KR20190067721A - Matrix Sparsificating Method and System in Distributed Computing System - Google Patents

Abstract

The present invention relates to a method and system for matrix sparsification in distributed computing. By ensuring that the matrix sparsified in a distributed computing system contains more zero components than conventional sparsification, the method and system may calculate an operation result faster than the distributed computing system by a conventional distributed computing matrix sparsification method.

Description

Technical Field [0001] The present invention relates to a method and system for scarcely dispersing computing matrices,

The present invention relates to a method for scaling a matrix in a distributed computing system and a distributed computing system using a distributed computing matrix scarcification method.

As the age of big data comes, parallel computing and distributed computing are playing a major role in a variety of applications, including machine learning and big data analysis. Conventional distributed computing methods divide the operation to be processed and instruct it to be operated by a plurality of computers, and then solve the huge calculation problem by merging the operations performed by all the computers.

However, this method has the problem that the speed of the whole operation is seriously slowed down when the speed of some of the computers on the distributed system is slowed down. As the size of the distributed system grows along with the big data age, the above problems frequently occur, and the above problem becomes more serious in the distributed system, and various methods are proposed to solve this problem.

In particular, recent studies have suggested methods to overcome the above problems based on ideas obtained from coding theory. These methods distribute calculations efficiently to a distributed system so that even if the computed output values are not obtained from some computers, the results obtained from the remaining computers can be used to obtain the result of the entire computation.

And, another method is matrix scarification. Matrix sparse means that the matrix is transformed so that 0 is included as much as possible in the matrix computed by the distributed computer.

However, the conventional distributed computing matrix scrambling method has a problem that the number of zeros is limited and the computing speed is slow.

The present invention is directed to solving the above-mentioned problems and other problems.

Another object is to disclose a matrix scarcification method capable of performing arithmetic operations of a matrix faster in a distributed computing system.

; n by (k-m))이 추가되어 증가된 희소화 대상 행렬(

; n by k)이 생성되는 단계; 및 상기 증가된 희소화 대상 행렬에 계수 행렬(B; k by p)이 내적 연산되어 희소화 행렬(F; n by p)이 생성되는 단계를 포함하는 것을 특징으로 하는 분산 컴퓨팅 행렬 희소화 방법을 제공한다.According to an aspect of the present invention, there is provided a distributed computing system comprising: k distributed computing systems that use k computing results in a p computerized distributed computing system, where p, k, n, and m are natural numbers; In the method, an addition matrix (A (n by m) having the same row as the matrix to be sparse

; n < / RTI > by (km)) is added to increase the sparse matrix

; n by k) is generated; And a step of generating a scalar matrix F (n by p) by internally computing a coefficient matrix B (k by p) to the increased matrix to be sparse. to provide.

(T * p ', t * p') of the increased matrix to be subjected to sparification is determined in the case where t and p 'are natural numbers, and the components of the increased matrix to be sparged and the coefficient matrix are determined. The (m + 1) th column to the k < th > column) are arbitrarily determined; The elements of the coefficient matrix are determined by the components of the increased matrix to be sparse (from the first row to the t * p 'row, the first to kth columns); And determining a component of (t * p '+ 1) th row through (n-th row, (m + 1) th column through kth column) of the increased matrix to be sparse by the determined coefficient matrix have.

C is a natural number less than or equal to t, i is a natural number less than or equal to p ', and d is a natural number less than or equal to kt, provided that when i is p', d is a natural number less than or equal to p- (I-1) * t + c rows of the scrambling matrix calculated by the inner product operation of the incremented subject matrix and the coefficient matrix, the (i-1) * (kt ) + d. < / RTI >

In addition, in the step of determining the components of the increased matrix to be sparged (t * p '+ 1 to nth rows, m + 1 to k columns) (T * p '+ 1) -th row to the (n + 1) th row, the n-th row, the first column to the k-th column) of the scalar matrix determined by the inner product operation of the coefficient matrix the elements of the coefficient matrix may be determined so that the elements of the matrix, n rows, first to pth columns, include a zero component having a constant pattern.

(T * p '+ 1) -th row to the (m + 1) -th column to the k-th column) of the scarification matrix, The components of the coefficient matrix may be determined so that the components of the matrix, i.e., the rows to the n-th row, the first to the p-th columns, include km 0 elements for each row.

