JP2011077958A - Dimensional compression device, dimensional compression method, and dimensional compression program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a dimensional compression device, a dimensional compression method and a dimensional compression program for reducing calculation costs, and for suppressing an increase in calculation time while maintaining high accuracy of approximation calculation. <P>SOLUTION: The dimensional compression device that employs cyclic matrix or inverse cyclic matrix of random series as a random matrix is provided with: a pseudo white noise vector processing part; a data sample vector processing part; and a multiplication part. In this case, the pseudo white noise vector processing part creates a pseudo white noise vector n, and performs pre-processing on the pseudo white noise vector n to create a vector r, and performs high speed Fourier transformation on the vector r to create a vector s, preferably. <P>COPYRIGHT: (C)2011,JPO&INPIT

Description

  The present invention relates to a dimension compression apparatus, a dimension compression method, and a dimension compression program.

  Many general large-scale databases accumulate a large number of samples (for example, documents and images). In order to search and classify similar samples, numerical values called attributes (for example, the application frequency and images of document words) In many cases, each sample is represented by a set of feature amounts, pixel values, and additional information. Each sample is represented by a vector having an attribute as a component, and similarity calculation using a vector inner product, norm or the like, or statistical processing is required.

  However, in practice, the number of dimensions of this vector (for example, the number of words in a dictionary, the number of pixels in an image, etc.) is very high, and a decrease in search efficiency due to high dimensions is known as a curse of dimensions. Therefore, calculation efficiency is improved by reducing the dimension by a technique called dimension compression or dimension reduction (simply expressed as “dimensional compression” in this specification).

  By the way, random projection is known as one of the techniques related to the dimensional compression. Here, “random projection” refers to linear projection of a high-dimensional vector to a low-dimensional vector using a matrix having random elements. Known techniques relating to random projection are described, for example, in Non-Patent Documents 1 and 2 below.

S. S. Vempala, The Random Projection Method, Volume 65 of Series in Discrete Materials and Theoretical Computer Science, American Mathematical Society 4 D. Achryoptas, Database-friendly random projections: Johnson-Lindenstrauss with binary coins, Journal of Computer and System Sciences, 661: 681-681. Tatsuya Watanabe, Eiji Enomoto, Akira Maruoka, Dimensional Compression by Random Projection, IEICE Technical Report COMP2001-92, pp. 73-79, IEICE, 2002 Hirohito Ouchi, Takao Miura, Isamu Shiotani, Searching News Streams Using Random Projection, Journal of the Database Society of Japan (DBSJ Letters), Vol. 3, No. 3, pp. 1-4, 2004

  However, in the random projection exemplified by the above-mentioned non-patent document, it is necessary to generate and store a random matrix having the size of the product of dimensions before and after the projection, which increases the calculation cost necessary for vector projection using the random matrix. There is a problem. For example, in the case of 1 million dimensions and 8000 dimensions, a storage area of about 32 GB is required even in single precision, and the storage area is unrealistic. In addition, the calculation time required for the random projection is proportional to the product of the number of dimensions before and after the projection, and if the number of dimensions after the projection is increased in order to improve the accuracy of the approximate calculation, the calculation time is increased.

  Therefore, in view of the above problems, the present invention provides a dimension compression apparatus, a dimension compression method, and a dimension compression program that can reduce calculation cost and suppress increase in calculation time while maintaining high accuracy of approximate calculation. Objective.

  As a result of intensive studies by the present inventors on the above-mentioned problem, the inventors have conceived that the above-mentioned problem can be solved by adopting a random sequence circulant matrix or inverse circulant matrix as a random matrix, thereby completing the present invention. It came to.

  That is, the dimension compression apparatus according to one aspect of the present invention employs a random sequence cyclic matrix or inverse cyclic matrix as a random matrix.

  A dimension compression apparatus according to an aspect of the present invention includes a pseudo white noise vector processing unit, a data sample vector processing unit, and a multiplication unit.

  As described above, the present invention provides a dimensional compression apparatus, a dimensional compression method, and a dimensional compression program that maintain a high accuracy of approximate calculation, have a lower calculation cost, and suppress an increase in calculation time.

It is a figure which shows the functional block which concerns on embodiment. It is a figure which shows the flow of a process in a pseudo | simulation white noise process part. It is a figure which shows the flow of the pre-processing in a pseudo process noise process part. It is a figure which shows the flow of a data sample vector process. It is a figure shown about the process of the multiplication part. It is a figure which shows the vector r, the cyclic matrix R, the vector b, and the diagonal matrix B.

  Hereinafter, embodiments of the present invention will be described with reference to the drawings. However, the present invention can be implemented in many different modes and is not limited to the embodiments shown below.

(Embodiment 1)
FIG. 1 is a diagram showing functional blocks of the dimension compression apparatus according to the present embodiment. As shown in the figure, the dimension compression apparatus 1 according to the present embodiment includes a pseudo white noise vector processing unit 2, a data sample vector processing unit 3, and a multiplication unit 4. The dimension compression apparatus 1 according to the present embodiment can be realized in various forms. For example, the dimensional compression apparatus 1 stores a computer program that is executed on a recording medium such as a so-called computer hard disk to function as each of the above-described units. It can be realized by executing. In particular, the program can be stored in a recording medium of a server on the Internet and executed.

