JPH08106505A - Information processor - Google Patents

Abstract

PURPOSE: To perform contention learning without losing the norm information of input data by using the inner product operation suitable for making into hardware as the distance reference to perform the contention learning. CONSTITUTION: This information processor operates the inner product between the input vector displayed on a liquid crystal television 101 and each vector of the weight vector group displayed on a liquid crystal television 102 to make the input vector correspond to one vector of the weight vector group and is provided with a norm extracting and adding means 2 which extracts information related to the norm of the input vector to add it to the component of the input vector before operation of the inner product.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an information processing device,
In particular, by determining a processing element that satisfies a certain distance criterion by using the inner product operation and performing some operation on the winning element and the element determined by the winning element,
The present invention relates to an information processing device that performs competitive learning for phase-preserving mapping and pattern recognition.

[0002]

2. Description of the Related Art A competitive learning algorithm for determining a winning element that satisfies a certain distance criterion and performing a phase-preserving mapping or pattern recognition by performing some operation on the winning element and the element determined by the winning element. Is well known (T. Kohonen, "Self-Organization and A
ssociative Memory, Third Edition, Springer-Verlag, Be
rlin, 1989.).

Each of these algorithms uses a distance criterion such as Euclidean distance, Manhattan distance, and inner product, and has a competition process for a certain input to select a winning element that satisfies the criterion. When creating a program and executing an algorithm on an ordinary computer, any distance criterion can be easily used. Therefore, the Euclidean distance, which is generally reported to have good performance, is often used as the distance standard.

However, when the Euclidean distance calculation is performed on hardware, a difference circuit, a square circuit, and a summing circuit are required, which makes it difficult to realize. Therefore, the inner product distance criterion is often used. Especially when it is realized using optics, the inner product calculation is most easily realized due to the parallelism of light. Some information processing devices that perform competitive learning with inner product calculation using optics have been reported (Taiwei et al., "Self-or
ganizing optical neural network for unsupervised l
earning ", Opt.Eng., VOL.29, No.9,1990.; J.Duvillier et
al., "All-optical implementation of a self-organiz
ing map ", Appl. Opt. Vol. 33, No. 2, 1994.).

[0005]

When competing to select a winning element using inner product arithmetic, it is necessary to standardize the data. This will be described with reference to FIG. The input data is a two-dimensional vector X, and the weight vector of the element group that is a candidate for competition is a two-dimensional vector m _i (i represents the element number). As shown in FIG. 1, it is assumed that the two-dimensional vector X is input and the candidate weight vectors are m ₁ and m ₂ . When the Euclidean distance is used, the element with the shortest distance between the vectors is the winning element, so d ₁
<D ₂ makes m _{1 the} winning element. On the other hand, when the inner product calculation is used, the one having the largest inner product value corresponds to the one most similar to the input vector, and becomes a winning element. Inner product value is 1, represented by the orthogonal projection D _i and the product of the norm of X to X of the m _i. Therefore, by comparing the magnitude of D _i, the magnitude of the inner product can be compared, and in this case, m ₂ is the winning element. In the competitive learning, the Euclidean distance between the input data and the weight vector and the similarity in the Manhattan distance and the like corresponding thereto are compared, and the element having the most similar weight vector is selected. However, when the inner product calculation is used as described above, a weight vector having a large norm has a large inner product value even if the Euclidean distance is large, and thus tends to be a winner. That is, the similarity in the inner product calculation depends on the norm of the vector, not on the magnitude of the Euclidean distance. Therefore, effective competitive learning cannot be performed.

Therefore, in order to perform effective competitive learning by inner product calculation, the input data and the weight data must be standardized. At this time, as shown in FIG. 2, d ₁
<D ₂ , D ₁ > D ₂ , and m ₁ is the winning element whether the Euclidean distance or the inner product operation is used. Therefore, effective competitive learning can be performed even by using the inner product calculation.

However, by performing the above-mentioned standardization, the norm information of the input data is lost. That is, for example, when there is a uniform distribution of the two-dimensional vector data as shown in FIG. 3, the points on the curve of the unit radius as shown in FIG. That is, all the points in the direction connecting the origin O and the data point are one point on the curve, the norm information of the input data is lost, and only the direction information remains. In the case of competitive learning only in the direction of vector data, the norm information of the data may be lost,
Norm information cannot be lost in competitive learning that also considers the norm of a vector.

Summarizing the above problems, the conditions required for the information processing apparatus of the present invention are as follows. A-1) As the distance reference, competitive learning using inner product calculation suitable for hardware implementation is performed. A-2) Competitive learning that does not lose norm information of input data can be performed.

The present invention has been made in view of the above situation, and an object thereof is to satisfy the above conditions A-1) and A-2) and to calculate an inner product suitable for hardware as a distance reference. It is an object of the present invention to provide an information processing device capable of performing competitive learning by using, and performing competitive learning without losing norm information of input data.

[0010]

An information processing apparatus of the present invention that achieves the above object is an information processing apparatus that associates an input vector with any vector of a weight vector group by taking an inner product with each vector of the weight vector group. In the device,
The present invention is characterized by having norm extraction / addition means for extracting information about the norm of the input vector before taking the inner product and adding it to the components of the input vector.

In this case, it is desirable to have an input vector normalizing means for normalizing the input vector to which the information on the norm is added before taking the inner product. Further, it is desirable to have a weight vector group normalizing means for normalizing each vector of the weight vector group before taking the above inner product. These normalizations may be performed by an electric signal or may be performed optically.

[0012]

The function and operation of adopting the above configuration will be described below. Theoretically, what kind of algorithm should be used in order to perform competitive learning that does not lose the norm information of the input data (A-2)) by using the inner product calculation as the distance reference (A-1) It will be described with reference to FIGS. 5 to 11.

As described above, when determining the degree of similarity using the inner product calculation, it is necessary to standardize the data. At this time, since the vector is divided by the norm to form a unit vector, the original norm information has heretofore been lost. In order not to lose the original norm information, in the present invention, it is considered to add a component indicating the norm to one component of the input vector. For example, the input data is a two-dimensional vector X = (x, y). The norm is D = (x ² +
y ² ) ^1/2 . If this is standardized, X / | X | =
(X / D, y / D). This is the input vector that is conventionally used when the similarity is determined using the inner product calculation. The vector norm component is added to this vector, and X '
= (X / D, y / D, f (D)) is created. next,
X ′ is standardized to create X ″ = X ′ / | X ′ |, and this is used as input data instead of X.

That is, X = (x, y), D = (x ² + y ² ) ^1/2 (1) X '= (x / D, y / D, f (D)) (2) X ″ = X ′ / | X ′ | (3) Since X ″ is standardized, it is possible to determine the degree of similarity using the inner product operation. In addition, since the norm information D is included in the vector component of X ″, not only the direction information of the input vector but also the norm information remains even after normalization. Therefore, X = (x, y If X ″ is used as the input data instead of), competitive learning is possible without losing the norm information of the input data even if the inner product operation is used as the distance reference.