Further, j is a natural number equal to or smaller than nt * p ', e is a natural number equal to or smaller than km, (t * p' + 1 to nth row, Th column) to (k-th column) may be a component that makes the column component of the (j + e-1) th row of the scrambling matrix be zero.

According to still another aspect of the present invention, there is provided a method of generating a scrambling matrix, comprising: converting the generated scrambling matrix into a scrambling matrix; Each row of the transformed scrambling matrix is distributed to the p computers; Wherein in each of the p computers, an inner product operation of one row of the dispensed sparse transpose matrix and the input matrix (x; n by 1) is performed; Receiving an inner product operation result value from k computers among the p computers; And a step of decoding the k inner product operation result values received to calculate an inner product value of the transposed matrix and the input matrix of the sparse object matrix. .

According to the distributed computing matrix scarification method according to an embodiment of the present invention, in the distributed computing system, by ensuring that the sparse matrix contains more zero components than the conventional scarification, It is possible to calculate the calculation result faster than the distributed computing system.

1 is a flowchart illustrating a distributed computing method using a distributed computing matrix scarcification method according to an embodiment of the present invention.
FIG. 2 illustrates a distributed computing method using a distributed computing matrix sparse method according to an embodiment of the present invention. Referring to FIG.
3 is a flowchart illustrating a method of scrambling a distributed computing matrix according to an embodiment of the present invention.
4 is a diagram illustrating a distributed computing matrix scoring method according to an embodiment of the present invention.
FIG. 5 is a flowchart illustrating a distributed computing matrix scrambling method according to another embodiment of the present invention.
FIG. 6 is a diagram illustrating a distributed computing matrix sparse method according to another embodiment of the present invention.
FIG. 7 is a diagram illustrating a distributed computing system using a distributed computing matrix sparse method according to an embodiment of the present invention.

Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings, wherein like reference numerals are used to designate identical or similar elements, and redundant description thereof will be omitted. In the following description of the embodiments of the present invention, a detailed description of related arts will be omitted when it is determined that the gist of the embodiments disclosed herein may be obscured. It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory and are intended to provide further explanation of the invention as claimed. , ≪ / RTI > equivalents, and alternatives.

The singular expressions include plural expressions unless the context clearly dictates otherwise.

In the present application, the terms "comprises", "having", and the like are used to specify that a feature, a number, a step, an operation, an element, a component, But do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, or combinations thereof.

As a basic premise of the present invention, it is assumed that the number of computers performing calculations on the distributed system is p, the computation speed of k computers is fast among p computers, and the computation speed of p-k computers which are other computers is slow. In other words, according to the basic premise of the present invention, it is necessary to merge only the result values calculated by only k computers out of the results computed by the p computers obtained in the overall distributed system to derive a desired final computation result .

A distributed computing method and system using a distributed computing matrix scarcification method according to an embodiment of the present invention is a distributed computing method and system using a scalarization matrix A (n by m) (A ^T x; m by 1) of the matrix (A ^T ; m by n) and the input matrix (x; n by 1) The purpose.

1 is a flowchart illustrating a distributed computing method using a distributed computing matrix scarcification method according to an embodiment of the present invention.

FIG. 2 illustrates a distributed computing method using a distributed computing matrix sparse method according to an embodiment of the present invention. Referring to FIG.

; n by (k-m))이 희소화 대상 행렬의 우측에 연장되어 붙여지는 방법으로 추가되어, 증가된 희소화 대상 행렬(

; n by k)이 생성된 후, 증가된 희소화 대상 행렬에 계수 행렬(B; k by p)이 내적 연산되어 희소화 행렬(F; n by p)이 생성 될 수 있다. 이에 대한 더욱 자세한 설명은 이하 도 3 내지 도6을 통하여 설명한다.Referring to FIGS. 1 and 2, a distributed computing method using a distributed computing matrix sparse method according to an embodiment of the present invention can generate a scoring matrix using a scarification target matrix (S 110) . In more detail, an addition matrix having the same row as the scar-

; n by (km)) is added to the right side of the scarification target matrix so that the increased scarification target matrix

; n by k) is generated, a scoring matrix F (n by p) can be generated by performing an inner product operation on the coefficient matrix B (k by p) to the increased matrix to be sparse. A more detailed description thereof will be described below with reference to FIG. 3 to FIG.