The pseudo white noise vector processing unit 2 is a unit for creating and processing a pseudo white noise vector, and is not limited, but specifically, a D-dimensional (D is a positive number) pseudo white noise. A vector n is created (S21), the pseudo white noise vector n is preprocessed to create a vector r (S22), and the vector r is subjected to fast Fourier transform (S23) to create a vector s. Here, the “pseudo white noise vector” refers to a vector in which the cross-correlation with the expected value of the component is zero and the autocorrelation is a constant. The vector s after the fast Fourier transform is recorded in a storage area such as a hard disk. The pseudo white noise vector processing unit 2 according to the present embodiment uses a fast Fourier transform that is widely used.
It is also possible to use a high-speed Walsh-Hadamard transform that can simply implement a dedicated arithmetic unit for integer arithmetic. In any of the above conversions, even if the speed is not high, the calculation time increases, but the advantage that random projection can be performed without securing a huge matrix remains. FIG. 2 shows a processing flow of the pseudo white noise vector processing unit.

  Here, the pre-processing (S22) is a pre-processing applied to the pseudo white noise vector in order to improve the accuracy of the approximate calculation using the vector compressed in the present embodiment, and depends on the application target of the present invention. Although it can be omitted, it is generally preferable to include a normalization process, and more preferably, as shown in FIG. 3, for example, the average value removal process (S221), the first normalization process (S222), the bias It is preferable to perform the process (S223) and the second normalization process (S224).

  Here, the average value removal process (S221) refers to a process of removing the average value from each component so that the average value of the vector components becomes zero. The first normalization process (S222) is a normalization process performed so that the square norm of the vector becomes 1. The bias process (S223) refers to a process of adding the reciprocal of the square root of D to each component of the vector. The second normalization process (S224) is a normalization process performed so that the square norm of the vector becomes D / K. Here, K is the number of dimensions after projection.

  In the present embodiment, the data sample vector processing unit 3 is a unit for performing processing on the data sample, and performs a multiplication process (S31) with the spread code b on the input vector x representing the data sample. After that, fast Fourier transform is performed (S32), further complex conjugate processing is performed (S33), and a vector z is created. Here, the “spreading code” is a vector having the same length as the input vector x representing the data sample and having a random number of ± 1 as an element. FIG. 4 shows the processing of the data sample vector processing unit 3.

  In this embodiment, the multiplication unit 4 multiplies the vector s created by the pseudo white noise vector unit 2 and the vector z created by the data sample processing unit 3 for each component (S41), and performs fast inverse Fourier transform. In step S42, an output vector y is created. Then, by arbitrarily extracting K components from the vector y, a K-dimensional vector obtained by randomly projecting the vector x can be obtained. FIG. 5 shows the processing of the multiplication unit 4.

  By the way, as shown in FIG. 6, if the matrix (cyclic matrix) constructed by circulating the D-dimensional vector r to the left is R and the diagonal matrix having the D-dimensional vector b as an element is B, the output vector y Is equivalent to a D-dimensional vector obtained by projecting the input vector x with the matrices B and R. In the description of the present embodiment, a matrix constructed by cycling to the left is used. However, when the complex conjugate processing in the data sample vector processing unit 3 is omitted, random projection is performed by the matrix that is cycled to the right. The direction of patrol may be right or left.

  In the present dimensional compression apparatus, due to the nature of white noise, the pre-processed vector r and the vector obtained by circulating the vector r become uncorrelated. Therefore, if K row vectors are arbitrarily extracted from the matrix R, a random matrix having a size of K × D is obtained. Based on this principle, the dimensional compression apparatus according to the present embodiment realizes dimensional compression having properties similar to the conventional random projection. Practically, pseudorandom numbers, uncorrelated codes {−1, + 1}, sequences that can be regarded as independent isomorphic distributions, and the like can be used as the components of the vector n. Further, any one row of the random matrix used in the conventional technique can be used as the vector n.

  As described above, the dimension compression apparatus according to the present embodiment can maintain high approximation calculation accuracy without sacrificing the approximation accuracy mathematically guaranteed by random projection, and further increase the storage area of the random matrix. It is possible to reduce the calculation cost, and it is possible to apply random projection to high-dimensional data of a scale that was almost impossible in the past. It is possible to provide a dimension compression apparatus, a dimension compression method, and a dimension compression program in which the increase is suppressed.

  The dimensional compression apparatus, the dimensional compression method, and the dimensional compression program can be used for searching and classifying similar samples in a database in which a large number of samples are accumulated, and have industrial applicability.

DESCRIPTION OF SYMBOLS 1 ... Dimension compression apparatus, 2 ... Pseudo white noise vector processing part, 3 ... Data sample vector processing part, 4 ... Multiplication part

Claims (3)

  A dimension compression apparatus that employs a cyclic matrix or a reverse cyclic matrix of a random sequence as a random matrix. A pseudo white noise vector processing unit;
A data sample vector processing unit;
A dimensional compression apparatus having a multiplication unit. The pseudo white noise vector processing unit creates a pseudo white noise vector n, pre-processes the pseudo white noise vector n to create a vector r, and performs a fast Fourier transform on the vector r to create a vector s. The dimensional compression apparatus according to claim 2.