KR100987028B1 - Apparatus and method for calculating uncertainty of alignment structure in random data, and the recording media storing the program performing the said method - Google Patents

Abstract

The present invention provides an apparatus and method for calculating the uncertainty of the alignment structure of the random data which calculates the structural uncertainty of the random data indicating the degree of violation of the order of the internal elements based on the set order order relation; A recording medium on which a program for implementing the method is recorded. The present invention relates to a sequence relation determining unit for assigning and arranging symbols to each element data using a probability of occurrence of element data included in random data; And a structural uncertainty calculation unit for calculating structural uncertainty of random data indicating whether there is a symbol located in violation of the ascending or descending order among the listed symbols. To provide. According to the present invention, it is possible to measure the amount of information according to the order structure that random data has, without being based on probabilities.

Random data, order relation, entropy, coding algorithm, compression algorithm, uniform distribution

Description

Apparatus and method for calculating uncertainty of alignment structure in random data, and the recording media storing the program performing the apparatus and method for calculating uncertainty of alignment structure possessed by random data said method}

The present invention relates to an apparatus for calculating the uncertainty of the alignment structure of random data, a method thereof, and a recording medium on which a program for implementing the method is recorded. More specifically, an apparatus for calculating the uncertainty of the alignment structure of random data related to calculating the structural uncertainty of the random data indicating the degree of violation of the order of internal elements based on the set-order order relation And a method for recording a recording medium on which a program for implementing the method is recorded.

1948 C.E. Since informative entropy has been defined by Shannon, many people have been developing algorithms for random data. Most compression systems are intermediate steps for compression. Each symbol is represented as an integer, and a small integer value is assigned to a symbol having a high probability, and a large integer value is assigned to a symbol having a low probability. Given a probabilistic model, the suitability of Huffman coding or arithmetic coding is already true in many literatures.

However, in the encoding algorithm of random data, the coding efficiency varies depending on how many symbols are in the probability of the symbols. In addition, what is pointed out as the biggest disadvantage of entropy is that it only indicates the amount of information of the symbols and does not provide information about how compressible it is.

On the other hand, in 1965, A. N. Kolmogorov defined algorithmic entropy as a measure of new information amount by using the structural complexity of the symbols to compensate for the shortcomings of entropy previously used as a measure of information amount. This measure, commonly known as Kolmogorov Complexity, is defined as the minimum length of a programming source that outputs random data as output for any random data. In other words, it represents the amount of information of the data as the minimum length of the source of the computer program for generating the random data. In terms of Kolmogorov Complexity, incompressibility refers to a case in which the length of a program source for generating the random data cannot be smaller than the length of the random data generated. When the probability distribution of the random data follows the uniform distribution, The same property is satisfied. In other words, the Kolmogorov Complexity of random data with a uniform distribution can never be smaller than the total length of the random data.

In conclusion, from the viewpoint of Shannon's entropy and Kolmogorov's algorithmic entropy, the probability of occurrence of all symbols and the amount of information are the same, so that if the random data has a uniform distribution, no further compression is possible. This is because the measure of information volume is based on probability.

As described above, when the probability model is determined, the existing measure of information based on probability is determined by the lower limit of compression based on the probability, and in particular, it is no longer possible to compress a data set having a uniform distribution. Therefore, a new method is needed to overcome the limitation of the measure of the amount of information based on probability.

SUMMARY OF THE INVENTION The present invention has been made to solve the above-mentioned problems, and an apparatus and method for calculating the uncertainty of the alignment structure of random data, which calculates the structural uncertainty of random data based on a set theory, It is an object of the present invention to provide a recorded recording medium.

The present invention has been made to achieve the above object, an order relationship determination unit for allocating symbols to each element data using the probability of occurrence of the element data included in the random data; And a structural uncertainty calculation unit for calculating a structural uncertainty of the random data indicating whether there is a symbol located in violation of the ascending or descending order among the listed symbols. It provides a device to.