Then, the generated scrambling matrix may be converted into a scrambling matrix (S120). More specifically, it is possible to reconstruct the matrix of rows and columns of the scrambling matrix to generate a transpose matrix. For example, the component value of the (l row column) of the scrambling matrix may be transformed to be the component value of (h row 1 column) in the scrambling transposition matrix.

Each row of the transformed scrambling matrix may be distributed to the p computers (S130). More specifically, the p rows of the transformed scrambling matrix may be separated into a single row and distributed to p computers, respectively. Thus, all of the p computers can perform operations on different rows. Fig rare transposed matrix screen to be distributed to the p number of the computer 2 from F ₁ to F ^{T T} _p Respectively.

In each of the p computers, an inner product operation of one row of the distributed scrambling matrix and the input matrix (x; n by 1) may be performed (S140). More specifically, each computer that has been partitioned with the scrambling transposition matrix may perform an inner computation of the distributed scrambling matrix and the input matrix. In this case, since all the computers execute different row operations, the computation speed may vary depending on the computational capabilities of the computer and the row component values of the distributed scrambling matrix.

An inner product operation result value may be received from k computers among the p computers (S150). More precisely, as described above, the computation speed of the p computers performing the inner product operation of the input matrix with one row of the distributed sparse transposition matrix may be different. At this time, among the p number of computers, the calculation result value can be received from k computers that have performed a relatively fast operation.

The received k inner product result values may be decoded to calculate an inner product value of the transpose matrix and the input matrix of the sparse target matrix (S160). More precisely, the decoding process knows the matrix values of the k scrambling transpose matrix, the input matrix, the coefficient matrix, the incremented scrambling matrix and the scalar matrix, and knows the matrix operation in which the scrambling matrix is generated. The inner product value of the candidate matrix to be subjected to the scrambling and the input matrix can be calculated.

3 to 4, a method for scarcely computing a distributed computing matrix according to an embodiment of the present invention corresponding to the scarification matrix generation step of FIG. 1 will be described in detail.

3 is a flowchart illustrating a method of scrambling a distributed computing matrix according to an embodiment of the present invention.

4 is a diagram illustrating a distributed computing matrix scoring method according to an embodiment of the present invention.

; n by (k-m))이 추가되어 증가된 희소화 대상 행렬(

; n by k)이 생성될 수 있다(S310). 보다 자세하게, 도 4 (a) 내지 도 4(b)에 도시된 바 와 같이, 희소화 대상 행렬의 우측에 추가 행렬을 결합하는 방법으로 증가된 희소화 대상 행렬이 생성될 수 있다. 3 to 4, a method for scaling a distributed computing matrix using k computing results in a p-computer distributed computing system, where p, k, n, and m are natural numbers, An adder matrix A (n by m) having the same row as the matrix to be subjected to the scrambling (

; n < / RTI > by (km)) is added to increase the sparse matrix

; n by k) may be generated (S310). More specifically, as shown in Fig. 4 (a) to Fig. 4 (b), an increased sparse matrix may be generated by combining additional matrices to the right of the matrix to be sparse.

The components of the incremented scoring matrix and the inner product matrix of the coefficient matrix may be determined (S320). More specifically, as shown in Fig. 4 (c), the components of the coefficient matrix may have predetermined fixed component values. For example, an encoding matrix having the same code as Reed-Solomon code, which is widely known in the code theory, can be used as an example of determining the component value of the coefficient matrix.

The component of the increased scrambling matrix may be determined by the determined coefficient matrix component (S330). More specifically, as shown in Figs. 4 (c) to 4 (d), the components of the increased matrix to be sparse (the first to nth rows and the (m + The components of the scrambling matrix (the first to n-th rows, the first to the p-th columns) include km 0 components for each row, and the 0-components of km are not arranged in the same column. The components can be determined. For example, when q is a natural number equal to or less than n and e is a natural number equal to or less than km, the number of rows (first through nth rows, m + 1th through kth columns) Component may be calculated as a component such that the q-th row, q + e-1 (mod p) column component of the scrambling matrix is zero, so that all component values of the increased matrix to be sparse can be determined. This can be easily calculated through linear equations. Here, q + e-1 (mod p) denotes a remainder value obtained by dividing q + e-1 by p.

