CN104298987B - The Handwritten Digit Recognition method of online FCM clusters is weighted based on dot density - Google Patents
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Abstract
The invention discloses a kind of Handwritten Digit Recognition method that online FCM clusters are weighted based on dot density, for handling large-scale Off-Line Handwritten Digit Recognition problem, including step：1) all handwritten numeral image collections are pre-processed；2) cluster centre is initialized, makes data dot sequency enter handling process；3) current data point and each cluster centre degree of membership are calculated, if 4) degree of membership reaches that threshold value updates nearest cluster centre position, 5) do not handle the point if not up to threshold value and be temporarily put into pending district, 6) pending district reaches that certain standard then calculates data in hair cluster pending district with dot density weighted FCM, update cluster centre, 7) continue to circulate until that data point is all disposed, 8) with the degree of membership of the cluster centre section technique total data point obtained, and classification is divided, completing data by single pass sorts out.The present invention can reduce space complexity and time complexity in terms of extensive Handwritten Digit Recognition problem is handled.
Description
Technical field
The invention belongs to electronic information technical field, it is related to the On-line Fuzzy C averages weighted based on dot density
(Weighted-FCM) Handwritten Digit Recognition of cluster, specifically a kind of hand-written number that online FCM clusters are weighted based on dot density
Word recognition methods.
Background technology
Handwritten Digit Recognition belongs to a branch of OCR, and how it is that computer is automatic that it if mainly being studied
Identification people is handwritten in the Arabic numerals on the media such as paper.This technology is all in bank, finance and postcode self-identifying etc.
It is multi-field to have wide practical use.In addition, Handwritten Digit Recognition also has as a major issue of area of pattern recognition
Important theory value.This current technology has turned into the focus that image procossing and area of pattern recognition are studied, and handwritten numeral is known
Method for distinguishing substantially has two classes, Classification and Identification and clustering recognition, and clustering recognition is that certain is similar according to digital picture characteristic use
Property measure, feature it is same or like be classified as a class, realize clustering.Fuzzy clustering have height ambiguity and
Fault-tolerance, but still have certain limitation in actual applications, when such as clustering object quantity is more huge, often beyond computer
The ability to bear of hardware, therefore original fuzzy clustering algorithm just failed.Current method is that data sampling is clustered again mostly
Post-processing determines the classification of non-sampled data, or carries out piecemeal processing to extensive sample, and then each fritter is clustered successively
Finally obtain cluster centre.But all also there is computationally intensive, the shortcomings of space complexity is high, so as to can not tackle more massive
Data acquisition system.
The content of the invention
It is an object of the invention to overcome above-mentioned the deficiencies in the prior art, it is proposed that one kind is online based on dot density weighting
The Handwritten Digit Recognition method of FCM clusters.
The technical scheme is that：The Handwritten Digit Recognition method of online FCM clusters is weighted based on dot density, including such as
Lower step：
Step 101：Handwritten numeral picture and normalization data are pre-processed, the purpose is to convert gray images into be adapted to gather
The high dimensional data of class computing；
Step 102：Set the parameter needed for clustering algorithm：X is made to represent data acquisition system, N is the sum of data, and c is classification
Number, m is the fuzziness of FCM Algorithms, and ζ is Studying factors, and U is degree of membership, UthFor degree of membership threshold value, V (k), k=1,2,
3 ... c are c cluster centre of initialization, and i is the integer more than 0 less than or equal to N, xiI-th of data point is represented, pool is to face
When data pool, being unsatisfactory for updating the data point of cluster centre condition, to be temporarily put into pool num be pool higher limits, and w is data
Point weights, e is clustering operator iteration precision judgment value；
Step 103：Read a data point xi, the data point and the degree of membership U of the cluster centre of initialization are calculated, is judged
The maximum U of degree of membershipmaxIf, UmaxMore than Uth, 104 are gone to step, 105 are otherwise gone to step；
Step 104：Update apart from xiClosest cluster centre position, goes to step 107；
Step 105：By xiIt is put into pool, data point number adds 1 in pool, judges whether data amount check reaches in pool
Preset value num.If reaching, num goes to step 106, otherwise goes to step 107；
Step 106：The use of existing cluster centre is initial cluster center, calculates each data point weight w in poolj, use
All data points in wFCM clusters pool, update Clustering Model, obtain after new Clustering Model that data in data pool pool are clear
It is empty；
Step 107：Judge whether i is less than data total amount N, made if N is less than and 103 are gone to step after i=i+1, otherwise turn step
Rapid 108；
Step 108：The data recalled in the new pool for obtaining but not yet participating in cluster of a wFCM operators cluster are obtained
Final cluster centre, calculate degree of membership a little with existing cluster centre, determine each data point category.
