Calculate the distance from the unknown object to each of the four classes.

8. Determine the class, the distance from the unknown object to which the minimum (in accordance with the selected combination of methods for calculating the measure of proximity between objects and the distance between the object and class).

9. Show the recognized object on the graph as a point, in the form and color of which coincides with the class to which it belongs.

A metric space is a set in which between any pair of elements a distance is defined that has certain properties, called a metric .

Definitions

Metric space is a pair   Study of geometric measures of proximity of objects and classes in recognition systems where   Study of geometric measures of proximity of objects and classes in recognition systems - many, and   Study of geometric measures of proximity of objects and classes in recognition systems - numeric function, which is defined on the Cartesian product   Study of geometric measures of proximity of objects and classes in recognition systems , takes values ​​in the set of real numbers, and is such that

  1.   Study of geometric measures of proximity of objects and classes in recognition systems ( identity axiom ).
  2.   Study of geometric measures of proximity of objects and classes in recognition systems ( axiom of symmetry ).
  3.   Study of geometric measures of proximity of objects and classes in recognition systems ( triangle axiom or triangle inequality).

Wherein

  • lots of   Study of geometric measures of proximity of objects and classes in recognition systems called the underlying set of metric space.
  • elements of the set   Study of geometric measures of proximity of objects and classes in recognition systems are called points of a metric space.
  • function   Study of geometric measures of proximity of objects and classes in recognition systems called metric .

Remarks

  • The axioms of the distance function follow from axioms, since

      Study of geometric measures of proximity of objects and classes in recognition systems .

  • If the triangle inequality is represented as

      Study of geometric measures of proximity of objects and classes in recognition systems for all   Study of geometric measures of proximity of objects and classes in recognition systems and   Study of geometric measures of proximity of objects and classes in recognition systems ,

then the symmetry axiom follows from the axiom of identity and inequality of a triangle.

Designations

Usually the distance between points   Study of geometric measures of proximity of objects and classes in recognition systems and   Study of geometric measures of proximity of objects and classes in recognition systems in metric space   Study of geometric measures of proximity of objects and classes in recognition systems denoted by   Study of geometric measures of proximity of objects and classes in recognition systems or   Study of geometric measures of proximity of objects and classes in recognition systems .

  • In metric geometry the designation is accepted.   Study of geometric measures of proximity of objects and classes in recognition systems or   Study of geometric measures of proximity of objects and classes in recognition systems if you need to emphasize that this is about   Study of geometric measures of proximity of objects and classes in recognition systems . Less commonly used symbols   Study of geometric measures of proximity of objects and classes in recognition systems and   Study of geometric measures of proximity of objects and classes in recognition systems .
  • In classical geometry, the notation   Study of geometric measures of proximity of objects and classes in recognition systems or   Study of geometric measures of proximity of objects and classes in recognition systems (dots are usually denoted by capital Latin letters).

Methods for calculating the distance between two objects in two-dimensional space.

  Study of geometric measures of proximity of objects and classes in recognition systems

Methods for calculating the distance between an object and a class.

  Study of geometric measures of proximity of objects and classes in recognition systems

An example of the implementation of the study of geometric measures of proximity objects and classes in recognition systems

created: 2016-12-27
updated: 2021-03-13
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Classification and recognition

Terms: Classification and recognition