The specific formula for obtaining the additional matrix component constituting the increased subject matter matrix is given by Equation 1 below.

(1)

이고,

는

에 해당하는 (k-m)개의 열벡터들을 나열한 계수 행렬(B)의 부분 행열이며,

는 추가 행렬의 (제q행, 제1열 내지 제k-m열)이고,

는 추가 행렬의 (제q행, 제1열 내지 제m열)이며,

는 추가 행렬의 부분 행렬의 제1행 내지 제m행이고,

는 추가 행렬의 부분 행렬의 제m+1행 내지 제k행이다.here,

ego,

The

A partial matrix of a coefficient matrix B that lists (km)

(Column q, column 1 to column km) of the additional matrix,

(Column q, column 1 to column m) of the additional matrix,

Are the first through m-th rows of the partial matrix of the additional matrix,

Th row to the k-th row of the partial matrix of the additional matrix.

Then, a scarification matrix may be generated (S340). More specifically, a scoring matrix may be generated through an inner product operation of the determined increased scoring target matrix and the coefficient matrix. The generated scoring matrix may have k-m 0 elements for each row, and the 0 elements may be arranged to be uniformly distributed in all rows.

5 to 6, a method for scarcely dividing a distributed computing matrix according to another embodiment of the present invention corresponding to the scarification matrix generation step of FIG. 1 will be described in detail.

FIG. 5 is a flowchart illustrating a distributed computing matrix scrambling method according to another embodiment of the present invention.

FIG. 6 is a diagram illustrating a distributed computing matrix sparse method according to another embodiment of the present invention.

또는

중에서 작은 값을 넘지 않는 최대 자연수이고, p'은 p/(k-t) 또는 n/t 중에서 작은 값을 넘지 않는 최대 자연수이다. In the following description, when p, k, n, and m are natural numbers, t is

or

, And p 'is the maximum natural number that does not exceed a small value among p / (kt) or n / t.

보다 큰 경우, 도 6 (h)에 도시된 바와 같이 희소화 행렬의 0 성분 생성 방식에 따른 범위가 나뉠 수 있도록, 주어진 희소화 대상 행렬을 각 분할된 행렬의 행의 개수가 t*p'개가 넘지 않도록 n/(t*p') 이하의 자연수의 개수로 행을 분할한 후, 아래의 분산 컴퓨팅 행렬 희소화를 실시 한다. 만약, n이

이하인 경우, 희소화 대상 행렬을 분할하지 않고 아래의 분산 컴퓨팅 행렬 희소화를 실시 한다.n is

6H, if the number of rows of each divided matrix is t * p ', that is, the number of rows of each divided matrix is set so that the range according to the 0 component generation method of the scarification matrix can be divided as shown in FIG. 6 The number of natural numbers not more than n / (t * p ') is not exceeded, and then the following distributed computing matrix is scarcely divided. If n

, The following distributed computing matrix scarification is performed without dividing the matrix to be sparse.

; n by (k-m))이 추가되어 증가된 희소화 대상 행렬(

; n by k)이 생성될 수 있다(S510). 보다 자세하게, 도 6 (a)에 도시된 바 와 같이, 희소화 대상 행렬의 우측에 추가 행렬을 결합하는 방법으로 증가된 희소화 대상 행렬이 생성될 수 있다. 5 to 6, in a distributed computing matrix scarceration method using k computing results in a p-computer distributed computing system, a scoring target matrix A (n by m) Lt; RTI ID = 0.0 > (

; n < / RTI > by (km)) is added to increase the sparse matrix

; n by k) may be generated (S510). More specifically, as shown in Fig. 6 (a), an increased sparse matrix may be generated by combining additional matrices to the right of the matrix to be sparse.

Some elements of the increased matrix to be sparged may be arbitrarily determined (S520). More specifically, as shown in Fig. 6 (d), when t and p 'are natural numbers, the components of the additional matrix (the first row to the t * p' (Corresponding to the first row to the t * p 'row, the (m + 1) th column to the k th column) of the corresponding increased candidate for the sparse target can be set to arbitrary values.