Above-mentioned steps 101, comprise the following steps：
Step 201：Preprocessing image data：By each 28*28 gray level image and be set to one 784 dimension characteristic value to
Amount；
Step 202：The normalization of data, because image intensity value is the integer between 0~255, then by and the institute that postpones
Directed quantity with divided by 255, obtain scope be 0~1 normalization data；
Step 203：It is random to upset data matrix order, cause to read in the randomness of data category.
Renewal described in above-mentioned steps 104 is apart from xiClosest cluster centre position, comprises the following steps：
Step 301：Calculate range data point xiNearest cluster centre V (knear)；
Step 302：Update nearest cluster centre position, V (knear)=ζ (x (i)-V (knear))+V(knear), ζ is
Studying factors, value ζ=0.03；
Data point weight w in pool is calculated in upper step 106j, comprise the following steps：
Step 401：The Euclidean distance of data point two-by-two in pool is calculated, the adjacency matrix d of data point is obtained, calculates public
Formula:
dij=| | x (i)-x (j) | |, 1≤i≤num, 1≤j≤num；
Step 402：Dot density is calculated using adjacency matrix d
Step 403：Dot density matrix z is normalized, weight coefficient is obtained
New Clustering Model is obtained using data point in wFCM clusters pool in above-mentioned steps 106, is comprised the following steps：
Step 501：Calculate the degree of membership of each point and current cluster centre in pool；
Step 502：Update cluster centre：
Step 503：Calculate e=max1≤i≤c{||vi,new-vi,old||2Value；
Step 504：If e is more than ε, 501 are gone to step, 505 are otherwise gone to step；
Step 505：Return to current cluster centre, the new Clustering Model after as updating.
Beneficial effects of the present invention：This method reads a data point, every time every time according to existing flow data clustering method
Circulation only calculates degree of membership to a point and existing cluster centre, is decided whether to make the point direct according to the maximum of degree of membership
Participate in the renewal of Clustering Model.The present invention committed step be exactly to devise a cluster framework based on flow data, with reference to
Line k-means algorithm models update method and the FCM algorithms of dot density weighting, realize one-by-one on-line talking to enter
The Handwritten Digit Recognition of the unsupervised mode of row.Present invention, avoiding all digital image datas are handled simultaneously, dramatically reduce
Requirement during large-scale data processing to computer hardware, while compared with the wFCM algorithms of existing piecemeal, due to major part
Point directly take part in the renewal of Clustering Model, reduces the number of times for calling wFCM operators, so as to save the calculating time, reduces
The complexity of time, is more suitable for handling large-scale data.
Brief description of the drawings
Fig. 1 is the general flow chart that the present invention is realized；
Fig. 2 is data prediction flow chart；
Fig. 3 is that data point directly updates Clustering Model flow chart；
Fig. 4 is the flow chart of calculating weights process in wFCM operators；
Fig. 5 is the flow chart of the cluster centre process of iteration acquisition stabilization in wFCM operators；
Fig. 6 is the experimental result schematic diagram of the present invention.
