Weather forecast apparatus and method based on recognition of echo patterns of radar images

The present invention provides a weather forecast apparatus and a method for the same, to systematically classify a measured radar image based on results of pattern classification of past radar images so as to use the classified radar image. In the present invention, rapid forecasting is possible by making the FNN model previously learn based on data of each class (and indexes for forecast times) obtained by classification of past weather data for every resembling pattern. In addition, a calculation procedure for improving the classifying ability of patterns can be established by varying the procedure for calculating feature quantities with regard to the radar image by using the learning of the TNN model. Furthermore, systematic classification of a pre-learned image can be realized by performing self organization with regard to compound feature quantities extracted from a radar image in the PNN model, a typical example of which is a competitive learning model.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention relates to a weather forecast apparatus and to a 
method for efficiently forecasting the amount of rainfall, snowfall, and 
the like, using pattern-recognition and the learning of weather radar 
images by using a neural network model and by systematically classifying 
the radar images. 
2. Description of the Related Art 
First of all, an example of the (artificial) neural network model (referred 
to as the "NN model", hereinafter) to which the present invention can be 
applied, will be disclosed. The NN model transforms input feature 
quantities so as to output them as output feature quantities. Here, a 
hierarchical NN model will be shown as a typical example of the NN model; 
however, it should be noted that another type NN model such as a 
cyclic-type having recursive combination can also be used. 
The hierarchical NN model is a layered model having an input layer, plural 
hidden layers, and an output layer. Each layer has units (neurons), 
weights, and a bias. In FIG. 15, circles represent the units, and smaller 
circles accompanying the units represent weights (synapses) which are 
connections to the units immediately in front of the unit. Furthermore, 
each square indicates a mechanism for adding a bias to the unit. 
The function of each unit is to receive a value of "the summation of 
products which are obtained by multiplying output O.sub.p,i of the pth 
middle layer (i=1, 2, . . . , L; L is the number of units belonging to the 
former layer) with ith weight W.sub.j,i belonging to the jth unit in the 
p+1th layer (i is the number of the weight and corresponds to the unit 
number in the former layer) and additional bias w.sub.j " as an input 
value and outputs value y(=o.sub.p+l,j) which is obtained by operating a 
non-linear transformation f(.multidot.) with respect to the input value, 
and transmits this output value to the next layer. This function is 
represented by Equation (1), where the input-output transformation 
function for the units of the input layer is linear, and as the non-linear 
transformation function f(.multidot.) for the units of the other layers, a 
Sigmoid function is adopted (see Equation (2)). Note that other 
input-output transformation functions may be used in accordance with the 
NN model to be used. 
##EQU1## 
In the above, .SIGMA. means the summation at i=1 to L. 
In a conventional weather forecast apparatus, a method has been proposed in 
which the movement of clouds ("clouds" indicate a rainfall or snowfall 
region hereinbelow, and thus "the movement of clouds" indicates weather 
dynamics) is learned by providing a measured radar image for the NN model, 
and a future radar image is forecast by using the NN model after learning. 
For example, in the case of U.S. Pat. No. 5,406,481, a measured radar 
image is provided for the NN model, which has a calculation unit for 
summing up products, so as to make the model learn the weather dynamics; 
and rainfall, snowfall, and the like are forecast by using the NN model 
after learning. Hereinafter, such a NN model for learning and forecasting 
is referred to as the "FNN model". 
However, no means for systematically classifying and utilizing radar images 
based on past radar images have been proposed. In addition, for a 
real-time forecast, the amount of calculations needed for the learning of 
the FNN model must be much further decreased; however, no means for this 
necessity has been available. 
Next, as a conventional pattern recognition method of images, 
feature-quantity extraction from an image has been known, and a typical 
example of it is a texture analysis (Reference 1: Murao, et al., "Kishoo 
Eisei Gazoo wo Mochiite Koosuiryoo-Suitei wo Okonau Fukugoo-gata 
Nyuuraru-Nettowaaku-Sisutemu ("Complex Neural Network System for 
Forecasting the Amount of Rainfall by Using Meteorological Satellite 
Images")", SICE (Society of Instrument and Control Engineers), Proc. of 
the 17th Intelligence System Symposium, pp. 107-112, 1993; or R. M. 
Haralick, "Statistical and Structural Approaches to Texture", Proc. of the 
IEEE, Vol. 67, No. 5, pp. 786-804, 1979). An example of the calculation 
procedure for feature quantities used in the texture analysis will be 
explained below. 
For an image in which each pixel has M-gradation, when taking notice of one 
pixel (x,y), it is called a "target pixel". Then, a pixel which exists in 
the direction of angle .theta. and at a distance of d from the target 
pixel is specified as an "object pixel". Here, the number C.sub.ij of 
combinations of the pixels satisfying the condition that the notice pixel 
(x,y) has gray level i and its object pixel has gray level j is counted, 
and a value obtained by dividing C.sub.ij by number C.sub.all which 
indicates the total number of combinations of the pixels existing distance 
d away from each other is defined as "combination probability density 
f(i,j) between two pixels". This is represented in equation (3). 
EQU f(i,j)=C.sub.ij /C.sub.all ( 3) 
Because of 0.ltoreq.i,j&lt;M, a matrix of M row, M column with each element 
f(i,j) can be defined as a co-occurrence matrix, as shown below. 
##EQU2## 
According to the co-occurrence matrix, some feature quantities such as 
energy E, entropy H, correlation C, local homogeneity L, and inertia I, 
can be calculated, as represented in the following equations. 
##EQU3## 
In the conventional method, as shown in the flow chart of FIG. 16, image 
data are input (see step 251), and the above-mentioned feature quantities 
are calculated for each image (see step 252). The calculated feature 
quantities are then compared to each other (see step 253) so as to 
recognize and classify the pattern of the image, and the recognized result 
is output (see step 254). 
In such a method, the calculation step of extracting the feature quantities 
from an image is fixed for every kind of image; thus, there is a problem 
that even if jointly using many kinds of feature quantities for 
recognizing an image, it is difficult to correctly recognize and classify 
the image. 
In addition, as a method of classifying such feature quantities for the 
purpose of systematically classifying images, a method of jointing SOM 
(Self-Organization Map) and LVQ (Learning Vector Quantization) is known 
(cf. above Reference 1, or Reference 2: Murao, et al., "Kishoo Eisei Gazoo 
niyoru Koosuiryoo-Suitei eno Nyuuraru-Nettowaaku no Ooyoo ("Application of 
Network System for Forecasting the Amount of Rainfall by Using 
Meteorological Satellite Images")", SICE, Proc. of the 18th System 
Symposium, pp. 303-309, 1992). 