The components of the coefficient matrix may be determined by the components of the increased matrix to be subjected to sparse (from the first row to the t * p 'th column, the first column to the k th column) (S530). More specifically, c is a natural number less than t, i is a natural number less than or equal to p ', and d is a natural number less than kt, provided that when i is p', d is a natural number less than or equal to p- (I-1) * t + c row, (i-1) * ((i-1)) th row of the scarification matrix calculated by the inner product operation of the incremented matrix to be subjected to the sparse addition and the coefficient matrix, lt; RTI ID = 0.0 > kt) + d < / RTI >

6 (f), the components of the scrambling matrix (the first row to the t-th column, the first column to the kt-th column) are set to be 0 as shown in Fig. 6 the component values of the coefficient matrix (the first row to the k-th row, the first column to the k < th > column) of the coefficient matrix can be calculated, and as shown in Fig. 6 (g) As shown in Fig. 6 (d), so that the components of the matrix (the t + 1th row to the 2t row, the k-t + 1 column to the 2 (K-th row to k-th row, k-th + 1 < th > column to second (kt) column) As shown in FIGS. 6 (d) and 6 (h), the component values of the coefficient matrix so that (kt) 0 components are included in each row up to the t * p ' All can be determined.

The remaining elements of the increased matrix to be sparse can be determined by the determined coefficient matrix (S540). More specifically, the components of (t * p '+ 1) th row to (n-th row, (m + 1) th column to kth column) of the increased matrix to be sparse can be determined by the determined coefficient matrix, (T * p '+ 1) -th row to the (n) th row of the matrix of the sparse target to be increased in the same manner as the method described with reference to FIG. 3 to FIG. 4 so that the (0) m + 1 < th > column to k < th > column) may be determined. More specifically, when j is a natural number equal to or smaller than nt * p 'and e is a natural number equal to or smaller than km, (t * p' + 1) th row to 1) th column to the k-th column) may be calculated and calculated as a component to make the column component of the (t + p '+ j) th column and the (j + e-1) th row of the scrambling matrix be zero. Here, j + e-1 (mod p) denotes a residual value obtained by dividing j + e-1 by p. The detailed mathematical calculation method will be omitted since it is the same as the description of FIG. 3 to FIG. 4 above.

The coefficient matrix may be internally computed to the increased target matrix to generate a scalar matrix (S550). More specifically, a scoring matrix may be generated by the determined inner product of the scoring target matrix and the determined coefficient matrix.

As described above, the scrambling matrix generated by the distributed computing matrix scrambling method according to an embodiment of the present invention has the effect of ensuring more zero components than the scrambling matrix generated by the conventional matrix scrambling method. Therefore, the distributed computing matrix scarcification method according to an embodiment of the present invention can improve the overall distributed computing operation speed.

FIG. 7 is a diagram illustrating a distributed computing system using a distributed computing matrix sparse method according to an embodiment of the present invention.

The method of scaling a distributed computing matrix according to an embodiment of the present invention may be performed in a distributed computing system 700 in which a distributed computing matrix scarcification method as described above can be performed. More specifically, the distributed computing system 700 using the distributed computing matrix scarcely includes an input matrix receiving unit 710, a scarification matrix generating unit 720, a computing unit 730, a decrypting unit 740, and a control unit 750 ).

The input matrix receiving unit 710 can receive an input matrix from the outside.

The scrambling matrix generator 720 may generate an increased scrambling matrix and a coefficient matrix from the scrambling target matrix to generate a scrambling matrix and convert the generated scrambling matrix into a transposing matrix.

The computing unit 730 may include a plurality of computers capable of performing matrix operations, each of which may receive a partial row of the transformed scrambling matrix and perform an inner product operation with the input matrix.

The decoding unit 740 may calculate an inner product of the permutation matrix and the input matrix of the sparse target matrix from the k resultant values computed by the computing unit 730. [ When k or more result values are received from the computing unit 730, the decoding unit 740 may calculate an inner product of the transpose matrix and the input matrix of the sparse matrix.