Embodiment
The problem of present invention realizes Handwritten Digit Recognition by unsupervised clustering method, primarily directed to destination object number
It is on a grand scale, the memory headroom needed for computer can not meet the memory requirements of original algorithm, is swept one by one by online method
Retouch data and the determination of classification is completed by single pass, so as to realize the identification problem of handwritten numeral, realize that environment is
MATLAB2008b.The method for the problem of realizing fairly large Handwritten Digit Recognition by the method for Unsupervised clustering is a lot, this
Invention uses the clustering method based on dot density Weighted Fuzzy C-Means, with flow data scan mode to order incoming data point
Handled, be put into for being unsatisfactory for the data point of update condition in temporal data pool pool, implementing for pool is in journey
A dimension and data point identical matrix defined in sequence, by data point be stored in matrix, pool pile after again in pool
Data clustered, it is to avoid cluster operation is all carried out to total data, it is therefore an objective to reduce the space complexity calculated, reduced
Reunion class number of times is to reduce time complexity.
As shown in figure 1, the main flow chart step of the present invention is as follows：
Step 101：Handwritten numeral picture is pre-processed, is the high dimensional data in cluster process, every by greyscale image transitions
Data line after image corresponding conversion, is easy to follow-up clustering processing；
Step 102：Set the parameter needed for clustering algorithm：X is made to represent data acquisition system, N is the sum of data, and c is cluster
Classification number, m is the fuzziness in FCM Algorithms cluster process, and ζ is updates the Studying factors during cluster centre, and U is
Degree of membership, UthFor degree of membership threshold value, V (k), k=1,2,3 ... c are the cluster centre of initialization, and i is less than or equal to N more than 0
Integer, xiRepresent i-th each data point, pool is not by the data pool of the data of degree of membership threshold decision, num after storage is calculated
For pool higher limits, w is data point weights, and e judges precision for the iteration stopping of dot density weighted FCM；
Step 103：Read a data point xi, calculate the data point and the degree of membership of the cluster centre of each initialization
U：
Judge the maximum U of degree of membershipmaxIf, UmaxMore than Uth, 104 are gone to step, 105 are otherwise gone to step；
Step 104：The point, which is met, updates cluster centre condition, and with a certain cluster centre apart from close, the dot-dash is grouped into
The category, then updates apart from the closest cluster centre position of the point, calculation formula is：
V(knear)=ζ (x (i)-V (knear))+V(knear),
Go to step 107；
Step 105：The point is close with existing cluster centre distance, then it is assumed that the point is in current cluster centre distribution situation
Under can not determine that classification belongs to, then temporarily the point data is stored in data pool pool, data point number adds 1 in pool, judged
Whether data amount check reaches preset value num in pool.If reaching, num goes to step 106, otherwise goes to step 107；
Step 106：Calculate each data point weight w in poolj, weights size is by the dense degree of ambient data point
Determine, the more big then weights of density are bigger, the possibility that the point turns into cluster centre is bigger, substitute into weights wFCM clustering algorithms
Using existing cluster centre V (k), k=1,2,3..., c clusters all data points in pool, more as initial cluster center
New c cluster centre V (knew), data pool pool can be emptied after updating cluster centre, waits and enters but can not be true to be placed into follow-up
Determine the data point of classification ownership；
Step 107：Judge whether i is less than data total amount N, made if N is less than and 103 are gone to step after i=i+1, otherwise turn step
Rapid 108；
Step 108：Available data point in a wFCM operators cluster pool is recalled, so far all data points have been calculated
Finish, obtain final cluster centre V (k), calculate degree of membership a little with existing cluster centre, degree of membership calculation formula：
Each data point category is determined according to degree of membership size, ARI (Adjusted Rand Index) is calculated.
As shown in Fig. 2
The step 101, comprises the following steps：
Step 201：Preprocessing image data：By each 28*28 gray level image and be set to one 784 dimension characteristic value to
Amount；
Step 202：The normalization of data, because image intensity value is the integer between 0~255, then by and the institute that postpones
Directed quantity with divided by 255, obtain scope be 0~1 normalization data；
Step 203：The phenomenon that flocks together is produced when being read in order to avoid data, i.e., continuous mass data belongs to same class and made
Into cluster centre skewness, so random upset data matrix order, cause to read in the randomness of data category.