The correspondence between a two-dimensional vector of input data and a three-dimensional vector obtained by adding a component indicating the norm to the vector is examined for various f (D). First, as a simple case, a) f (D) = D, b) f
(D) = 1 / D is selected, and each point A ₁ , B ₁ , A ₂ , B ₂ of X on the two-dimensional plane shown in FIG. 5 is converted into each point of X ″ on the three-dimensional space. 6 and 7 respectively show that there is a one-to-one correspondence, and points A ₁ , B ₁ and A _{2 are also shown.} , B ₂
There is no such thing as a twist that breaks the order. However, the case where the phase of the input data is better preserved is in the case of b). The reason for this will be described below.

Comparing the distance between A ₁ and B _{1 and} the distance between A ₂ and B ₂ on the two-dimensional plane shown in FIG. 5, A ₁ and B ₁ are closer. Comparing these converted points in a three-dimensional space, in FIG. 6, the points A ₁ ″ corresponding to A ₁ and B ₁ are
B ₁ ″ is closer than the points A ₂ ″ and B ₂ ″ corresponding to A ₂ and B ₂ , but in FIG. 7, the opposite is true.
Therefore, in FIG. 7, the relative perspective relationship on the two-dimensional plane can be reflected, and the phase of the input data is better preserved.

In order to further clarify the superiority or inferiority of whether the phase of the input data is better preserved, an experimental example is shown. As an example of competitive learning, self-organizing feature map (T.Kohone
n, "Self-Organization and Associative Memory, Third
Edition, Springer-Verlag, Berlin, 1989., Below, SOM
Call. ) Was used to perform the phase-preserving mapping. Below, SO
The M will be briefly described.

As shown in FIG. 8, the SOM is composed of a layer of two-dimensionally arranged element groups (hereinafter referred to as a map layer ML) and an input layer IP for inputting data. Although the map layer ML shows elements arranged two-dimensionally in FIG. 8, elements arranged one-dimensionally may be used. Input layer IP is map layer M
It is coupled to all the elements of L, and the input data can be given to all the elements of the map layer ML. The input data may be a scalar or a vector, but here, it is generally set as a vector X (n-dimensional). It is assumed that all the elements i of the map layer ML (i is the order on the map and the total number of elements is k) have a weight vector m _i (n-dimensional). The SOM algorithm determines the weight vector to be updated from the similarity between the input vector X and the weight vector m _{i of} each element <similarity matching>, and brings the weight vector m _i closer to the input vector X. <Update>
Can be divided into Then, by repeating the actions of both, the weight vector m reflecting the distribution of the input vector X
_i (1 ≦ i ≦ k) is generated. The specific expressions of <similarity matching> and <update> are shown below.

<Similarity Matching> _{<Update> m i (t + 1)} = m i (t) + α (t) {X (t) -m i (t)} i∈N c m i (t + 1) = m i (t) Others ... ( 5) where | X−m _i | is the Euclidean distance between X and m _i ,
C is the element with the smallest distance (victory element), N _c
Is the neighborhood of the winning element C in the map layer ML, α (t) is a positive constant, and t is the time. While repeating the update, N
The magnitudes of _c and α (t) are gradually reduced. Also, α
(T) can be selected so as to become smaller as the distance from the victory element C increases.

In the above algorithm, since Euclidean distance is used in <similarity matching>, X is also m _i
Need not be standardized. When the inner product operation is used in <similarity matching> as in the present invention, specific expressions of <similarity matching> and <update> of the SOM algorithm are as follows.

<Similarity Matching> <Update> m _i (t + 1) = [m _i (t) + α (t) {X (t) −m _i (t)}] ÷ | m _i (t) + α (t) {X (t) -m _{i (t)} | i∈N c} m i (t + 1) = m i (t) Others (7) wherein, X is a is normalized. _{mi is} also standardized after updating.

[0022] randomly enter sequentially choose X from the set of input vectors X, by repeating the update of the weight vector m _i, the weight vector m _i which reflects the distribution of the input vector X (1 ≦ i ≦ k) is To generate. That is, the weight vector m _i (1 ≦ i ≦ k) is a prototype of the distribution of the input vector. Then, when the weight vector of a certain element is updated so as to be closer to the input vector, the elements in the vicinity of that element on the map are also updated in the same manner. It corresponds to a close vector. Therefore, the SOM algorithm can create a set of prototypes that reflect the topology of the input data space.
The SOM algorithm has the following features.

B-1) Weight vector m _i (1≤i≤k)
A proper map can be created regardless of the initial state of. B-2) An appropriate map can be created regardless of the input order of the input vector X.

B-3) Since the map is one-dimensional or two-dimensional, the phase of the input data can be visually seen. B-4) Since the simple operations of <similarity matching> and <update> are repeated, the algorithm is simple.

The SOM has been described above. This SO
In M, an inner product operation using X ″ is performed by changing the way of taking f (D). Then, the superiority or inferiority of the phase preservation state of the input data depending on the way of taking f (D) is compared.

In the SOM, the elements are 10 × 10 2 elements.
Two-dimensional vector group X = (x, y), {0 ≦ x ≦
1, 0 ≦ y ≦ 1}. To see if the phase of the input data is better preserved, check the shape of each area by displaying the two-dimensional vector group X = (x, y) in the square for each element to which the data corresponds. Done by. In order to make it easy to distinguish between the elements to which the data correspond, 2
Adjacent elements in a three-dimensional grid are shown divided into white and black.

Normally, in SOM, X = (x, y) is input as it is, and Euclidean distance is used as a distance reference for competitive learning. The results in that case are shown in FIGS. 9 (a) and 9 (b). FIG. 9B is a diagram in which the weight vectors of the respective elements are connected to each other, and FIG. 9A is a diagram showing a region corresponding to the element (hereinafter referred to as a region diagram). Since the two-dimensional vector group X in the square is divided into two-dimensional lattices, each region has a structure in which small square lattices are regularly arranged in this manner. If X = (x, y) is input as it is and the Euclidean distance is used as the distance reference for competitive learning, the phase of the input data can be best saved. This result will be called the standard result. When X ″ is input and the competitive learning is performed by the inner product calculation, it can be said that the closer to the standard result, the better the phase of the input data is stored.

Therefore, the above-mentioned a) f (D) = D, b)
For the case of f (D) = 1 / D, SOM of inner product calculation was performed. The area diagrams are shown in FIGS. 10 (a) and 10 (b), respectively. In FIG. 10 (b), the regions spread in a grid pattern, whereas in FIG. 10 (a), the regions are disturbed and distributed radially near the origin on the upper left. Therefore, it can be said that the case (b) obviously preserves the phase of the input data better. Note that the radial distribution is X =
It shows that the angle dependence of (x, y) is strong. The reason for this is that, as described above with reference to FIG. 6, A ₁ and B ₁ near the origin, which should be close in the two-dimensional plane, are relatively separated in the three-dimensional space, and the angle information is emphasized more than the norm information. It can be interpreted as being done.

As a supplementary experiment, without using size information, X
= (X, y) is standardized and input
OM was performed. A region diagram at this time is shown in FIG. As described above in [Problems to be Solved by the Invention], norm information of input data is lost by normalization. Therefore, the entire region has a radial distribution that depends only on the angle information, and the discriminative ability regarding the norm of the element is lost. In the case of FIG. 10A described above, FIG.
It can be seen from comparison with FIG. 10 (c) that the region is disturbed as compared with, but the discrimination ability regarding the norm remains.