However, in this method, only the feature quantities calculated from the 
co-occurrence matrix are proceeded; other feature quantities as image 
patterns are not taken into account. Furthermore, in the learning rules 
known by the classification method according to References 1 or 2, no 
convergence can be obtained if the distribution of input data is 
discontinuous, or the distribution has some deviation. Hereinafter, the 
method of jointing the SOM and the LVQ will be explained in more detail. 
As a model, a competitive learning model is used, an example of which is 
shown in FIG. 17. The competitive learning model is a kind of NN model, a 
layered network model having one input layer 91 and one output layer 92. 
In the figure, each unit (neuron) is shown by a circle. Each unit in input 
layer 91 has a linear input-output function, and an output value of it is 
propagated to each unit in output layer 92. Each unit in output layer 92 
has a reference vector. At the time of learning, with respect to one input 
vector, one output unit is selected from among all the output units, and 
by renewing the reference vector of the selected unit, input vectors, that 
is, as shown in FIG. 18, input data (represented by the marks 
".circle-solid.") are quantized (or approximated) by each reference vector 
(represented by the mark "x") in input space (which has dimensions 
corresponding to the number of the reference vectors) 93. According to 
this, the same number of clusters as that of the units in the output layer 
(that is, the number of the reference vectors) are formed. Each cluster is 
represented by the reference vector. 
These learning rules will be shown below. The input data are represented by 
x and the reference vectors (N is the number of them) are defined as 
follows. 
EQU {y.sub.j, j=1, . . . , N} 
The next equation defines the quantization error (or quantization 
distortion) at the approximation of the input data by using the reference 
vectors. 
##EQU4## 
In the LVQ method, learning is performed such that the above quantization 
error is minimized. First, for input data x, reference vector y.sub.c 
which has a minimum quantization error is chosen, where c is represented 
as follows. 
EQU c=arg min.sub.j d(x,y.sub.j) (11) 
Next, only this chosen reference vector is renewed by using the following 
equation. 
EQU y.sub.c (t+1)=y.sub.c (t)+.alpha.(t)(x-y.sub.c (t)) (12) 
where t is the repetition number and .alpha.(t) is a learning coefficient 
as follows. 
##EQU5## 
On the other hand, in the learning rules of the SOM, both the reference 
vector which has a minimum quantization error with respect to the input 
data and other reference vector which is in a topological neighborhood 
relationship with this reference vector are renewed by the following 
equation. 
EQU y.sub.c (t+1)=y.sub.c (t)+h.sub.ci (x-y.sub.c (t)) (14) 
where h.sub.ci is a coefficient, called a "neighborhood kernel", 
represented by the following equation (15), such that if .parallel.y.sub.c 
-y.sub.i `.fwdarw..infin., then h.sub.ci .fwdarw.0. By such a kernel, a 
reference vector which is in the topological neighborhood relationship 
with the reference vector having a minimum quantization error is chosen. 
##EQU6## 
In the learning of the SOM or the LVQ method, if the distribution of the 
input data is discontinuous, or the distribution has some deviation, the 
quantization error (or quantization distortion) at each cluster is 
increased, whereby there occurs a problem that desired results for the 
clustering cannot be obtained. 
In order to solve such a problem, a selective algorithm has been proposed 
such that a function of the combination probability density of input data 
x is defined as 
EQU p(x)=p(x.sub.1, x.sub.2, . . . , x.sub.k) 
and expected distortion G is defined as the next equation so as to search 
for an initial value of the reference vector, which minimizes such 
distortion (cf. Reference 3: Ueda, et al., "Competitive and Selective 
Learning Method for Vector Quantizer Design-Equidistortion principle and 
Its Algorithm-, IEICE(D-II), Vol. J77-D-II, No. 11, pp. 2265-2278, 1994). 
##EQU7## 
where E.multidot.! means an expected value, Q(x) is a N-level vector 
quantizer, and 
EQU Q(x)=x.sub.j if x.epsilon.S.sub.i (i=1, 2, . . . , N) 
where S.sub.i means an area which is dominated by reference vector y.sub.j. 
In this selective algorithm, according to the increase of repetition number 
m, the number sm! of reference vectors which are to be selected is 
decreased. After ranking the reference vectors according to their 
subdistortion D.sub.i, the reference vectors with the highest and lowest 
ranks are alternatively selected. As shown above, the reference vectors 
which are selected from reference vectors y.sub.i (i=1, . . . , N) is 
defined as y.sub.j (j=1, . . . , sm!). This selective algorithm will be 
explained below. 
First Step 
For each reference vector y.sub.j, subdistortion D.sub.j m! which is 
represented by Equation (17) and normalization adaptive degree g.sub.i 
which is represented by Equation (18) are calculated. 
##EQU8## 
In the above, S.sub.j indicates a dominant area of reference vector 
y.sub.j, as shown in next Equation (19), and .tau. (&lt;1.0) is a constant 
which is not negative. 
##EQU9## 
Second Step 
The following selections 1 and 2 are performed to determine the number 
u.sub.j (j=1, . . . , sm!) of duplicates of the reference vectors. 
1 For each j, the following formula is calculated. 
EQU .left brkt-bot.g.sub.i sm!.right brkt-bot. 
where .left brkt-bot.a.right brkt-bot. means the maximum integer not 
exceeding a. 
2 From g.sub.j m! (j=1, . . . , sm!), some are selected (the number of 
g.sub.j m! to be selected is represented by the following formula) in 
order of amount. 
##EQU10## 
Then, "1" is added to u.sub.j which corresponds to the selected "j". 
Third Step 
According to number u.sub.j of duplicates of the reference vectors, 
perturbation shown as 
EQU .delta..sub.jl, l=1, . . . u.sub.j -1 
which satisfies the following condition 
EQU .parallel..delta..sub.jl .parallel.&lt;&lt;.parallel.y.sub.j .parallel. 
is added to each reference vector so as to generate u.sub.j -1 of reference 
vectors in the neighborhood of reference vector y.sub.j. 
Hereinafter, the joint rules of the above selective algorithm and the LVQ 
learning rules (see Equations (10).about.(13)) are referred to as "Ueda 
learning rules". 