As shown in figure 3, affiliated step 104, comprises the following steps：
Step 301：Calculate range data point xiNearest cluster centre V (knear)；
Step 302：Update nearest cluster centre position, V (knear)=ζ (x (i)-V (knear))+V(knear), ζ is
Studying factors, the amplitude that this value effect cluster centre updates, having on Clustering Effect necessarily influences, it is necessary to adjust as the case may be
Section, the value is a smaller value, can typically take ζ=0.03；
As shown in figure 4, calculating data point weight w in pool in affiliated step 106j, comprise the following steps：
Step 401：The Euclidean distance of data point two-by-two in pool is calculated, the adjacency matrix d of data point, Euclidean distance is obtained
Calculation formula:
dij=| | x (i)-x (j) | |, 1≤i≤num, 1≤j≤num；
Step 402：The dot density each put in pool is calculated using adjacency matrix d, dot density matrix z, dot density is obtained
Calculation formula：
Step 403：Dot density matrix z is normalized, weight matrix, weight coefficient calculation formula is obtained：
As shown in figure 5, new Clustering Model is obtained using data point in wFCM clusters pool in affiliated step 106, including such as
Lower step：
Step 501：The degree of membership for calculating each point and current cluster centre in pool obtains subordinated-degree matrix U:
Step 502：Cluster centre is updated according to subordinated-degree matrix U:
Step 503：Calculate e=max1≤i≤c{||vi,new-vi,old||2Value；
Step 504：If e is more than ε, 501 are gone to step, 505 are otherwise gone to step；
Step 505：Return to current cluster centre, the new Clustering Model after as updating；
It is illustrated in figure 6 experimental result schematic diagram of the present invention, it can be seen that the present invention obtains preferable cluster centre, can be with
Ten class digital pictures are clearly found out from Fig. 5,0,2,5,6,4,8,7,3,9,1 is followed successively by from top to bottom from left to right.This hair
Bright experiment total degree is more than 50 times, and it is 0.3401 to calculate ARI (Adjusted Random Index) average value, and maximum is
0.4002, minimum value is 0.2813, and variance is 0.0159.
To sum up, the present invention reads a data point, circulation is only to one every time every time according to existing flow data clustering method
Point and existing cluster centre calculate degree of membership, are decided whether to make the point directly participate in Clustering Model according to the maximum of degree of membership
Renewal.It is for example existing that a data xi and each cluster centre calculating degree of membership U are read from data set, if degree of membership maximum is big
It is much bigger compared with its residual value in being worth, more than default threshold value Uth, then the point directly participate in more new model.If U maximums are not less than threshold
Value, then it is assumed that the point wouldn't belong to any one class, and the point is temporarily stored into pool, when the data points in pool reach certain
One numerical value, just carries out the Fuzzy C of dot density weighting using existing cluster centre for the initial classes center of the total data in pool
Mean cluster, the cluster centre after being updated is current Clustering Model, proceeds the processing of follow-up data.The present invention's
Committed step is exactly to devise a cluster framework based on flow data, with reference to online k-means algorithm models update method and
The FCM algorithms of dot density weighting, realize one-by-one on-line talking to carry out the Handwritten Digit Recognition of unsupervised mode,
It is more suitable for handling large-scale data acquisition system.
Present invention, avoiding all digital image datas are handled simultaneously, dramatically reduce when large-scale data is handled to meter
The requirement of calculation machine hardware, while compared with the wFCM algorithms of existing piecemeal, because most of point directly take part in Clustering Model
Renewal, reduce the number of times for calling wFCM operators, so as to save the calculating time, reduce the complexity of time, be more suitable for
Handle large-scale data.
There is no the part described in detail to belong to the known conventional means of the industry in present embodiment, do not chat one by one here
State.It is exemplified as above be only to the present invention for example, do not constitute the limitation to protection scope of the present invention, it is every with this
The same or analogous design of invention is belonged within protection scope of the present invention.