Now, a) f (D) = D, b) f (D) =
In the case of 1 / D, it can be said that b) preserves the phase of the input data better, but in order to preserve the phase of the input data better, what f (D) can be selected Find out what to do. In other words, what kind of f (D) should be selected and whether X = (x, y) can be directly input to obtain the same result as when the Euclidean distance is used as the distance criterion for competitive learning is investigated. . Whether or not the phase of the input data can be completely saved is a problem of the SOM itself. In the description of the present invention, the best preservation of the phase of the input data corresponds to obtaining the same result as the case where the Euclidean distance is used as the distance criterion of the competitive learning, and the preservation of the phase of the input data completely. Note that not. With this in mind, X = (x,
y) is input as it is, and the condition for obtaining the same result as when the Euclidean distance is used is obtained.

Again, the four points A ₁ , B ₁ , A ₂ , in FIG.
Consider B ₂ . In order to obtain the same result as using the Euclidean distance, the ratio of the line segments in the two-dimensional plane must be preserved in the three-dimensional space. This condition is expressed by an equation.

First, the coordinates of the four points A ₁ , B ₁ , A ₂ , and B ₂ and the norms D ₁ and D ₂ are expressed by equation (8). A ₁ = (r ₁ cos θ _A , r ₁ sin θ _A ), A ₂ = (r ₂ cos θ _A , r ₂ sin θ _A ), B ₁ = (r ₁ cos θ _B , r ₁ sin θ _B ), B ₂ = (r ₂ cos θ _B , r ₂ sin θ _B ), D ₁ = r ₁ , D ₂ = r ₂ (8) These coordinates correspond to the input vector X = (x, y). X '= (x / D, y / D, f (D)) obtained by normalizing this vector and adding a component indicating the norm is expressed by the equation (9).

A ₁ ′ = (cos θ _A , sin θ _A , f (D ₁ )), A ₂ ′ = (cos θ _A , sin θ _A , f (D ₂ )), B ₁ ′ = (cos θ _B , sin θ _B , f (D ₁ )), B ₂ ′ = (cos θ _B , sin θ _B , f (D ₂ )) (9) The standardized X ″ is expressed by equation (10).

A ₁ ″ = (cos θ _A , sin θ _A , f (D ₁ )) / {1 + f (D ₁ ) ² } ^1/2 A ₂ ″ = (cos θ _A , sin θ _A , f (D ₂ )) / {1 + f (D ₂ ) ² } ^1/2 B ₁ ″ = (cos θ _B , sin θ _B , f (D ₁ )) / {1 + f (D ₁ ) ² } ^1/2 B ₂ ″ = (cos θ _B , sin θ _B , F (D ₂ )) / {1 + f (D ₂ ) ² } ^1/2 ... (10) Arc A ₁ , B on a plane of x ² + y ² + z ² = 1 in a three-dimensional space
The length between ₁ and the length between arcs A ₂ and B ₂ are (1
1), (12) given by equation (arc, expressed as <A ₁ B _1>.). Here, it is assumed that the position vectors of A ₁ , B ₁ , A ₂ , and B ₂ are considered (the vector is expressed as A ₁ ).

<A ₁ ″B ₁ ″> = cos ⁻¹ { A ₁ ″ · B ₁ ″ / (| A ₁ ″ || B ₁ ″ |)} = cos ⁻¹ [{cos θ _A cos θ _B + sin θ _A + Sin θ _B + f (D ₁ ) ² } / {1 + f (D ₁ ) ² }] = cos ^-1 [{cos (θ _A −θ _B ) + f (D ₁ ) ² } / {1 + f (D ₁ ) ² } ] = Cos ⁻¹ [{cos Δθ + f (D ₁ ) ² } / {1 + f (D ₁ ) ² }] (11) <A ₂ ″B ₂ ″> = cos ⁻¹ [{cos Δθ + f (D ₂ ) ² } / {1 + f (D ₂ ) ² }] (12) The ratio of the lengths of the line segment A ₁ B ₁ and the line segment A ₂ B _{2 in} the two-dimensional plane is given by the equation (13).

│A ₁ -B ₁ │: │A ₂ -B ₂ │ = r ₁ : r ₂ = D ₁ : D ₂ ··· (13) As shown in the equation (14), the line segments A ₁ B ₁ and When the length ratio of the line segment A ₂ B ₂ is equal to the length ratio of <A ₁ ″B ₁ ″> and <A ₂ ″B ₂ ″>, the condition shown in equation (14) is satisfied.

│A ₁ -B ₁ │ / │A ₂ -B ₂ │ = <A ₁ ″B ₁ ″> / <A ₂ ″B ₂ ″> (14) Equation (11) in (11) , (12) and (13) are substituted, the result is as shown in Expression (15).

D ₁ / D ₂ = cos ⁻¹ [{cos Δθ + f (D ₁ ) ² } / {1 + f (D ₁ ) ² }] ÷ cos ⁻¹ [{cos Δθ + f (D ₂ ) ² } / {1 + f (D ₂ ) ² }] (15) Equation (15) is obtained by using the proportional constant k (k ≠ 0) in (16)
You can write like a formula.

KD _i = cos ⁻¹ [{cos Δθ + f (D _i ) ² } / {1 + f (D _i ) ² }] (i = 1, 2) (16) This is solved for f (D _i ). Then, it becomes like the expression (17).

F (D _i ) = {(coskD _i −cosΔθ) / (1−coskD _i )} ^1/2 (i = 1, 2) (17) Here, the definitions and radicals of various quantities Since the inside is positive, there is the following limiting condition (18).

CoskD _i − cosΔθ> 0,0 <kD _i <π / 2 (= 1, 2) (18) The expressions (17) and (18) have the following meanings. When converting two points forming Δθ in a two-dimensional plane into a three-dimensional space according to the above-mentioned rule, if the formula of f (D) such as the formula (17) is used, such a two-dimensional plane of the two-dimensional plane can be obtained. The ratio of the line segment comrades between points is x ² + y ² + z ² = 1 in the corresponding three-dimensional space.
Equal to the length ratio between points on the face.

According to the equation (18), when a certain constant of proportionality k is determined, D _i does not become larger than the amount determined by k and Δθ. This will be explained qualitatively. As D _i becomes larger, the distance between two points becomes larger as much as possible in the two-dimensional plane, but x ² + y ² + z ² = in the corresponding three-dimensional space.
The length between the points on the hem on one side cannot be larger than the width of the hem. Therefore, if D _i becomes large, it becomes difficult to satisfy the condition.

In order to investigate the effect when f (D _i ) is selected as in equation (17), the SOM of the inner product operation as described above is used.
I went. The parameters of f (D _i ) were selected as k = 0.3 and Δθ = π / 3 so as to satisfy the equation (18). (1
Equation 8) is an equation for a certain Δθ. In competitive learning, since there are various input vectors, Δθ takes various values accordingly, but in actual simulation, (1
In consideration of the maximum value of D _i , k is satisfied so that the expression (8) is satisfied.
And Δθ will be appropriately determined in advance. As can be seen from the result of the area diagram, there is no problem if k and Δθ are fixed.

FIG. 11 is a region diagram when the equation (17) is used.
Shown in According to FIG. 11, as in FIG. 9A, the small square lattice has a regular arrangement. this is,
The alignment is better than when f (D) = 1 / D is selected.
This can be understood from the fact that the number of small vertical and horizontal regions is 10.