In the above-explained conventional technique, only feature quantities 
extracted from the co-occurrence matrix are used as those extracted from 
images; therefore, there is a problem that the images cannot be classified 
in accordance with detailed features. For example, when radar weather 
images are processed, it is necessary to extract a feature as a pattern, 
such as cirrus clouds, and clouds accompanying a rotating low pressure 
system, which are seen in typhoons; furthermore, it is also necessary to 
extract features such as moving directions and speed of clouds. However, 
conventional techniques cannot extract such features. 
Furthermore, in the Ueda learning rules, the method of decreasing the 
number sm! of the reference vectors to be selected in each repetition and 
the method of selecting the reference vectors to be selected are 
heuristic; thus, in the case that the distribution of each subdistortion 
has some deviation, it takes a long time for the selection to be 
completed. 
SUMMARY OF THE INVENTION 
In consideration of the above problems, it is an object of the present 
invention to provide an apparatus and a method for weather forecasting, by 
which it is possible to systematically classify a measured radar image 
based on results of pattern classification of past radar images, and to 
use the classified radar image. Other objects of the present invention 
include shortening the learning time for a radar image, accurately 
recognizing and classifying a pre-learned image, and forecasting a radar 
image at any future time using a small amount of calculation. 
Therefore, the present invention provides a weather forecast apparatus 
which provides a weather radar image to an FNN model so that the model 
learns weather dynamics and forecasts weather by using the FNN model after 
the learning, comprising: a pattern recognition means, including a PNN 
model prepared based on classification criteria according to past radar 
images (that is, a "PNN model" indicates a NN model for pattern 
classification, and this abbreviated form will be used hereinbelow), for 
pattern-recognizing a measured radar image by providing the image to the 
PNN model so as to pattern-classify the radar image; a memory means for 
storing plural weights for the FNN model, which are determined based on 
past plural radar images; and a learning means, including the FNN model, 
for selecting a weight which corresponds to a pattern resembling the 
pattern of the measured radar image from among those stored in the memory 
means in accordance with the pattern-recognized result obtained by the 
pattern recognition means; setting the selected weight as an initial value 
of the FNN model; and making the FNN model re-learn. 
According to the above invention comprising the PNN model based on 
classification criteria according to past radar images, automatic pattern 
recognition based on judgment by humans, such as resemblance between the 
measured radar image and a past radar image, can be realized. 
Additionally, the initial value of the weight for the FNN model is 
automatically set in accordance with degree of the resemblance of the 
radar image pattern; thus, the time required for re-learning can be 
shortened. 
Furthermore, by previously making the FNN model learn by providing the 
indexes representing plural forecast times, it is possible to forecast a 
radar image corresponding to any forecast time obtained by any combination 
of the indexes, with a small amount of calculation. 
The present invention also provides a weather forecast method which also 
performs weather forecasting based on the learning of weather dynamics, 
the method performing pattern recognition of the radar image by using a 
TNN model which transforms and outputs feature quantities which were input 
into the TNN model (that is, a TNN model indicates a NN model for 
transforming feature quantities, and this abbreviated form will be used 
hereinbelow), comprising the steps of: calculating and extracting one or 
more feature quantities from a radar image; providing the feature 
quantities extracted in the calculating and extracting step for the TNN 
model as input and teacher data, and learning identical transformation 
from the feature quantities to the feature quantities; calculating an 
estimated value based on a criterion for recognition from the output 
feature quantities which were identically transformed and output from the 
TNN model; adding perturbation to the output feature quantities; and 
performing re-learning of the TNN model such that the estimated value is 
maximized or minimized; and pattern-recognizing a pre-learned image by 
providing feature quantities calculated and extracted from the pre-learned 
image for the TNN model after the re-learning. 
This method makes it possible to vary the calculation procedure for 
extracting feature quantities which are used for recognition and 
classification of images, and to automatically establish a procedure for 
calculating feature quantities, which are most suitable for the introduced 
criterion, in the TNN model. As a result, when performing the pattern 
recognition and classification of a pre-learned image by using the TNN 
model after the re-learning, recognition accuracy can be improved in 
comparison with the case of conventional recognizing and classifying 
method in which only feature quantities extracted from the image are used. 
In addition, by adopting a means for adding perturbation for the output 
value of the TNN model at the re-learning, it is possible to renew the 
weight by a smaller amount of calculation than in the case of directly 
adding perturbation to the weight of the NN model. 
As an apparatus for implementing this method, the present invention 
provides a weather forecast apparatus comprising a feature quantity 
calculating means for calculating and extracting one or more feature 
quantities from a radar image; a TNN model for transforming and outputting 
the feature quantities which are input from the feature quantity 
calculating means; a perturbation generating means for generating an 
amount of perturbation; a means for calculating an estimated value from 
the feature quantities output from the TNN model, based on a criterion for 
recognition; a learning means for providing the feature quantities 
extracted by the feature quantity calculating means for the TNN model as 
input and teacher data; and performing identical transformation from the 
feature quantities to the feature quantities; adding the amount of 
perturbation to the output feature quantities after the transformation; 
and performing re-learning of the TNN model such that the estimated value 
is maximized or minimized; and a recognizing means for pattern-recognizing 
a pre-learned image according to the estimated value which is obtained 
when feature quantities calculated and extracted from the pre-learned 
image are input into the TNN model after the re-learning. 
Furthermore, the present invention provides a weather forecast method which 
also performs weather forecast based on the learning of weather dynamics, 
the method performing systematic classification of the radar image by 
using a PNN model which selects reference vectors based on input feature 
quantities, comprising the steps of: calculating and extracting plural 
feature quantities from the radar image; providing the feature quantities 
extracted in the calculating and extracting step for the PNN model, and 
performing learning of the PNN model by finding a minimum value of an 
object function such that the quantization error of each reference vector 
which belongs to each output unit of the PNN model is minimized; and 
classifying a pre-learned image by providing the feature quantities 
calculated and extracted from the pre-learned image for the PNN model 
after the learning. 
In this method, by means of providing the object function, for example, in 
quadratic form, such that the quantization error of each reference vector 
which belongs to each output unit of the PNN model is minimized, and 
finding the minimum value of the object function, distortion is 
monotonically decreased in every repetition time; thus, convergence can be 
realized by a small number of repetitions. Therefore, it is possible to 
precisely classify radar images. In addition, if using feature quantities 
obtained by, for example, a gray level difference method (GLDM) and a gray 
level run length method (GLRLM) as well as those obtained by the 
co-occurrence matrix, it becomes possible to recognize a pattern of cirrus 
clouds or clouds accompanying a rotating low pressure system. Accordingly, 
detailed classification can be performed. 