Preferably, the apparatus for calculating the uncertainty of the alignment structure further includes a positional instability determination unit that determines whether the element data having the greatest probability of occurrence is in the original position when following the ascending or descending alignment. In particular, the positional instability determining unit is configured to assign 0 to the element data having the greatest probability of occurrence in the original position according to the ascending or descending order, and to assign 1 otherwise. In addition, the positional instability determination unit preferably determines whether the elementary data having the highest occurrence probability is removed from the remaining element data in the original position whenever element data having the highest occurrence probability is removed.

In addition, the present invention comprises the steps of: (a) assigning a symbol to each element data using the probability of occurrence of the element data included in the random data; And (b) calculating a structural uncertainty of the random data indicating whether there is a symbol located in violation of the ascending or descending order among the listed symbols. Provide a method for calculating.

According to the present invention, it is possible to measure the amount of information according to the order structure of the random data, unlike the existing probability by calculating the structural uncertainty that the random data based on the set-order order relationship.

Hereinafter, exemplary embodiments of the present invention will be described in detail with reference to the accompanying drawings. First of all, in adding reference numerals to the components of each drawing, it should be noted that the same reference numerals are used as much as possible even if displayed on different drawings. In addition, in describing the present invention, when it is determined that the detailed description of the related known configuration or function may obscure the gist of the present invention, the detailed description thereof will be omitted. In addition, the following will describe a preferred embodiment of the present invention, but the technical idea of the present invention is not limited thereto and may be variously modified and modified by those skilled in the art.

1 is a block diagram illustrating an internal configuration of an apparatus for calculating an uncertainty of an alignment structure of random data according to a preferred embodiment of the present invention. As shown in FIG. 1, the apparatus 100 for calculating the uncertainty of the alignment structure according to the preferred embodiment of the present invention includes an element data extractor 110, an order relationship determiner 120, and a positional instability determiner 130. ) And a structural uncertainty calculator 190 and a controller 150 having an adder 140.

The element data extractor 110 performs a function of extracting element data from random data in an embodiment of the present invention. Here, the element data is part of random data, for example, pixels of a predetermined size constituting an image frame.

The order relation determiner 120 performs a function of allocating a symbol according to a probability of occurrence (frequency) of the extracted element data. In addition, the order relationship determination unit 120 performs a function of determining the priority relationship of symbols allocated to each element data in the embodiment of the present invention. In the embodiment of the present invention, a symbol is generally used as a positive number, but is not necessarily limited thereto. Thus, a, b, c, d, e,... , z or a, b, c, d,. , ㅎ or going, me, da, la,… It is also possible to use word order of language such as, ha ha.

The structural uncertainty calculator 190 calculates the uncertainty of the alignment structure of the random data in the embodiment of the present invention. Specifically, the structural uncertainty calculator 190 calculates the uncertainty of the alignment structure resulting from the positional instability of all the element data constituting the random data. The structural uncertainty calculation unit 190 includes a positional instability determining unit 130 and a summing unit 140.

The positional instability determination unit 130 performs a function of determining the positional instability of each element data in the embodiment of the present invention. The positional instability determination unit 130 performs a function of deriving information on the positional instability of all element data. The function performed by the positional instability determining unit 130 may be described by Equation 1 to be described later.

The adding unit 140 calculates structural uncertainty by summing the results determined by the positional instability determining unit 130 in the embodiment of the present invention. The function performed by the summing unit 140 may be described by Equations 2 and 3 below.

The above-described element data extraction unit 110, order relationship determination unit 120, positional instability determination unit 130, summing unit 140, structural uncertainty calculation unit 190, etc. The description will be described later with reference to FIG. 2.

The controller 150 controls the overall operation of all components 110 to 140 and 190 constituting the uncertainty calculating apparatus 100 of the alignment structure in the embodiment of the present invention.