Therefore, from this experiment, if f (D _i ) given by the equation (17) is used, X = (x, y) is input as it is, and Euclidean distance is used as the distance reference for competitive learning. It is possible to get the same result,
It can be seen that the mapping that best preserves the phase of the input data can be realized.

Next, the formulas (14) and (15) will be supplemented. Expressions (14) and (15) are strict conditions,
If only the magnitude relationship of the denominator numerator on both sides is preserved, f
It is sufficient that (D) is a function that decreases with respect to D,
It can be understood by considering the property of the function. That is, f (D) = D
And f (D) = 1 / D are compared, the result of f (D) = 1 / D is better because f (D) = 1 / D is a decreasing function with respect to D. .

Of course, the function is not limited to f (D) = 1 / D. To preserve the phase well, D
Any decreasing function may be chosen for. Further, even if a function other than a decreasing function is taken for D, it becomes difficult to store the phase, but it is possible to perform learning to some extent without losing norm information, as described above.

As described above, the inner product calculation is used as the distance criterion, and theoretically explained what kind of algorithm should be used in order to perform competitive learning without losing norm information of input data. The summary is as follows. C
-1) In competitive learning using the inner product operation as a distance reference, 2
When the dimension vector X = (x, y) is input, (1)
~ If you perform the conversion as in equation (3) and input X ",
Norm information is not lost by normalization for inner product calculation.

X = (x, y), D = (x ² + y ² ) ^1/2 (1) X ′ = (x / D, y / D, f (D)) (2) ) X ″ = X ′ / | X ′ | (3) C-2) For f (D), various functions can be used. Regarding D, an increasing function and a decreasing function are the decreasing functions. Can store the phase well, for example, f (D) = D and f
In the case of (D) = 1 / D, the latter is better.

If C-3) f (D) is expressed by the equation (17) ', the phase can be further saved. f (D) = {(coskD− cos Δθ) / (1− coskD)} ^1/2 (17) ′ In addition, since the expression (17) ′ is generally described, D _i
I was deleted.

In the above discussion and summary, since it is easy to show in the figure, the two-dimensional vector X = (x, y) is input.
However, the n-dimensional vector X = (x ₁ , x ₂
..., x _n ), (n = 1, 2, 3 ...) In the same manner. At this time (1), (2), (3)
The formula becomes the following formula.

X = (x ₁ , x ₂ ···, x _n ), D = (x ₁ ² + x ₂ ² + ·· x _n ² ) ^1/2 ... (19) X ′ = (x ₁ / D, x ₂ / D, ..., X _n / D, f (D)) ... (20) X ″ = X ′ / | X ′ | (21) Further, in the equation (8), n 4 points in dimensional space A ₁ ,
The coordinates of B ₁ , A ₂ , and B ₂ and the norms D ₁ and D ₂ are (2
If the direction cosine is used as in the expression (2), the same expression as the expression (17) can be derived.

A ₁ = (r ₁ cosθ _A1 , r ₁ cosθ _A2 , ..., r ₁ cosθ _An ), A ₂ = (r ₂ cosθ _A1 , r ₂ cosθ _A2 , ..., R ₂ cosθ _An ), B ₁ = (r ₁ cos θ _B1 , r ₁ cos θ _B2 , ..., r ₁ cos θ _Bn ), B ₂ = (r ₂ cos θ _B1 , r ₂ cos θ _B2 , ..., r ₂ cos θ _Bn ), D ₁ = r ₁ , D ₂ = r (22) where (cos θ _A1 , cos θ _A2 , ..., Cos θ _An ) is A
Direction cosines of ₁ and A ₂ , (cos θ _B1 , cos θ _B2 , ...
cos θ _Bn ) indicates the direction cosine of B ₁ and B ₂ . In the case of n dimensions, Δθ in equation (17) corresponds to the angle formed by these two direction cosines. It can be seen that if n is selected as 2 in the case of an n-dimensional vector, it agrees with the discussion of the two-dimensional vector up to now. From the above, the above discussion and summary are
It is obvious that the present invention is not limited to a dimensional vector and can be extended to a multidimensional vector.

Finally, the case of an n-dimensional vector will be summarized. D-1) n-dimensional vector X (n = 1, 2, 3, ...) In competitive learning using inner product calculation as a distance reference
When inputting, the conversion as in equations (19) to (21) is performed, and when X ″ is input, norm information is not lost due to normalization for inner product calculation.

X = (x ₁ , x ₂ ···, x _n ), D = (x ₁ ² + x ₂ ² + ·· x _n ² ) ^1/2 (19) X ′ = (x ₁ / _{D, x 2 / D, ··} , x n / D, f (D)) ·· (20) X "= X '/ | X' | ··· (21) D-2) f (D) is , Various functions can be used, but comparing the increasing function and the decreasing function with respect to D, the decreasing function can better preserve the phase, for example, f (D) =
With D and f (D) = 1 / D, the latter is better.

If D (3) f (D) is expressed by the equation (17) ', the phase can be further saved. f (D) = {(coskD− cos Δθ) / (1− coskD)} ^1/2 (17) ′ As described above, the inner product calculation is used as the distance reference, and the competitive learning without losing the norm information of the input data can be performed. In order to achieve this, we theoretically explained and summarized what kind of algorithm should be used. The present invention based on the above discussion is the following information processing apparatus.

[1] In an information processing apparatus that associates an input vector with each vector of the weight vector group to correspond to any vector of the weight vector group, extracts information about the norm of the input vector before taking the inner product. An information processing apparatus having a norm extracting / adding means for adding to the component of the input vector.

[2] The information processing apparatus according to the above [1], further comprising an input vector normalizing means for normalizing an input vector to which information on the norm is added before taking the inner product. [3] The information processing apparatus according to the above [1], further including weight vector normalizing means for normalizing each vector of the weight vector group before taking the inner product.

[4] The information processing apparatus according to the above [2] or [3], wherein the normalization is performed by an electric signal.

[5] The information processing apparatus according to the above [2] or [3], wherein the normalization is optically performed.

The information processing apparatus of the present invention described above has the following A-
The conditions 1) and A-2) are satisfied.

A-1) An inner product calculation suitable for hardware is used as the distance reference.

A-2) It is possible to perform competitive learning without losing norm information of input data.

[0064]

DESCRIPTION OF THE PREFERRED EMBODIMENTS Preferred first and second embodiments of the information processing apparatus of the present invention will be described below. Prior to the description, the principle of the optical inner product computing device used in these embodiments will be described.