As an apparatus for implementing this method, the present invention 
presents a weather forecast apparatus comprising a feature quantity 
calculating means for calculating and extracting plural feature quantities 
from a radar image; a PNN model for selecting reference vectors based on 
the feature quantities which are input from the feature quantity 
calculating means; a learning means for providing the feature quantities 
extracted by the calculating and extracting means for the PNN model, and 
performing learning of the PNN model by finding a minimum value of an 
object function such that the quantization error of each reference vector 
which belong to each output unit of the PNN model is minimized; and a 
classifying means for classifying a class of the image according to the 
reference vectors which were selected by the PNN model, wherein: 
systematic classification of a pre-learned image is performed by inputting 
the feature quantities calculated and extracted from the pre-learned image 
into the PNN model after the learning.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 
Hereinafter, embodiments according to the present invention will be 
explained with reference to the figures. 
First Embodiment 
FIG. 1 is a block diagram showing the arrangement of the weather forecast 
apparatus of the first embodiment according to the present invention. In 
the figure, reference numeral 100 indicates an input section, reference 
numeral 200 indicates a data processor, and reference numeral 300 
indicates an output section. 
The input section 100 comprises weather radar 101 for measuring a rainfall 
or snowfall area, and file reader 102 for reading information items 
required for the learning of the FNN model, the pattern recognition, and 
the forecast. 
The data processor 200 comprises pattern recognizer 201 for recognizing the 
pattern for the measured radar image; database 202 for systematically 
classifying and managing the past radar images and optimized weights for 
the FNN model; and learning and forecasting part 203 for learning the 
weather dynamics and forecasting a future radar image. 
In this weather forecast apparatus, a radar image which was measured by 
using weather radar 101 in input section 100 is input to be transferred to 
data processor 200. In addition, data or a coefficient required for the 
learning is read from file reader 102 to be transferred to pattern 
recognizer 201 and learning and forecasting part 203. 
The pattern recognizer 201 inputs the radar image transferred from input 
section 100 into the PNN model of its own, and outputs an index for 
judging which cluster of the database the image belongs to. 
In addition, this previously-set PNN model was made to learn with reference 
to the degree of similarity of radar images with respect to each cluster. 
Such a degree is determined by humans. The clusters for radar images can 
be variously determined based on, for example, rain clouds or the shapes 
of clouds. 
The database 202 newly adds the radar image to a cluster which has a 
resemblance to the pattern with respect to the radar image, according to 
the judgment of the pattern recognizer. In addition, database 202 
transfers the optimized weights and the past radar image which belong to 
the cluster to the learning and forecasting part 203. 
The learning and forecasting part 203 comprises the FNN model such as one 
shown in FIG. 15, which already learned with reference to the past radar 
images. The learning and forecasting part 203 gives the optimized weights 
transferred from the database 202 to the FNN model as initial values, and 
performs re-learning by using the radar image transferred from input 
section 100 and the past radar image transferred from the database 202. 
After re-learning, the learning and forecasting part 203 fixes the weights 
of the FNN model, and forecasts a radar image at any time after the 
measuring of the radar image. The forecast result is transferred to output 
section 300. In the output section 300, the result is shown in a display 
and the like. 
If the measured radar image does not belong to any cluster as a result of 
the pattern recognition, a new cluster is added to the database. At this 
time, optimized weights of the FNN model for the added cluster are 
generated by, for example, performing a mean operation using the optimized 
weights of the other clusters. It is possible to judge whether a radar 
image belongs to any cluster or not by comparing the maximum degree of 
similarity to the existing clusters with a predetermined threshold value. 
In addition, by previously designating an upper limit for the number of the 
clusters (i.e., the cluster number) for the pattern classification of 
radar images, and by varying the cluster number by using the learning 
function of the PNN model, it is possible to enlarge or reduce the size of 
the database which contains radar images, values of the weights for the 
FNN model after learning, etc. In this case, if a radar image which has 
not yet been registered in the database is input, a new cluster can be 
added within the limits up to the designated upper limit. 
Furthermore, if the size of the database is too enlarged, it is possible to 
reduce the cluster number by unifying the clusters whose radar patterns 
resemble each other. 
Second Embodiment 
In this embodiment, information (t) relating to the forecast time is input 
to the input side of the FNN model in the weather forecast apparatus, as 
shown in FIG. 2. According to the time information, the FNN model can 
arbitrarily change the time intervals of mappings constructed between the 
input and the output of the model (that is, the time intervals of radar 
images between the input and the output). 
If the hierarchical NN model is used as the FNN model of the weather 
forecast apparatus of the present embodiment, the input-output 
characteristic of a middle layer can be represented by the following 
equation, where t is an index of the forecast time for a radar image 
output from the FNN model. 
##EQU11## 
where .SIGMA. means the summation at i=1 to L (L is the number of the 
units of the former layer). 
FIG. 3 is a block diagram showing the weather forecast apparatus of the 
present embodiment. In the figure, parts which are identical to those 
shown in FIG. 1 are given identical reference numbers. Reference numeral 
204 indicates an input selector for changing radar images as an input, 
reference numeral 205 indicates a forecast time designator for designating 
a time at which the forecast is performed. 
In case of this embodiment, input selector 204 is usually set so as to 
select the radar image measured by the weather radar 101 as the input for 
the learning and forecast section 203. The forecast time designator 205 
provides information t relating to the forecast time to learning and 
forecasting part 203. As a result, the forecast of any future time 
corresponding to some times which are learned can be realized. 
For example, in the case in which indexes which indicate forecast times of 
every five minutes from 5 to 30 minutes are given for the learning, the 
forecast result up to 30 minutes into the future can be obtained with one 
time input for the FNN model in the later forecast steps. In case of 
forecasting a radar image more than 30 minutes into the future, the radar 
image of 30 minutes into the future, which was forecasted by the learning 
and forecasting part 203, is provided to the same part 203 via input 
selector 204 and a next necessary forecast time is designated so as to 
repeat the forecast by the learning and forecasting part 203. In this way, 
a future radar image at any desired time can be forecast with a relatively 
small number of calculations. 
In the weather forecast apparatus of the above first embodiment, the 
mappings between the input and output could be formed by the FNN model 
only at fixed intervals. For example, it is assumed that the learning was 
performed so as to output a future radar image at five minutes into the 
future with respect to the input radar image. In this case, for 
forecasting future radar images of 30 minutes and 2 hours into the future, 
6 and 24 times of the cyclic operation via learning and forecasting part 
203 and input selector 204 are needed, respectively. 