In addition, the uncertainty calculator 100 of the alignment structure may further include a power supply unit 160, an input unit 170, an output unit 180, and the like. The power supply unit 160 performs a function of supplying power so that all components constituting the device 100 can be operated smoothly. The input unit 170 performs a function of receiving random data from the outside so that the element data extracting unit 110 can extract the element data from the random data. The output unit 180 displays a structural uncertainty of the random data calculated by the structural uncertainty calculator 190.

The apparatus 100 for calculating an uncertainty of the alignment structure having the components as described above performs the function of calculating the uncertainty of the alignment structure included in the random data in the embodiment of the present invention. Hereinafter, a method of calculating the uncertainty of the alignment structure of the random data performed by the apparatus 100 for calculating the uncertainty of the alignment structure will be described.

Next, a method of calculating the uncertainty of the alignment structure of the random data according to the preferred embodiment of the present invention will be described. 2 is a flowchart illustrating a method of calculating an uncertainty of an alignment structure of random data according to a preferred embodiment of the present invention. A description with reference to FIGS. 1 and 2 is as follows.

First, the element data extractor 110 extracts one or more element data from random data (S200). Thereafter, the element data extraction unit 110 arranges the extracted element data according to a predetermined rule (S205).

Thereafter, the order relationship determination unit 120 determines an order according to the occurrence probability of each element data (S210), and allocates a symbol (here, a positive integer) to each element data according to the determined order (S215). According to the above steps S210 and S215, when there are N kinds of element data extracted and arranged from random data, the elements are allocated from 1 to N as symbols for each element data. If the probability of occurrence of each element data is different, 1 is assigned from the element data having a relatively high probability of occurrence. On the other hand, if some of the element data having the same probability of occurrence exists, an arbitrary integer is assigned to them.

Typically, the integer has a relationship of "1≤2≤ ... ≤N". Therefore, if integers 1 to N are allocated to each element data as described above, the element data may be arranged in the order of the size of the assigned integers (S220). For example, a set of element data extracted from random data is {a, b, c, d, e, f, g}, and a symbol assigned to each element data is a → 3, b → 5, c → 2, When d → 1, e → 4, f → 6, g → 7, the set of symbols is X = {3, 5, 2, 1, 4, 6, 7}.

On the other hand, in the above case, the ordered 1 to N are assigned to each element data. If the priority relationship of 1 to N allocated to each element data is unclear, it is necessary to clarify the priority relationship beforehand. . If this process is necessary, it is preferable to perform this process before step S210 or between steps S210 and S215.

In the embodiment of the present invention, the order relationship determiner 120 may define the order relationship between symbols because it is based on the well-ordering principle of the set theory that all sets may define the order between the elements. .

After the step S220, the positional instability determination unit 130 determines the positional instability of each symbol (S225). According to this determination, the positional instability determination unit 130 may derive information on the positional instability based on the set-order order relationship of each element data (S230). Hereinafter, this content is demonstrated with reference to a mathematical formula. First, the set of symbols X is X = {x ₁ , x ₂ ,... , x _n }.

In the above, f (X) represents the degree to which a particular symbol is in place based on the order relationship. max (X) represents the symbol having the maximum value in the set X, and ρ (x) represents the position value of the symbol x. X represents cardinality of the set X, that is, the total number of symbols included in the set X. According to Equation 1, when a specific symbol has a value of 1, the symbol may be determined to have positional instability. On the other hand, if a particular symbol has a value of 0, it can be determined that the positional instability does not exist.

As shown above, using Equation 1, it is possible to determine the positional instability of the element data having the maximum value and to derive information on the positional instability of the element data having the maximum value. . For example, a set of element data extracted from random data is {a, b, c, d, e, f, g}, and a symbol assigned to each element data is a → 3, b → 5, c → 2, d → 1, e → 4, f → 6, g → 7, and the element with the maximum value if the set of symbols derived from it is X = {3, 5, 2, 1, 4, 6, 7} Information about the positional instability of data g can be expressed as follows.