For simplicity, the vector for which the inner product is taken is four-dimensional (2 × 2), and the input vector X (x ₁ , x ₂ , x ₃ ,
x ₄ ) and nine weight vector groups m _i (m _i1 , m _i2 , m
_i3 , m _i4 ) (i = 1 to 9; 3 × 3) is taken as the inner product. First, FIG. 12 shows an inner product calculation optical system (Taiwei et al., "Self-organizing opt" used in the first embodiment.
ical neural network for unsupervised learning ", Op
t.Eng., VOL.29, No.9, pp.1107-1113, 1990.) is a diagram showing the principle of two liquid crystal televisions 101 and 102, and the second liquid crystal television 101 has 2 × The 2 X components (x ₁ , x ₂ , x ₃ , x ₄ ) are displayed in the order shown in the figure. Further, the first liquid crystal television 102 is arranged submatrix m _i of 2 × 2 is the 3 × 3, for each submatrix m _i to m _i component of _{(m i1, m i2, m} i3, m i4) view It is displayed in order. Viewing the order of arrangement of the vector components X and m _i, one is in the relationship of the other inverted image. The optical system is
The first liquid crystal television 102 and the first liquid crystal television 102, which are arranged in the optical axis direction.
A lens array 105 composed of 3 × 3 lenses L _i corresponding to a 3 × 3 sub-matrix m _i arrangement of the liquid crystal television 102, a second liquid crystal television 101, and an imaging lens 106.
And the 3 × 3 sub-matrix m _i arrangement of the first liquid crystal television 102 and the 3 × 3 lens L _{i of the} lens array 105.
The CCD camera 107 has 3 × 3 light receiving regions corresponding to the arrangement.

Then, the components of m _i (m _i1 , m _i2 , m _i3 , m _i4 ) are divided into 2 × 2 areas of the first liquid crystal television 102.
The image of one submatrix m _i in which is displayed is
The lenses L _i at corresponding positions of the lens array 105 are optically arranged so as to form an image on the second liquid crystal television 101 while making the vector components correspond to each other.
Further, the second liquid crystal television 101 is arranged at the entrance pupil position of the imaging lens 106, and the imaging lens 106 directs the pupil of each 3 × 3 lens L _i of the lens array 105 to the CCD camera 1.
The optical arrangement is such that an image is formed on 3 × 3 light receiving areas of 07.

Therefore, the total amount of light that has passed through the lens L _i at the corresponding position of the lens array 105 is incident on the i-th (i = 1 to 9) light receiving area of the CCD camera 107.
As is clear from the optical path in the figure, the total amount of light that has passed through the lens L _i means the components (m _i1 , m _i2 , m _i3 , m _i4) of the 2 × 2 sub-matrix m _i of the first liquid crystal television 102. ) And the 2 × 2 X component (x ₁ , x ₂ ,
x ₃ , x ₄ ) and corresponding components are superposed (mathematically multiplied) and added, which is nothing but an inner product. Therefore, the CCD camera 107 shown in FIGS.
X · m _{1 to} X · m ₉ are obtained in the light receiving regions of, respectively.

Next, FIG. 13 shows an inner product calculation optical system (J. Duvillier et al., "All-optical im" used in the second embodiment.
plementation of a self-organizing map ", Appl.Opt.Vo
l.33, pp.258-266, 1990.), which uses two spatial modulators 27a and 207a for obtaining the inner product, and the inner product is obtained on another spatial modulator 210a. Is. In this case, the spatial modulators 27a and 207a are superposed and read by the parallel light emitted from the spatial modulator 27a side. As in the case of FIG. 12, 2 × 2 X components (x ₁ , x ₂ , x ₃ , x ₄ ) are displayed on the spatial modulator 27a in the order shown in the figure. In addition, the spatial modulator 207a
, The components of _nine vectors m _{1 to} m ₉ are combined into one 3 × 3 submatrix M _{1 to} M _{4 respectively.}
Is displayed to configure. That is, as shown in the figure, each vector m _{1 to} m ₉ is included in the sub-matrix M _i.
The i-th component of is displayed as arranged in a 3x3 matrix. Then, the spatial modulators 27a and 207a
, The components x _{1 to} x of the spatial modulator 27a are overlapped.
_Fourth region is formed is both spatial modulator 27a and 207a so that each correspond to a region of the sub-matrices M ₁ ~M ₄ spatial modulator 207a. The optical system includes a spatial modulator 27a and a spatial modulator 20 arranged in the optical axis direction.
7a and the 2 × 2 matrix arrangement of the spatial modulator 27a, and the sub-matrix M ₁ of the spatial modulator 207a.
A lens array 208 composed of 2 × 2 lenses L _i corresponding to the arrangement ˜M ₄ , an imaging lens 209, and a spatial modulator 210 a. A spatial modulator 207 a is provided at the front focal position of the lens L _i . The imaging lens 20 at the rear focal position
9 is the spatial modulator 2 at the rear focal position of the imaging lens 209.
10a is located. The lens L _i and the imaging lens 2 are formed so that each sub-matrix M _i of the spatial modulator 207a is enlarged and imaged in the entire area of the spatial modulator 210a.
A focal length ratio of 09 is defined.

Therefore, on the spatial modulator 210a,
By superimposing the spatial modulator 27a and 207a, the sub-matrix M _i and the corresponding component x _i of X is (are multiplied) is superimposed, those sub-matrices M _i is Kasanea' the same position by the action of the lens array 208 It is imaged. Therefore, j of the sub-matrix M _i of the spatial modulator 210a is
At the position corresponding to the m-th component (j = 1 to 9) m _ji , the j-th component (m _j1 , m _j2 , m _j3 , m _j4 ) of all the sub-matrices M _{1 to} M ₄ corresponds to X. that sum by multiplying the component _{(x 1, x 2, x} 3, x 4) that, i.e., the inner product is incident. Therefore, in the illustrated regions 1 to 9 of the spatial modulator 210a, X · m ₁
~ X · m ₉ is obtained.

Although the inner product calculation optical system used in the first and second embodiments described below has been described by taking a four-dimensional vector as an example, it is easy to use a vector having more or less dimensions. It is clear from the configuration of the optical system that the above can be dealt with.

In the present invention, the norm information of the vector consisting of other components is applied to at least one component of the vector for which the inner product is obtained. For example, in the case of the above four-dimensional vector, x ₄ is the norm information of the vector consisting of (x ₁ , x ₂ , x ₃ ). Hereinafter, FIGS.
Based on this, a preferred embodiment of the present invention will be described.

[First Embodiment] As shown in the configuration of FIG. 14, the information processing apparatus according to the present embodiment has an input vector acquisition means 1 for acquiring data for processing, and an input vector acquisition means 1 for inputting the data. D-2) or D described above from the vector
Input vector processing means 2 for generating the norm information described in -3), adding the generated norm information to the input vector, and normalizing according to the condition of D-1).
And a competitive learning means 3 for inputting and processing the vector to which the norm information has been added.

In this embodiment, the above-mentioned device such as TaiweiLu is improved and used as the competitive learning means 3 of the information processing device. First, referring to FIG. 14, Taiw
The parts common to the device such as ei Lu will be described. In the competitive learning means 3, the input vector composed of 8 × 8 pixels is used as the second input vector.
A memory matrix (64 × 64) which is displayed on the liquid crystal television 101 and has 8 × 8 sub-matrixes of 8 × 8 pixels corresponding to one weight vector is displayed on the first liquid crystal television 10
2, and the light of the xenon lamp 103 is emitted from the back of the first liquid crystal television 102 through the diffuser 104. The memory matrix can store a set of element weight vectors as described above. The illuminated information on the memory matrix on the first liquid crystal television 102 is imaged by the 8 × 8 lens array 105 so that all the sub-matrices corresponding to each weight vector are superposed on the second liquid crystal television 101. It is designed to be superimposed on the input vector. Further, the information of the sub-matrix on which the input vector is superimposed is made to enter the 8 × 8 areas of the CCD camera 107 by the imaging lens 106, respectively, and by this series of operations, the input vector and the memory are stored. The matrix inner product calculation is performed in each area (see FIG. 12).