In contrast, by using the weather forecast apparatus of the present 
embodiment for forecasting future radar images of 30 minutes and 2 hours 
into the future by using a model which learned with the maximum forecast 
time of 30 minutes, only 1 and 4 times of the cyclic operation via 
learning and forecasting part 203 and input selector 204 can realize the 
respective forecasted results. 
By using the above stated embodiments, an application of forecasting the 
number of the sales of commodities can be realized by making the FNN model 
learn the sales results of commodities which are influenced by the weather 
as well as the radar image. 
Third Embodiment 
In this embodiment, the pattern recognition of radar images is effectively 
incorporated into the weather forecast apparatus which provides a weather 
radar image to the FNN model so as to make the model learn the weather 
dynamics and forecasts the weather such as rainfall and snowfall in a 
short time by using the FNN model after learning. Hereinbelow, a method of 
the pattern recognition and the apparatus for implementing such a method 
will be explained. The basic forecasting part based on the weather 
dynamics is similar to, for example, that of the above-mentioned U.S. Pat. 
No. 5,406,481; thus, the explanation for it will be omitted here. 
FIG. 4 is a flow chart showing the procedure of pattern recognition which 
is used in the third embodiment according to the present invention. The 
recognition method of this embodiment performs recognition and 
classification by using a TNN model. The steps of the procedure are 
roughly divided into three sections: data input section 151 for inputting 
radar images, learning section 161 in which learning and re-learning of 
the TNN model is performed, and classification section 162 in which 
feature quantities (calculated from pre-learned image data) are given to 
the TNN model after re-learning so as to recognize and classify the image. 
First, image data are input (see step 151), and then learning section 161 
is performed. In the learning section, feature quantities which are 
effective for the recognition and classification of the image are 
extracted from the image data (see step 152). 
As the feature quantities, besides energy E, entropy H, correlation C, 
local homogeneity L, and inertia I, which were explained by using 
respective Equations (5)-(9), the following quantities are newly 
introduced. 
(A) Feature quantity obtained by the gray level difference method (GLDM) 
(cf. Reference 4: J. S. Weszka, "A Comparative Study of Texture Measures 
for Terrain Classification", IEEE Trans. on Syst. Man. and Cybern., Vol. 
SMC-6, pp. 269-285, 1976) 
With the gray level of the target pixel (n,m) as g(n,m) and the gray level 
of the object pixel being distance .delta. away from this target pixel as 
g(n+.DELTA.n,m+.DELTA.m), the gradient of gray level at this target pixel 
(n,m) is defined by the following equation. 
EQU g.sub.67 (n,m)=.vertline.g(n,m)-g(n+.DELTA.n,m+.DELTA.m).vertline. 
If the probability of the above gradient g.sub..delta. (n,m) being i is 
defined as 
EQU f(i.vertline..delta.)=P(g.sub..delta. (n,m)=i) 
contrast CON, angular second moment ASM, entropy ENT, mean MEAN, and 
inverse difference moment IDM can be obtained, as shown by Equations 
(20)-(24). These quantities will be used as the feature quantities. 
##EQU12## 
(B) Feature quantity obtained by the gray level run length method (GLRLM) 
(cf. Reference 5: M. M. Galloway, "Texture an Analysis Using Gray Level 
Run Length", Comput. Graphic Image Processing, Vol. 4, pp. 172-179, 1975) 
When it is assumed that the number of times of the existence of a run with 
gray level i and length j on an image is defined as 
EQU r(i,j.vertline..theta.) 
the following matrix with this definition as element (i,j) can be defined 
as follows. 
EQU R(.theta.)=r(i,j.vertline..theta.)! 
By using this matrix R(.theta.), short run emphasis RF.sub.1 {R(.theta.)}, 
long run emphasis RF.sub.2 {R(.theta.)}, gray level distribution RF.sub.3 
{R(.theta.)}, run length distribution RF.sub.4 {R(.theta.)}, run 
percentage RF.sub.5 {R(.theta.)}, and the like can be obtained, as shown 
by Equation (25)-(29). These quantities will also be used as the feature 
quantities. 
##EQU13## 
where N.sub.G is the total number of gray levels, and N.sub.R is the total 
number of run lengths with respect to matrix R(.theta.). In addition, 
T.sub.R is the total number of runs regardless of the length or the gray 
level, as follows. 
##EQU14## 
The feature quantity obtained by the GLRLM is particularly effective for 
systematic classification of cirrus clouds. In this embodiment, any other 
feature quantities than those stated here may also be used. It should be 
noted that the feature quantities to be extracted are selected such that 
the number of the selected feature quantities is the same as that of 
variables which are used for an evaluation criterion for recognition and 
classification of images, which will be explained later. 
Next, feature quantities calculated from image data (referred to as 
"feature quantities 1", hereinafter) are provided as input and teacher 
data to the TNN model, and identity learning by using the TNN model is 
performed (see step 153). Here, with the output from the TNN model as 
o.sub.i and the teacher data as t.sub.i, the TNN model is controlled to 
learn in order that the error "Error" shown by Equation (31) is minimized. 
Note that the number of the units in the output layer is N. 
##EQU15## 
FIG. 5 is a conceptual view for explaining the identity learning of the TNN 
model. In the figure, the word "feature quantities" is abbreviated as 
"F.Q.". By the identity learning, such a calculation step as the feature 
quantities 1 obtained from the image are identically transformed into the 
feature quantities 1 themselves (this means the identity mapping) can be 
established. In this step, the number N of units in the output layer of 
the TNN model is set equal as the number of the variables necessary for 
calculating a value of the criterion. 
Next, the criterion is introduced at the output side of the TNN model (see 
step 154). Here, Fisher's criterion in which the class of each image is 
estimated based on a covariance matrix with respect to input data is 
introduced as an example. In the present embodiment, other criteria than 
Fisher's can also be introduced. 
With a vector having an element of each feature quantity calculated by the 
TNN model as o, and vector sets belonging to two classes as 
EQU (O.sub.1.sup.1, . . . , O.sub.M.sbsb.1.sup.1), (O.sub.1.sup.2, . . . , 
O.sub.M.sbsb.2.sup.2) 
Fisher's criterion can be represented by the following equation. 
##EQU16## 
In this criterion, larger estimated value F makes the separation of data on 
a given feature space (where the feature quantity vectors exist) easier. 