Claims (5)
1. the Handwritten Digit Recognition method of online FCM clusters is weighted based on dot density, it is characterized in that：Comprise the following steps：
Step 101：Handwritten numeral picture and normalization data are pre-processed, the purpose is to convert gray images into be adapted to cluster fortune
The high dimensional data of calculation；
Step 102：Set the parameter needed for clustering algorithm：X is made to represent data acquisition system, N is the sum of data, and c is classification number, m
For the fuzziness of FCM Algorithms, ζ is Studying factors, and U is degree of membership, UthFor degree of membership threshold value, V (k), k=1,2,3 ... c
For c cluster centre of initialization, i is the integer more than 0 less than or equal to N, xiI-th of data point is represented, pool is nonce
According to pond, being unsatisfactory for updating the data point of cluster centre condition, to be temporarily put into num in pool be pool higher limits, and w is data point power
Value, e is clustering operator iteration precision judgment value；
Step 103：Read a data point xi, the data point and the degree of membership U of the cluster centre of initialization are calculated, judges to be subordinate to
The maximum U of degreemaxIf, UmaxMore than Uth, 104 are gone to step, 105 are otherwise gone to step；
Step 104：Update apart from xiClosest cluster centre position, goes to step 107；
Step 105：By xiIt is put into pool, data point number adds 1 in pool, judges in pool whether data amount check reaches default
Value num, if reaching, num goes to step 106, otherwise goes to step 107；
Step 106：The use of existing cluster centre is initial cluster center, calculates each data point weight w in poolj, clustered with wFCM
All data points in pool, update Clustering Model, empty data in data pool pool after updating Clustering Model；
Step 107：Judge whether i is less than data total amount N, made if N is less than and 103 are gone to step after i=i+1, otherwise gone to step
108；
Step 108：The data recalled in the new pool for obtaining but not yet participating in cluster of a wFCM operators cluster obtain final
Cluster centre, calculate degree of membership a little with existing cluster centre, determine each data point category.
2. the Handwritten Digit Recognition method according to claim 1 that online FCM clusters are weighted based on dot density, its feature
It is：The step 101, comprises the following steps：
Step 201：Preprocessing image data：By each 28*28 gray level image and be set to one 784 dimension feature value vector；
Step 202：The normalization of data, due to image intensity value be 0~255 between integer, then by and postpone institute it is oriented
Amount with divided by 255, obtain scope be 0~1 normalization data；
Step 203：It is random to upset data matrix order, cause to read in the randomness of data category.
3. the Handwritten Digit Recognition method according to claim 1 that online FCM clusters are weighted based on dot density, its feature
It is：Renewal described in step 104 is apart from xiClosest cluster centre position, comprises the following steps：
Step 301：Calculate range data point xiNearest cluster centre V (knear)；
Step 302：Update nearest cluster centre position, V (knear)=ζ (x (i)-V (knear))+V(knear), ζ is study
The factor, value ζ=0.03.
4. the Handwritten Digit Recognition method according to claim 1 that online FCM clusters are weighted based on dot density, its feature
It is：Data point weight w in pool is calculated in the step 106j, comprise the following steps：
Step 401：The Euclidean distance of data point two-by-two in pool is calculated, the adjacency matrix d of data point, calculation formula is obtained:
dij=‖ x (i)-x (j) ‖, 1≤i≤num, 1≤j≤num；
Step 402：Dot density is calculated using adjacency matrix d
Step 403：Dot density matrix z is normalized, weight coefficient is obtained
。
5. the Handwritten Digit Recognition method according to claim 1 that online FCM clusters are weighted based on dot density, its feature
It is：New Clustering Model is obtained using data point in wFCM clusters pool in the step 106, is comprised the following steps：
Step 501：Calculate the degree of membership of each point and current cluster centre in pool；
Step 502：Update cluster centre：
；
Step 503：Calculate e=max1≤i≤c{‖vi,new-vi,old‖2Value；
Step 504：If e is more than ε, 501 are gone to step, 505 are otherwise gone to step；
Step 505：Return to current cluster centre, the new Clustering Model after as updating.
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| 点密度加权 FCM 算法的聚类有效性研究;刘小芳;《计算机工程与应用》;20060521(第15期);第20页第1栏第2段至第21页第2栏第5段 * |
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