Further, the result of the inner product calculation obtained by the CCD camera 107 is loaded into a computer, and the matrix updating means 108 implemented by software in the computer updates the memory matrix required for competitive learning. Is decided and updated.
The display of the first liquid crystal television 102 and the second liquid crystal television 101 is also controlled by the computer. In the competitive learning means of the information processing apparatus of the present invention,
This is a part common to devices such as aiwei Lu.

In this embodiment, it is assumed that this information processing apparatus processes a grayscale image. In this case, the input vector acquisition means 1 takes in an image to be processed by an image pickup device such as a CCD and a frame memory into a computer and outputs it to a predetermined input vector (8 × 8− in the case of this embodiment).
1 (= 63) component) (the minus one is
Assign to the norm information to be added. ). How to deploy
The frame area on the frame memory may be divided into 8 × 8 areas, and the average brightness may be calculated for each area to obtain the value of each component. At this time, the component corresponding to the lower right area of the image is ignored, and norm information to be added to this portion is assigned. In the case of the present embodiment, this expansion is realized by software in the computer.

Next, the input vector processing means 2 uses D-
The developed vector is processed as in 1) to D-3). First, D is calculated from the expanded 63 vectors according to the equation (19) of D-1). Next, according to the equation (17) ′ of D-3), from D to f
(D) is calculated, and as the 64th vector component, D−
This f (D) is added according to the equation (20) of 1), and the other 63 vectors are normalized using D.
The f (D) in the equation (20) can be easily selected as in D-2) or D-3) by controlling software in the computer. Finally, according to the equation (21) of D-1), the normalization is performed again and the processing of the input vector is finished. The input vector processing means 2 described above is also realized by software in a computer in the case of the present embodiment. The input vector processed by the input vector processing means 2 is sent to the matrix updating means 108 in the competitive learning means 3 and the second liquid crystal television 101,
The processing by the competitive learning means proceeds.

The updating of the memory matrix is carried out by finding the largest one of the output vectors obtained from the CCD camera 107 in the matrix updating means 108 and updating the memory matrix in the vicinity of this component. Update rule _{is, m i (t + 1)} = m i (t) + α (t) {X (t) -m i (t)} i∈N c (t) m i (t + 1) = m i (t) Others (23), where α (t) is a coefficient indicating the learning speed, N _c (t) indicates the update range, and this update range elapses with time (as the update progresses). I made it smaller with
Ultimately, only the above maximum components are used. The above memory matrix update is also realized by software in the computer.

With the above configuration, the information processing apparatus according to the present embodiment can perform the processing in which the norm information is not lost even if the apparatus includes the competitive learning means having the inner product calculation part. it is obvious.

In this information processing apparatus, the input vector acquisition means 1 uses an image pickup device such as a CCD because an image is assumed as a vector, but other means may be used. For example, in the case of voice, a microphone and an AD converter may be used, and in the case of concentration, a concentration sensor,
Any flow rate sensor such as a flow rate sensor may be used as long as it is a flow rate. Basically, the desired information may be acquired by the sensor and the information obtained by the sensor may be loaded into the computer.

The number of vectors that can be handled is not limited to 63 (8 × 8-1), and it is clear that the number can be adjusted by increasing or decreasing the number of pixels in the spatial light modulator or the number of lenses in the lens array. is there.

[Second Embodiment] As in the first embodiment, the information processing apparatus of the present embodiment also has an input vector acquisition means for acquiring data for processing, as shown in FIG. 1 and D− from this input vector
2) Or generate the norm information given in D-3),
Further, the generated norm information is added to the input vector, and the input vector processing means 2 for normalizing as in D-1) and the processed vector to which the norm information is added are input and processed. The competition learning means 3 is included, and the difference is that most of the input vector processing means 2 and the competition learning means 3 are configured by an optical system.

More specifically, the information processing apparatus of the present embodiment, as shown in FIG.
And D− acquired by this input vector acquisition means 1.
The first vector component total sum detecting means 21 for detecting the total sum of the data corresponding to the equation (19) of 1) and the obtained total sum of the vector components are made to correspond to the equation (20) of D-1). First normalizing means 2 for normalizing the data
2 and norm information generating means 23 for generating norm information of the input vector corresponding to the equation (17) ′ of D-2) and D-3) from the total sum of the obtained vector components, and this normalization. Norm information adding means 24 for adding norm information to the input vector corresponding to the equation (20) of D-1).
And second vector component total sum detection means 2 for detecting the total sum of the input vector components to which the norm information is added.
5 and (2) of D-1) from the obtained sum of vector components.
Input vector processing means 2 including a second normalization means 26 for normalizing the data corresponding to the expression 1) and a processing result display means 27 for displaying the above data processing result, and It is intended to achieve the object of the present invention by using the competitive learning means 3 for inputting and processing the processed and displayed data.

FIG. 16 specifically shows an optical system of the input vector acquisition means 1 and the input vector processing means 2 among the above. In the present embodiment as well, processing of a grayscale image is first assumed. In the input vector acquisition means 1,
An image that is a vector to be processed is acquired by the image pickup device 11 (specifically, for example, a CCD camera equipped with a zoom lens), and this signal is input by the driver 12 to the spatial light modulator 1.
3 (in the case of this embodiment, for example, a transmissive electronic address liquid crystal spatial light modulator). The displayed image to be processed is read out by the substantially parallel light flux 20 and sent to the input vector processing means 2. In the input vector processing means 2, first, the beam splitter 21 a and the condenser lens 21
The first vector component sum total detection means 21 including the detector b and the detector 21c calculates the sum total of the image which is the vector to be processed. Specifically, the input image information is branched by the beam splitter 21a, and the condensing lens 21b is used.
The light amount is collected by the detector 21c, the light amount is detected by the detector 21c as the total D, and converted into an electric signal. The detected electric signal of the total sum D is sent to the driver 22b of the light quantity adjusting filter 22a which is the first normalizing means 22 so that the light quantity passing therethrough becomes constant, that is, is normalized. Adjustments are made. Specifically, a liquid crystal shutter capable of changing the amount of light passing therethrough according to an applied voltage is used as the light amount adjustment filter 22a, and the voltage applied to the liquid crystal shutter is controlled by the driver 22b by the electric signal of the detected sum D. , The amount of light passing through here is constant. Further, the electric signal of the detected sum D is f by the divider which is the norm information generating means 23.
As an example of how to select (D), it is converted into the 1 / D information described in D-2).

The 1 / D signal which is the converted norm information is sent to the driver 24b which drives the light emitting element 24a of the norm information adding means 24, and the light emitting element 24a generates a light amount proportional to 1 / D. . In the norm information adding means 24, the input vector displayed on the spatial light modulator 13 is further coupled to the spatial light modulator 24c (in the case of the present embodiment, for example, a reflection type and an optical addressing type liquid crystal spatial light modulator). An image forming lens 24d for forming an image and a driver 24e for driving the spatial light modulator 24c are included. With this configuration, the normalized input vector is displayed on the spatial light modulator 24c. In this spatial light modulator 24c, as shown in the front view of FIG. 17A and the side view of FIG. 17B, an 8 × 8 area is set, and one area (in the figure, , A region at the lower right corner) is used as a light emitting element 24a, and a light amount proportional to 1 / D is emitted by a light emitting diode LD used in this embodiment and a lens CL that condenses light from the light emitting diode LD. As a result, the input vector normalized to 63 regions of 8 × 8-1, and the norm information proportional to 1 / D are displayed in the remaining one region.