Therefore, in this embodiment, by performing re-learning of the TNN model 
so that estimated value F (i.e., Fisher's criterion) could be maximized, a 
TNN model by which more effective feature quantities can be extracted is 
constructed (see step 155). Hereinbelow, the re-learning of the TNN model 
will be explained in detail. 
For making the TNN model re-learn, the following partial differential value 
of the Fisher's function with respect to weight W.sub.j,i is necessary. 
##EQU17## 
However, it is often difficult to analytically calculate the formula of 
such a partial differential. Therefore, the use of a perturbation method 
may be considered, in which some perturbation is added to the weight, and 
from the corresponding increase or decrease of criterion F, it is 
determined whether or not the weight is to be renewed. However, the 
following amount of calculation is necessary from the addition of the 
perturbation to the weight up to the renewal of the weights. Here, the 
output feature quantities from the TNN model are generally termed "feature 
quantities 2". 
(Amount of calculation necessary for obtaining feature quantities 2 by 
forward-calculation when providing feature quantities 1 to the TNN model 
to which perturbation was added)+(Amount of calculation necessary for 
calculating the criterion for the recognition and classification of the 
image) 
On the other hand, if adding some perturbation to feature quantities 2 
obtained as output values from the TNN model, and renewing the weight 
according to this, the following amount of calculation is necessary. 
(Amount of calculation necessary for calculating the criterion from feature 
quantities 2)+(Amount of calculation necessary, only in the case that the 
criterion is maximized or minimized, for obtaining a correction amount for 
the weight by back-propagating the amount of the perturbation which was 
added to feature quantities 2) 
In the case of using the former method, the whole calculation must be 
performed every time the perturbation is added. In contrast, in the case 
of the latter method, the calculation of the back-propagation of the 
amount of perturbation must be performed only when the criterion is 
increased (or decreased at the case of minimization); thus, the amount of 
calculation necessary for the renewal of the weight is decreased. 
Accordingly, in this embodiment, the latter method is adopted. FIG. 6 is a 
conceptual view for showing the concept of this renewal method, that is, 
the re-learning of the TNN model in the present embodiment. 
Next, a method for back-propagating the amount of perturbation will be 
examined. That is, it will be examined to calculate the variation of the 
Fisher's criterion (Equation (32)) and to back-propagate the variation 
(cf. a book for reference: D. E. Rumelhart and J. K. McClelland, "Parallel 
Distributed Processing", MIT Press, 1986). 
With feature quantities 2 output from jth unit of the TNN model as o.sub.j, 
and adding small perturbation .epsilon..sub.p,j to o.sub.j, and difference 
dif f(.epsilon..sub.p,j)=F.sub.1 -F.sub.2 is calculated, where F.sub.1 is 
the estimated value in case of no perturbation, while F.sub.2 is the 
estimated value in case of adding perturbation. If dif 
f(.epsilon..sub.p,j)&lt;0 (or f(.epsilon..sub.p,j)&gt;0 in case of the 
minimization of the estimated value), that is, if the estimated value is 
increased (or decreased in case of the minimization of the estimated 
value), a partial differential value represented by Equation (33) is 
calculated by back-propagating the amount of the perturbation. The partial 
differential value with respect to the units in the output layer can be 
obtained by the following Equation. 
##EQU18## 
Here, the amount of back-propagation is defined as follows. 
EQU .delta..sub.p+l,j =.epsilon..sub.p+l,j .multidot.f'(net.sub.p+l,j)(35) 
By further back-propagating this amount, the following recursion formula 
can be obtained. Here, k represents the whole of the units which receive 
the output from unit j in a middle layer. 
##EQU19## 
By using this, the partial difference in connection with the weight which 
belongs to the unit of the middle layer can be calculated by Equation 
(37). 
##EQU20## 
Here, based on the amount of the back-propagation obtained by Equations 
(33) and (37), the weight is renewed by the following equation, where k 
means the number of repetitions and .eta. means a rate for learning. 
##EQU21## 
By the above-explained learning, the step of transformation from feature 
quantities 1 extracted from an image to feature quantities 2 being 
effective by the pattern recognition and classification of the image is 
established. 
The learning section 161 is performed as explained above, and the learning 
and re-learning of the TNN model is realized. 
Hereinbelow, the classification section 162 will be explained. In this 
section, feature quantities 1 are extracted from pre-learned image data, 
i.e., image data which will be practically pattern-recognized and 
classified. These extracted feature quantities are then input into the TNN 
model in which the re-learning was performed in learning section 161. 
Then, from feature quantities 2 which are output from the TNN model, 
estimated value F is computed based on the above-explained criterion so as 
to recognize and classify the pattern of the image (see step 156). After 
that, the classified result is output (see step 160), and now all 
sequential steps are completed. FIG. 7 is a conceptual view for explaining 
the pattern recognition and classification of the image by using the TNN 
model after re-learning. 
The pattern recognition method used in the present embodiment has been 
explained above. Next, a radar image feature quantity extracting apparatus 
for implementing the method will be explained with reference to FIG. 8. In 
the figure, parts which are identical to those shown in FIG. 1 are given 
identical reference numbers. In this apparatus, data processor 400, 
including a TNN model, for performing the pattern recognition and 
classification of radar images according to the method of the present 
invention is provided. 
The data processor 400 comprises feature quantity calculator 401 for 
calculating and extracting feature quantities 1 calculated in the feature 
quantity calculator 401 from the input radar image; feature quantity 
transformer 402, including the TNN model, for providing the feature 
quantities 1 calculated in the feature quantity calculator 401 to the TNN 
model so as to transform them to be output as feature quantities 2; 
estimator 403 for estimating the class (or the kind) of the image based on 
the feature quantities 2 output from the feature quantity transformer (the 
TNN model) 402; learning controller 404 for making the feature quantity 
transformer 402 learn; and perturbation generator 405 for generating 
perturbation which is used for the learning. 
As the TNN model included in feature quantity transformer 402, the 
above-stated hierarchical model may be used. The estimator 403 introduces 
a criterion of the image recognition and classification for feature 
quantities 2 output from the TNN model and classifies images for each 
class. For example, the estimator outputs estimated value F based on the 
above-stated Fisher's criterion. In output section 300, the recognized and 
classified results and the like are displayed. 
Next, the pattern recognition and classification of radar images by using 
this radar image feature quantity extracting apparatus will be explained. 
For performing such pattern recognition and classification by using this 
apparatus, the learning of the TNN model in the feature quantity 
transformer 402 must be previously performed via learning controller 404. 
Therefore, the operation at the learning will be explained, here. 