ρ (max (x)) = 7, │X│ = 7 → 7 <7 ⇒ f (X _g ) = 0

However, since the information indicates only the positional instability of the element data g having the maximum value, it is necessary to determine the positional instability of the remaining elemental data. In the present invention, the equation (1) can be applied to a subset of n pieces of X to obtain information on the positional instability of all element data.

In the above, i is 0 <i <n, i∈N.

According to Equation 1 and Equation 2, information on the positional instability of each element data can be obtained from all symbols constituting X. Information on the positional instability of each element data is as follows.

When max (x) is 7: ρ (max (x)) = 7, │X│ = 7 → 7 <7 ⇒ f (X _g ) = 0

When max (x) is 6: ρ (max (x)) = 6, │X│ = 6 → 6 <6 ⇒ f (X _f ) = 0

When max (x) is 5: ρ (max (x)) = 2, │X│ = 5 → 2 <5 ⇒ f (X _e ) = 1

When max (x) is 4: ρ (max (x)) = 4, │X│ = 4 → 4 <4 ⇒ f (X _d ) = 0

When max (x) is 3: ρ (max (x)) = 1, │X│ = 3 → 1 <3 ⇒ f (X _c ) = 1

When max (x) is 2: ρ (max (x)) = 1, │X│ = 2 → 1 <2 ⇒ f (X _b ) = 1

After the step S230, the adder 140 calculates the uncertainty of the alignment structure of the random data (S235). In detail, when the positional instability determination unit 130 derives information on the positional instability of each elemental data from symbols representing the elemental data, the summation unit 140 adds all the elemental data to sum them. It is determined whether the position is at the position, and the uncertainty of the alignment structure of the random data is calculated from the determination result.

The calculated structural uncertainty is a sum of a function f (X _i ) for a subset X _i of n Xs, which can be derived from Equation 3.

In the above, F refers to the structural uncertainty of random data.

When the information on the positional instability of each element data is as described above, the structural uncertainty of the random data obtained from Equation 3 is as follows.

F = f (X _g ) + f (X _f ) + f (X _e ) + f (X _d ) + f (X _c ) + f (X _b ) = 0 + 0 + 1 + 0 + 1 + 1 = 3

In addition, the following judgment is also possible.

F (X _g ) = 0 ⇒ The element data g is in position.

F (X _f ) = 0 ⇒ If element data g is excluded, element data f is in position.

③ f (X _e ) = 1 ⇒ element data e is not in place.

F (X _d ) = 0 ⇒ If the element data e, f, g are excluded, the element data d is in position.

F (X _c ) = 1 ⇒ The element data c is not in place.

F (X _b ) = 1 ⇒ The element data b is not in place.

Meanwhile, the above-described embodiments of the present invention can be written as a program that can be executed in a computer, and can be implemented in a general-purpose digital computer that operates the program using a computer-readable recording medium. The computer-readable recording medium may be a magnetic storage medium (for example, a ROM, a floppy disk, a hard disk, a magnetic tape, etc.), an optical reading medium (for example, a CD-ROM, a DVD, an optical data storage device, etc.). And storage media such as carrier waves (eg, transmission over the Internet).

The above description is merely illustrative of the technical spirit of the present invention, and those skilled in the art to which the present invention pertains various modifications, changes, and substitutions without departing from the essential characteristics of the present invention. will be. Accordingly, the embodiments disclosed in the present invention and the accompanying drawings are not intended to limit the technical spirit of the present invention but to describe the present invention, and the scope of the technical idea of the present invention is not limited by the embodiments and the accompanying drawings. . The scope of protection of the present invention should be interpreted by the following claims, and all technical ideas within the scope equivalent thereto should be construed as being included in the scope of the present invention.

