CN109933579A - A kind of part k nearest neighbor missing values interpolation system and method - Google Patents
A kind of part k nearest neighbor missing values interpolation system and method Download PDFInfo
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Abstract
The present invention provides a kind of local k nearest neighbor missing values interpolation system, and judgment module is for judging fragmentary sample TiIn each missing attribute j, projection module projects data set T, and the data set T ' of the condition of satisfaction is acquired in data set T: the attribute in data set T ' is in TiIn the attribute that does not lack do not lack, in TiThe attribute j of current interpolation is not also lacked.Secondly, data computation module acquires T in T 'iK nearest neighbor TiK.Logic processing module is to fragmentary sample TiMissing attribute j analyzed, if the missing attribute j of current sample is categorical attribute, by TiKT is incorporated into the mode of the value of attribute jiMissing attribute j in；Otherwise by TiKT is incorporated into the average of the value of attribute jiMissing attribute j in.For a kind of local k nearest neighbor interpolation system provided by the invention in the case where miss rate is small, performance is slightly better than traditional k nearest neighbor interpolation；In the biggish situation of miss rate, performance outclass traditional k nearest neighbor interpolation.
Description
Technical field
The invention belongs to data analysis preprocessing technical field more particularly to a kind of local k nearest neighbor missing values interpolation system and sides
Method.
Background technique
With the development of information age, various fields have accumulated mass data, how to effectively utilize these data, have become
For current one big research hotspot.However, often will appear in practice shortage of data, noise, repetition and it is inconsistent situations such as, this is very
Affect to big degree the stabilization of data digging method.Therefore, handle and just seem particularly significant to missing data collection.It makes
It may be since data can not obtain or be missed in operation, in the feelings handled without missing values at shortage of data
Under condition, certain machine learning methods even can not be used directly.Therefore, missing values interpolation is data mining and machine learning field
In a practical and challenging problem.
K nearest neighbor interpolation (KNearest Neighbor Imputation) is a kind of base that Olga Troyanskaya is proposed
In the interpolating method of data local similarity.The basic thought of k nearest neighbor interpolation is, for the sample containing missing values, to lack
Data can refer to and its most similar K sample.Specifically, data set is divided into two set, a collection by k nearest neighbor interpolation
It closes comprising all Complete Samples (being free of the sample of missing values), another is gathered comprising all fragmentary samples (i.e.
There are the samples of missing values).For each fragmentary sample, missing values are point by the k nearest neighbor for asking it to concentrate in Complete Sample
Generic attribute, then in interpolation k nearest neighbor sample the attribute value mode；It is numerical attribute for missing values, then interpolation k nearest neighbor sample
The average of the attribute value in this.Since the missing values of fragmentary sample are acquired according to " adjacent " sample, k nearest neighbor interpolation
Method not will increase excessive new samples information.
Although k nearest neighbor interpolation is an outstanding interpolating method, the interpolation effect of k nearest neighbor interpolation dramatically by
The influence of miss rate.For k nearest neighbor interpolating method when data set miss rate is larger, the Complete Sample in data set is considerably less, this meaning
Taste, for fragmentary sample, the k nearest neighbor sample calculated in Complete Sample may not be truly at this time
" neighbour ".This will lead to the k nearest neighbor referred to when missing sample interpolation, and actually there are also a certain distance with sample itself, finally
Cause the numerical error of interpolation larger.
Therefore, it is necessary to be improved k nearest neighbor interpolation, makes it in the biggish situation of miss rate, still there is preferable interpolation
Performance.
Summary of the invention
In order to lack the k nearest neighbor referred to when sample interpolation actually the asking there are also a certain distance with sample itself at present
Topic.The present invention proposes a kind of local k nearest neighbor missing values interpolation system.