First, a radar image and so on are read from input section to be 
transferred to data processor 400. In addition, data required for the 
learning of the NN model, such as a rate for learning, are previously 
transferred from file reader 102 to feature quantity transformer 402. 
Subsequently, feature quantities such as energy, entropy, correlation, and 
so on are calculated as image patterns by using feature quantity 
calculator 401, and the calculated quantities are transferred to feature 
quantity transformer 402. 
The learning of the TNN model can be classified into the first learning and 
the re-learning. In case of performing the first learning, identity 
mappings of feature quantities 1 which are sent from feature quantity 
calculator 401 are learned. That is, the learning is performed in a manner 
such that feature quantities 1 from feature quantity calculator 401 are 
given as input and teacher data and the error of the output from the TNN 
model with respect to the teacher data (i.e., given feature quantities 1) 
is minimized by means of the back-propagation. The re-learning is 
subsequently performed after the first learning. 
At the re-learning, feature quantity transformer 402 inputs feature 
quantities 1, which are transferred from the feature quantity calculator 
401, into the TNN model, and transforms those into feature quantities 2 by 
a one-time forward calculation. The feature quantity transformer then 
transfers the feature quantities 2 to estimator 403 so as to calculate an 
estimated value. 
On the other hand, some perturbation based on, for example, random numbers 
is generated by perturbation generator 405 in accordance with learning 
controller 404, and the generated perturbation is added to the output from 
the TNN model. Such perturbation-added feature quantities are also 
transferred to estimator 403, and the estimated value is calculated. If 
the estimated value after adding the perturbation is larger (or smaller) 
than that before the addition of the perturbation, the weights of the TNN 
model are renewed. By repeating such a re-learning operation, a feature 
quantity calculation procedure which is more suitable for classifying 
patterns can be established in the TNN model. 
When completing the learning of the TNN model as stated above, practical 
pattern recognition and classification of a radar image is performed. 
First, a pre-learned radar image is read from input section 100, and the 
image is transferred to the data processor 400 where feature quantities 1 
are extracted from the image data. The extracted feature quantities 1 are 
transferred to feature quantity transformer 402 to be input into the TNN 
model. The feature quantities 2 output from the TNN model are transferred 
to estimator 403. The estimator 403 judges which class the image belongs 
to. The result of such judgment is output into the output section 300. By 
the above-explained operations, the pattern recognition and classification 
of the pre-learned image is completed. By utilizing such recognition and 
classification, the forecasting with respect to the rainfall, snowfall and 
the like can be improved. 
Fourth Embodiment 
In this embodiment, systematic classification of radar images is 
effectively incorporated into the weather forecast apparatus which 
provides a weather radar image to the FNN model so as to make the model 
learn the weather dynamics and forecasts the weather such as rainfall and 
snowfall in a short time by using the FNN model after learning. 
Hereinbelow, a method of the systematic classification and the apparatus 
for implementing such a method will be explained. The explanation of the 
basic forecasting part based on the weather dynamics will be omitted here, 
as it was in the third embodiment. 
FIG. 9 is a flow chart showing the procedure of the systematic 
classification of images, which is used in this fourth embodiment. In the 
figure, steps which are identical to those shown in FIG. 4 are given 
identical reference numbers. 
The classification method of this embodiment systematically classifies 
image patterns by using a competitive learning model which is a kind of 
the PNN models. The steps of this method are roughly divided into three 
sections: data input section 151 for inputting radar images, learning 
section 161' in which learning of the competitive learning model is 
performed, and classification section 162' in which image data which are 
not yet learned are introduced into the competitive learning model after 
learning, so as to systematically classify the image. As the competitive 
learning model, one which was explained with reference to FIG. 17 can be 
used as it stands. 
First, the input of image data is performed (see step 151), and then 
learning section 161' is performed. At the first of the learning section, 
feature quantities are extracted from the image data (see step 152). In 
this embodiment of processing weather radar images, any feature quantities 
as stated in the third embodiment can be used for the purpose of 
extracting a feature as a pattern such as cirrus clouds and clouds 
accompanying a rotating low pressure system, which are seen in typhoons; 
furthermore, features of moving directions or speed of clouds may also be 
extracted. Some of the feature quantities may be chosen according to on 
which view-point the systematic classification of images is performed. The 
feature quantities stated in the third embodiment can be extracted from 
one image. However, for example, for extracting the moving direction or 
speed of clouds as feature quantities from a radar image, those extracted 
from more than two images must be used. In this embodiment, the following 
feature quantities by using a cross correlation method, which will be 
explained below, are used. 
(C) Feature quantities representing the moving direction and speed of an 
object, obtained by using the cross correlation method 
Here, a case of extracting the moving direction and speed of clouds which 
are recorded in a weather radar image will be explained as an example. As 
shown in FIG. 10, a cross correlation value .sigma..sub.K,L is computed by 
the next equation in accordance with two weather radar images R.sub.1 and 
R.sub.2 which were observed with an interval of time .DELTA.t. Here, 
gradation of the lattice point (i,j) on the radar image, that is, 
intensities of the rainfall and snowfall are defined as R.sub.l,i,j and 
R.sub.2,i,j, respectively, and the area for examining correlation and the 
difference of the two radar images for finding a correlation value are 
defined as (M,N) and (k,l), respectively. In FIG. 10, the rectangle with 
short slanted lines indicates the area for examining correlation, and the 
center bold arrow indicates the moving direction of rain cloud 81. 
##EQU22## 
The cross correlation value obtained by the above calculation indicates, 
for example, a distribution shown in FIG. 11. Here, with respect to the 
maximum cross correlation value .sigma..sub.K,L at lattice point (K,L) and 
other four cross correlation values .sigma..sub.-X, .sigma..sub.+X, 
.sigma..sub.-y, .sigma..sub.+y at four neighboring points of the above 
lattice point, interpolation with a quadratic function is performed 
according to the following equation to find a difference (k',l') between 
lattice point (K,L) and a point (not always a lattice point) with a 
maximum cross correlation after the interpolation. 
##EQU23## 
FIG. 12 is for the purpose of explaining this interpolation calculation. In 
this figure, for the sake of clarity, only the X-direction is shown. 
As a result, the above two images have a maximum cross correlation value 
when these are (K+k', L+l') away from each other. Accordingly, moving 
vector (V.sub.X, V.sub.y) of rain cloud 81 can be obtained by the 
following equation. This vector quantities mean the moving direction and 
speed of the rain cloud 81. 