The present invention can be applied to a program that requires compression, such as a compression algorithm, album, MPEG, signal processing. According to the present invention, it is possible to measure the amount of information according to the order structure of random data, unlike the conventional one, by calculating the structural uncertainty of random data based on the set-order order relationship. It can also be used for the development of compression programs. There is also a movement to specify new compression standards to overcome the limitations of recent compression algorithms, which is expected to contribute.

1 is a block diagram showing an internal configuration of an apparatus for calculating the uncertainty of an alignment structure of random data according to a preferred embodiment of the present invention;

2 is a flowchart illustrating a method of calculating an uncertainty of an alignment structure of random data according to a preferred embodiment of the present invention.

<Description of Symbols for Main Parts of Drawings>

100: uncertainty calculation device of the alignment structure 110: element data extraction unit

120: sequence relationship determination unit 130: positional instability determination unit

140: structural uncertainty calculation unit 150: control unit

160: power supply unit 170: input unit

180: output unit

Claims (15)

A symbol is assigned to each element data according to a frequency value of element data included in random data, and a symbol is allocated from element data having a large frequency value, and a symbol is arbitrarily assigned to element data having the same frequency value. An order relationship determining unit for enumerating the symbol-allocated element data according to the order of predetermined symbols, and determining the order of the symbols before performing the enumerating when the order of the symbols is not predetermined; By using the assigned symbol, it is determined whether to be in the original position when following the ascending or descending order for each of the listed element data, and removing the element data having the maximum frequency value among the remaining element data. The determination is performed on element data, and when the determination is performed, the symbol position value of the element data to be removed is compared with the total number of remaining element data before the removal, and the symbol position value is smaller than the total number. A positional instability judging unit which gives a first judgment value, and if not, gives a second judgment value; And A summation unit that calculates a structural uncertainty value of the random data by adding the first determination value or the second determination value when all of the element data is provided with the first determination value or the second determination value; Uncertainty calculation device of the alignment structure of the random data, characterized in that it comprises a. delete delete The method of claim 1, And the positional instability determining unit assigns 0 as the first determination value and grants 1 as the second determination value. The method of claim 1, An element data extraction unit which extracts the element data from the random data and arranges the extracted element data according to a predetermined rule Uncertainty calculation device of the alignment structure of the random data, characterized in that it further comprises. The method of claim 1, And a symbol assigned by the order relation determination unit is a number or a letter arranged in ascending or descending order. delete (a) A symbol is assigned to each element data according to a frequency value of element data included in random data, and a symbol is allocated from element data having a large frequency value, and a symbol is arbitrarily assigned to element data having the same frequency value. Making; (b) enumerating the symbol-allocated element data according to a predetermined order of symbols, and if the order of the symbols is not predetermined, determining the order of the symbols before performing the enumeration; (c) using the assigned symbol to determine whether or not to be in the original position when following the ascending or descending order for each of the listed element data, while removing the element data having the maximum frequency value from the remaining element data The determination is performed on the element data to be removed, and when performing the determination, the symbol position value is compared with the total number of element data remaining before the removal and the symbol position value is the total number. Giving a first judgment value when less and giving a second judgment value otherwise; And (d) calculating the structural uncertainty value of the random data by adding the first determination value or the second determination value when the first determination value or the second determination value is given to all the element data; Uncertainty calculation method of the alignment structure of the random data, characterized in that it comprises a. delete delete The method of claim 8, In the step (c), the uncertainty calculation method of the alignment structure of the random data, characterized in that 0 is assigned as the first determination value and 1 is assigned as the second determination value. As a previous step of step (a), Extracting the element data from the random data and arranging the extracted element data according to a predetermined rule Uncertainty calculation method of the alignment structure of the random data, characterized in that it comprises a. The method of claim 8, The method of calculating uncertainty of the alignment structure of the random data, wherein the symbols allocated in the step (a) are numbers or letters arranged in ascending or descending order. delete In a computer-readable recording medium, 14. A recording medium on which a program for implementing the method according to any one of claims 8 or 11 is recorded.

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