The displayed input vector information is used as the substantially parallel light beam 28 guided into the system by the beam splitter 28a.
Is read out by the second vector component summation detection means 25 and is sent to the second vector component summation detection means 25 to detect the summation. Further, the second normalization means 26 normalizes the summation. The second vector component total sum detection means 25 and the second normalization means 26 are respectively the first vector component total sum detection means 2
The beam splitter 25a, the condenser lens 25b, and the detector 25, which are the same elements as those of the first and second normalizing means 22,
c and a light amount adjustment filter 26 which is a liquid crystal shutter
a and a driver 26b.

In the processing result display means 27, the vector displayed on the spatial light modulator 24c is imaged on the liquid crystal spatial light modulator of the reflection type and optical address type used in this embodiment as the spatial light modulator 27a. It is composed of an imaging lens 27b for driving the light and a driver 27c for driving the spatial light modulator 27a. With this configuration, 8 × 8−
The input vector is normalized to 63 regions of 1 and the norm information proportional to 1 / D is displayed in the remaining 1 region, and the normalized result is the spatial light modulator. 27a.

In this embodiment, as the competitive learning means 3 of the information processing apparatus, the above-mentioned J. A device such as Duviller is improved and used. Next, referring to FIG. 18, Du
Description will be given of a part that is substantially common to the device such as Villier.
The optical system shown in FIG. 16 corresponds to the portions within the cutting planes AA ′, BB ′, and CC ′ of FIG. 18.

First, in the inner product calculation phase, the light beam from the laser 200 is incident on the beam expander 202 via the mirror 201 and becomes a substantially parallel light beam 203. This luminous flux is transmitted to the beam splitters 204, 223, 2
The input information (see FIG. 16) of 8 × 8 elements displayed at the position of the spatial light modulator 27a is input into the system via 24,
Further, this input information is sent to the spatial light modulator 207a (in the present embodiment, for example, a transmissive optical writing liquid crystal spatial light modulator) controlled by a dedicated driver 207b by the imaging lenses 205 and 206. The information is read out after being superimposed on the information of the displayed 8 × 8 element memory matrix (the device such as J. Duvillier reads the input information transparently, but in the present embodiment, the input information is spatial Since the reading is performed by reflection from the optical modulator 27a, the configuration of this portion is partially changed.) The information obtained by superimposing the information of the memory matrix on this input information further passes through the 8 × 8 lens array 208 and the imaging lens 209, and is controlled by the dedicated driver 210b (the spatial light modulator 210a (in this embodiment). In this case, for example, it is further superposed on a transmission type and optical writing type binary liquid crystal spatial light modulator. Through this series of operations, the inner product calculation result of the input information and the memory matrix is threshold-operated and stored on the spatial light modulator 210a (see FIG. 13).

Next, in the memory matrix updating phase, the spatial light modulator 21 is operated in the inner product calculating phase.
The result of the inner product calculation stored on 0a is the light beam 20 that is substantially parallel.
3, the light beam 214 passes through the beam splitter 204 and is further read by the substantially parallel light beam 214 guided into the system via the mirrors 211 and 212 and the beam splitter 213. This read information is further read by the mirror 215,
216, 217, beam splitters 223, 224, lenses 218, 219, 220, 221 and Damm
By passing through the Ann type grating 222,
The input information of the 8 × 8 element which is duplicated in 8 × 8 and displayed at the position of the spatial light modulator 27a is read again. The amount of update of the memory matrix is determined by this operation. This update information is imaged on the spatial light modulator 207a by the imaging lenses 205 and 206, and further, by controlling the driver 207b to change the applied voltage. The memory matrix is updated in the form of addition or subtraction.

Here, regarding the updating of the memory matrix, the output vector y of the inner product operation is set to the spatial light modulator 20.
Thresholded by 7a and binarized is defined as Y, and the Y is reduced by the lenses 218 to 221 and the Dammann type grating 222 to restore the original size, and at the same time 8 × 8 as the input vector. Replicated to
Overlay on input vector. This is the update amount ΔM _{i of the} memory matrix. This update rule is: M _i (t + 1) = M _i (t) + a (t) NO {ΔM _i (t)} ΔM _i = X (D _i Y) (24) where a (t) Is a coefficient indicating the learning speed similar to α (t) in the equation (23), NO is a function indicating the update range,
It plays the same role as N _{c in} equation (23). Also, D _i is Y
Represents the sub-matrix of 8 × 8. This update is based on the already stored spatial light modulator 207a.
This is done by adding or subtracting the ΔM _i determined above to the above memory matrix information M _i (t) to make a change. Spatial light modulator 207 at this time
The operation a is a gray scale operation, and the sign of the drive voltage may be changed. Further, if the magnitude of the drive voltage is changed, NO, that is, the update range and the learning speed can be changed. This is performed by controlling the driver 207b with a computer or the like.

In the above, there is a part where the system is commonly used in the inner product calculation phase and the memory matrix update phase, so the shutters 225, 22
6, 227 and 231, of course, prevent information from interfering with each other. That is, in the inner product calculation phase, the shutter 225 is opened and the shutter 22
6, 227 and 231 are closed, and in the memory matrix update phase, the shutters 225 and 231 are closed and the shutters 226 and 227 are open. The above is the procedure of the J. This is a part that is substantially common to the device such as Duviller.

The present embodiment is different from the preceding example in FIG.
As described above with reference to FIG. 16 and FIG. 16, the input vector acquisition unit 1 and the input vector processing unit 2 are newly added to the competition learning unit 3. In this embodiment, FIG.
The input vector acquisition means 1 and the input vector processing means 2 shown in FIG. 2 are connected to the cutting planes AA ′, BB ′ and C− in the figure.
C'is installed so as to correspond to the corresponding portion in FIG. At this time, the substantially parallel light beam 203 passes through the middle beam splitter 204, and further, the beam splitter 234.
The light beam incident on the system of the input vector acquisition means 1 and the input vector processing means 2 via is made into a substantially parallel light beam 20, and the light beam reflected by the beam splitter 204 in the substantially parallel light beam 203 is The light is input into the same system through the beam splitter 228 to form a substantially parallel light beam 28. Further, in the present embodiment, in order to normalize the inner product calculation result and the memory matrix as well, as shown in the figure, the third vector component sum total detection means 229 and the third normalization means 2
30 is inserted. The third vector component sum total detection means 229 and the third normalization means 230 are respectively the first
Vector component sum detection means 21 and first normalization means 2
2 (FIG. 16), which is the same element as the beam splitter 22.
9a, a condenser lens 229b, a detector 229c, and a light amount adjustment filter 230a which is a liquid crystal shutter,
It is composed of a driver 230b. With this configuration,
In the inner product operation phase, the inner product operation result is normalized.
On the other hand, in the update phase of the memory matrix, after updating the memory matrix, the shutter 227 is closed and the shutters 225 and 231 are opened,
The substantially parallel light beam 203 that has passed through the beam splitter 223 is further incident on the spatial light modulator 207a via the mirror 232 and the beam splitter 233, and the updated information in the memory matrix is read out and normalized. It is a thing. Since it is not necessary to normalize the inner product operation result as an algorithm for competitive learning, the third vector component sum total detection means 229 and the third normalization means 230
May be omitted in the inner product calculation phase. However, by normalizing the inner product calculation result, it is possible to prevent the problem of hardware adjustment due to divergence and saturation of the signal amount.