##EQU24## 
After extracting the feature quantities as stated above, these feature 
quantities are given as input data to a competitive learning model to make 
the model learn with no-teacher learning rules, and each reference vector 
is self-organized (see step 158). If the above-mentioned Ueda learning 
rules are used for the learning, after ranking the reference vectors 
according to each subdistortion, the reference vectors with the highest 
and lowest subdistortions are alternatively selected to determine the 
reference vectors to be selected. However, as the case shown in FIG. 13, 
that is, if the distribution of the input data has deviation and the 
distribution of values of the subdistortions also has deviation, many 
repetitions are necessary until the selection is completed. 
Therefore, a more simple selective algorithm, and an algorithm for 
minimizing sum G of all subdistortions (see Equation (16)) will be 
examined. 
First, the former will be examined. The reference vectors with the minimum 
subdistortion is selected to be rearranged in the neighborhood of the 
reference vector with the maximum subdistortion. Such a rearrangement 
operation is completed when the variance .sigma..sub.D m! (see the 
following equation) of the distribution of the subdistortions goes below a 
predetermined value .epsilon.. That is, the selection is completed when 
the subdistortions of the reference vectors are equalized. In the 
following equation, .upsilon..sub.D m! represents a mean value. At the 
end of the selection, each subdistortion has a minimum value. 
##EQU25## 
Next, an algorithm for minimizing sum G of all subdistortions will be 
examined. 
With each reference vector as {y.sub.j,j=1, . . . , N} and each 
subdistortion belonging to the reference vector as {D.sub.j, j=1, . . . , 
N}, a space constructed by these subdistortions is assumed. In this case, 
distortion G can be defined with respect to the points 
EQU D=(D.sub.1, . . . , D.sub.N) 
in the space. 
For minimizing this, the partial difference of distortion G with respect to 
ith element y.sub.i,j of reference vector y.sub.j is found according to 
the following equation. 
##EQU26## 
Here, according to the definition of the subdistortion as shown in Equation 
(17), the next equation can be obtained. 
##EQU27## 
Therefore, the following method will be examined: the partial difference 
value of G with element 
##EQU28## 
is defined as 
##EQU29## 
and quadratic partial difference matrix B.sub.j =.gradient..sup.2 G.sub.j 
with respect to each reference vector y.sub.j is considered, and its 
inverse matrix H.sub.j =B.sub.j.sup.-1 is reconstructed by using 
.gradient.G.sub.j and D so as to renew reference vector y.sub.j. Here, 
with the repetition number of the competitive learning model as m, the 
following amounts are defined. 
EQU s(m)-D(m+1)-D(m) 
EQU r(m)=.gradient.G.sub.j (m+1)-.gradient.G.sub.j (m) 
The renewal of approximate quadratic partial difference matrix H can be 
represented by the following equation by using a nonlinear optimizing 
method such as a BFGS method (cf. Reference 6: R. Fletcher, "Practical 
Method of Optimization", second ed., John Whiley & Sons, 1987) The BFGS 
method is used in the present embodiment, and a unit matrix is provided as 
an initial value of matrix H. 
##EQU30## 
According to this, renewal rules of the reference vector y.sub.j can be 
represented by the following equation. 
EQU y.sub.j (m+1)=-H.sub.j (m).gradient.G.sub.j (m) (50) 
These renewal rules mean minimizing a quadratic form with metric 
.gradient..sup.2 G.sub.j in the space of reference vector y.sub.j. 
By the above-explained renewal of the reference vectors, the learning 
section 161' is performed, and the learning of the competitive learning 
model is realized. 
Hereinbelow, the classification section 162' will be explained. In this 
section, feature quantities are extracted from pre-learned image data, 
i.e., image data to be systematically classified in practice. These 
extracted feature quantities are then input into the competitive learning 
model in which the learning was performed in learning section 161'. From 
all output units, one with the reference vector which is nearest with 
respect to the input vector is found, and according to this found unit, a 
class suitable for the image is judged to systematically classify the 
image (see step 159). After that, the classified result is output (see 
step 160), and now all sequential steps are completed. 
The systematic classification method used in the present embodiment has 
been explained above. Next, a radar image classifying apparatus for 
implementing this classification method will be explained with reference 
to FIG. 14. In the figure, parts which are identical to those shown in 
FIG. 8 are given identical reference numbers. In this radar image 
classifying apparatus, data processor 500, including a competitive 
learning model, for performing the systematic classification of radar 
images according to the present invention, is provided. 
The data processor 500 comprises feature quantity calculator 501 for 
calculating and extracting feature quantities from the input radar image; 
competitive learning model 502 for selecting, with the feature quantities 
as inputs, reference vectors having minimum distortion; learning 
controller 503 for making the competitive learning model learn by 
providing the feature quantities to the model; and classifier 504 for 
determining the class of the image based on the reference vectors selected 
by the competitive learning model 502 after learning. 
Next, the systematic classification of radar images by using this radar 
image classification apparatus will be explained. For performing such a 
systematic classification by using the apparatus, the learning of the 
competitive learning model 502 must be previously performed via learning 
controller 503. Therefore, the operation at the learning will be explained 
here. 
First, a radar image and so on are read from input section 100 to be 
transferred to data processor 500. In addition, data required for the 
learning of the competitive learning model, such as a rate for learning, 
are previously transferred from file reader 102 to feature quantity 
calculator 501. Subsequently, feature quantities as image patterns, such 
as energy, entropy, correlation, each amount according to the GLDM and the 
GLRLM, which are represented by the above Equations (5)-(9), (20)-29), 
(44), and (45) are calculated with respect to the image data by using 
feature quantity calculator 501, and the calculated quantities are 
transferred to the competitive learning model 502. Then, the learning of 
reference vectors is performed via the learning controller 503 according 
to Equation (49) and (50) so that the distortion could be minimized. 
When completing the learning of the competitive learning model 502 as 
stated above, the systematic classification of images is practically 
performed. First, a pre-learned radar image is read from input section 
100, and the image is transferred to the data processor 500, where feature 
quantities are extracted from the image data by the feature quantity 
calculator 501. The extracted feature quantities are transferred to the 
competitive learning model which selects reference vectors by which the 
distortion is minimized. Then, the classifier 504 assigns the class to 
which the selected reference vector belongs as a class for the image. The 
result of such classification is output into the output section 300. By 
the above-explained operations, the classification of the pre-learned 
image is completed. By utilizing such classification, the forecasting with 
respect to the rainfall, snowfall and the like can be improved.