The control unit 750 transmits the input matrix received by the input matrix receiving unit 710 to the scrambling matrix generator 720 to generate the scrambling matrix and outputs the scrambling matrix generated by the scrambling matrix generator 720 to the scrambling matrix generator 720, The p number of rows of the matrix can be distributed to each computer of the computing unit 730 and the k number of results computed from the computing unit 730 can be transmitted to the decrypting unit 740, It is possible to calculate the inner product value of the transpose matrix and the input matrix of the target matrix.

It will be apparent to those skilled in the art that the present invention may be embodied in other specific forms without departing from the spirit or essential characteristics thereof.

The scope of the present invention should be determined by rational interpretation of the appended claims, and all changes within the scope of equivalents of the present invention are included in the scope of the present invention.

700: Distributed computing system using distributed computing matrix sparse method
710: Input matrix receiver
720: scarification matrix generation unit
730:
740:
750:

Claims (8)

When p, k, n and m are natural numbers,
1. A distributed computing matrix scarceration method using k computing results in a distributed computing system comprising p computers,
An additional matrix (A (n by m)) having the same row as the matrix to be subjected to the scarification (

; n < / RTI > by (km)) is added to increase the sparse matrix

; n by k) is generated; And
Wherein the step of generating a scoring matrix F (n by p) is performed by internally computing a coefficient matrix B (k by p) to the increased matrix to be sparse.
The method according to claim 1,
When t and p 'are natural numbers,
Wherein in the determination of the elements of the increased matrix to be sparse and the coefficient matrix,
A step of arbitrarily defining the components of the increased matrix (the first row to the t * p 'row, the (m + 1) th column to the k th column);
The elements of the coefficient matrix are determined by the components of the increased matrix to be sparse (from the first row to the t * p 'row, the first to kth columns); And
(T * p '+ 1) th row to the (n + 1) th row to the k-th column) of the increased target matrix by the determined coefficient matrix;
The method comprising the steps of:
3. The method of claim 2,
where c is a natural number less than or equal to t, i is a natural number less than or equal to p ', and d is a natural number less than or equal to kt, provided that when i is p, d is a natural number less than or equal to p-
Wherein the coefficient matrix comprises:
(I-1) * t + c rows and (i-1) * (kt) + d columns of the scarification matrix calculated by the inner product operation of the incremented sparse matrix and the coefficient matrix are 0 ≪ / RTI > wherein the matrix is a matrix having elements that allow the matrix to be transformed into a matrix.
3. The method of claim 2,
In the step of determining the components of the increased matrix to be sparged (t * p '+ 1 to n-th rows, m + 1 -th column to k-th column)
(T) of the scarification matrix determined by an inner product operation of the coefficient matrix and the components of the incremented matrix to be sparged (t * p '+ 1 to nth rows, first to kth columns) the elements of the coefficient matrix are determined so that the components of the matrix * p '+ 1 to n-th rows, the first to pth columns) include a zero component having a constant pattern.
5. The method of claim 4,
(T * p '+ 1) -th row to the (k + 1) th column in the scarification matrix, Wherein the elements of the coefficient matrix are determined so that the components of the first to nth rows, the nth row, the first to the pth columns include km 0 elements for each row.
5. The method of claim 4,
j is a natural number equal to or smaller than nt * p ', and e is a natural number equal to or smaller than km,
(T + p '+ 1) th row to the (n + 1) th column to the (k-th column)
Th column of the scrambling matrix, and the j + e-1 (mod p) column component of the t * p '+ j row of the scrambling matrix.
The method according to any one of claims 1 to 6,
A distributed computing system using a distributed computing matrix sparse method, comprising a computer in which the distributed computing matrix sparing method of any one of claims 1 to 6 is performed.
The method according to claim 1,
Transforming the generated scrambling matrix into a scrambling transposition matrix;
Each row of the transformed scrambling matrix is distributed to the p computers;
Wherein in each of the p computers, an inner product operation of one row of the dispensed sparse transpose matrix and the input matrix (x; n by 1) is performed;
Receiving an inner product operation result value from k computers among the p computers; And
The received k inner product result values are decoded to calculate an inner product value of the transposed matrix and the input matrix of the scrambled subject matrix;
And a distributed computing matrix scarceration method.

Images