In this embodiment, liquid crystal spatial light modulators of transmissive type, reflective type, electronic address type and optical address type are used, but these are not limited to the combinations given in the above examples. Needless to say, various combinations are possible.

In the normalizing means described above, its purpose is to set the norm of the vector to 1 in a mathematically strict sense. However, the same effect as the strict normalization can be obtained even if the light amount is roughly adjusted according to the norm on the hardware, instead of being strictly fixed. Therefore, the definition of normalization in the present invention is broad and means adjusting the magnitude of the vector component according to the magnitude of the norm. Also, D-
When strict conversion formulas such as 2) and D-3) are realized on hardware, the action may be approximately obtained by changing the characteristics of various devices.

Further, in the above, one norm information is given to one input, but a plurality of information may be given.
That is, the dimension to be added is not limited to one dimension and may be multiple dimensions.

With the above configuration, it is clear from the above description that the information processing apparatus of the present invention can perform the processing in which the norm information is not lost even if the apparatus includes the competitive learning means having the inner product calculating section. is there.

Also in this information processing apparatus, the input vector acquisition means is not limited to the image pickup element as in the first embodiment, but may be a microphone, a density sensor, or the like.
Any sensor such as a flow sensor may be used. It is also clear that the number of vectors that can be handled can be adjusted as in the first embodiment.

Although the information processing apparatus of the present invention has been described based on its principle and embodiments, the present invention is not limited to these embodiments and various modifications can be made.

[0099]

As is apparent from the above description, according to the information processing apparatus of the present invention, it is possible to provide an information processing apparatus satisfying the following conditions. A-1) As the distance reference, competitive learning using inner product calculation suitable for hardware implementation is performed. A-2) Competitive learning that does not lose norm information of input data can be performed.

[Brief description of drawings]

FIG. 1 is a diagram showing a process of determining a winning vector by inner product calculation without normalization.

FIG. 2 is a diagram showing a process of determining a winning vector by inner product calculation in the case of normalization.

FIG. 3 is a diagram showing two-dimensional uniform distribution vector data.

FIG. 4 is a diagram showing a distribution when two-dimensional uniform distribution vector data is standardized.

FIG. 5 is a diagram showing four points on a two-dimensional plane which are input to the information processing apparatus of the present invention.

FIG. 6 is a diagram showing positions of four points in a three-dimensional space when D is selected as a component indicating a norm.

FIG. 7 is a diagram showing positions of four points in a three-dimensional space when 1 / D is selected as a component indicating a norm.

FIG. 8 is a diagram showing a structure of a self-organizing feature map.

FIG. 9 is a diagram in which a region diagram when Euclidean distance is used as a distance reference for competitive learning and a weight vector of adjacent elements are connected to each other.

FIG. 10 is a region diagram when D and 1 / D are selected and not selected as components indicating a norm.

FIG. 11 is a region diagram when a theoretical component is selected as a component indicating a norm.

FIG. 12 is a diagram showing the principle of an inner product calculation optical system used in the first embodiment of the present invention.

FIG. 13 is a diagram showing the principle of an inner product calculation optical system used in the second embodiment of the present invention.

FIG. 14 is a diagram showing a schematic configuration of a first embodiment of the present invention.

FIG. 15 is a diagram showing a schematic configuration of a second embodiment of the present invention.

FIG. 16 is a diagram showing a specific configuration of a second exemplary embodiment of the present invention.

17A and 17B are a front view and a side view of a spatial light modulator for adding norm information used in the second embodiment.

FIG. 18 is a diagram showing a configuration of a competitive learning unit according to a second embodiment of the present invention.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 ... Input vector acquisition means 2 ... Input vector processing means 3 ... Competitive learning means 11 ... Imaging device 12 ... Driver 13 ... Spatial light modulator 20 ... Luminous flux 21 ... 1st vector component sum total detection means 21a ... Beam splitter 21b ... Collection Optical lens 21c ... Detector 22 ... First normalizing means 22a ... Light quantity adjusting filter 22b ... Driver 23 ... Norm information generating means 24 ... Norm information adding means 24a ... Light emitting element 24b ... Driver 24c ... Spatial light modulator 24d ... Imaging Lens 24e ... Driver 25 ... Second vector component sum total detection means 25a ... Beam splitter 25b ... Condenser lens 25c ... Detector 26 ... Second normalization means 26a ... Light quantity adjusting filter 26b ... Driver 27 ... Processing result display means 27a ... Spatial light modulator 27b ... Imaging lens 27c ... driver 28a ... beam splitter 28 ... luminous flux 101 ... second liquid crystal television 102 ... first liquid crystal television 103 ... xenon lamp 104 ... diffuser 105 ... lens array 106 ... imaging lens 107 ... CCD camera 108 ... matrix updating means 200 ... laser 201 Mirror 202 ... Beam expander 203 ... Luminous flux 204, 223, 224 ... Beam splitter 205, 206 ... Imaging lens 207a ... Spatial light modulator 207b ... Driver 208 ... Lens array 209 ... Imaging lens 210a ... Spatial light modulator 210b ... drivers 211, 212 ... mirrors 213 ... beam splitters 214 ... luminous flux 215, 216, 217 ... mirrors 218, 219, 220, 221 ... lenses 222 ... Dammann type grating 223 Beam splitter 225, 226, 227, 231 ... Shutter 228 ... Beam splitter 229 ... Third vector component sum total detection means 229a ... Beam splitter 229b ... Condenser lens 229c ... Detector 230 ... Third normalization means 230a ... Light quantity adjustment filter 230b ... driver 232 ... mirror 233 ... beam splitter 234 ... beam splitter LD ... light emitting diode CL ... lens

 ─────────────────────────────────────────────────── ─── Continuation of the front page (72) Inventor Ikutoshi Fukushima 2-43-2 Hatagaya, Shibuya-ku, Tokyo Olympus Optical Co., Ltd.

Claims (5)

[Claims] 1. An information processing apparatus for correlating an input vector with each vector of a weight vector group to correspond to any vector of the weight vector group, by extracting information about the norm of the input vector before taking the inner product. An information processing apparatus, comprising: norm extraction / addition means for adding to a component of the input vector. 2. The information processing apparatus according to claim 1, further comprising an input vector normalizing means for normalizing an input vector to which information on the norm is added before taking the inner product. 3. The information processing apparatus according to claim 1, further comprising a weight vector group normalizing means for normalizing each vector of the weight vector group before taking the inner product. 4. The information processing apparatus according to claim 2, wherein the normalization is performed by an electric signal. 5. The information processing apparatus according to claim 2, wherein the normalization is performed optically.