A kind of part k nearest neighbor missing values interpolation system, including input module, normalization module, judgment module, projective module
Block, data computation module and output module；
The input module is used to input the parameter K of the data set T comprising fragmentary sample and k nearest neighbor；
The normalization module is for being normalized operation to data set T；
The judgment module is used to judge the fragmentary sample T in data set TiMissing attribute, if j be current interpolation
Missing attribute；
The projection module traverses T, finds out in data set T and meet corresponding requirements for projecting to data set T
Sample set T ', wherein sample TiIn the attribute that does not lack also do not lacked in T '；Sample TiCurrent missing attribute j is in T '
It does not lack；
The data computation module is for calculating fragmentary sample TiWith each sample T ' in sample set T 'sDistance,
Fragmentary sample T is obtained according to the distance of calculatingiK nearest samples TiK；
The logic processing module is used for fragmentary sample TiMissing attribute j analyzed, if fragmentary sample Ti
Missing attribute j be categorical attribute, then by K nearest samples TiKFragmentary sample is incorporated into the mode of the value of attribute j
TiMissing attribute j in；If fragmentary sample TiMissing attribute j be numerical attribute, then by K nearest samples TiKIn attribute
The average of the value of j is incorporated into fragmentary sample TiMissing attribute j in；
The output module is used to export the data set T of interpolation completion.
Preferably, the normalization operation of the normalization module is as follows:
Wherein, TijIndicate the raw value of the i-th row j column, T 'ijNumerical value after indicating the i-th row j row normalization, Min (Tj)
Indicate the minimum value of jth column, Max (Tj) indicate the maximum value that jth arranges.
Preferably, the data computation module calculates fragmentary sample TiWith sample T ' each in T 'sDistance include with
Lower step:
Wherein, N is fragmentary sample TiThe numerical attribute number not lacked, M are fragmentary sample TiThe classification category not lacked
Property number, i (Tim, T 'sm) it is indicator function, T is worked as in expressionimWith T 'smIt is 0 when equal, is 1 when unequal.
The present invention also provides a kind of local k nearest neighbor missing values interpolating methods, comprising the following steps:
S1. the parameter K of data set T and k nearest neighbor of the input module input containing missing data；
S2. operation is normalized to the numerical attribute of data set T in normalization module；
S3. judgment module judges the fragmentary sample T in data set TiMissing attribute, if j be current interpolation missing
Attribute；
S4. projection module is projected, and is traversed T, is found out the sample set T ' for meeting corresponding requirements in T, wherein sample TiIn
The attribute not lacked does not also lack in T '；Sample TiCurrent missing attribute j is not also lacked in T '；
S5. data computation module calculates fragmentary sample TiAt a distance from each sample in sample set T '；According to step
The resulting distance value of S5 obtains K arest neighbors TiK；
S6. logic processing module is to fragmentary sample TiMissing attribute j analyzed, if fragmentary sample TiMissing
Attribute j is categorical attribute, then by K nearest samples TiKFragmentary sample T is incorporated into the mode of the value of attribute jiLack
It loses in attribute j；If fragmentary sample TiMissing attribute j be numerical attribute, then by K nearest samples TiKIn taking for attribute j
The average of value is incorporated into fragmentary sample TiMissing attribute j in；
S7. judgment module judges the complete fragmentary sample T of interpolationiIt whether is still fragmentary sample, it is no if then returning to S3
Then enter S8；
S8. judgment module judges whether data set T contains fragmentary sample, takes another fragmentary sample if then enabling and returns
S3 is returned, S9 is otherwise entered；
S9. the data set T that output module output interpolation is completed.
Preferably, the normalization operation in the S2 is as follows:
Wherein, TijIndicate the raw value of the i-th row j column, T 'ijNumerical value after indicating the i-th row j row normalization, Min (Tj)
Indicate the minimum value of jth column, Max (Tj) indicate the maximum value that jth arranges.
Preferably, in the S4 sample set T ' meet it is claimed below: sample TiIn the attribute that does not lack in T ' not yet
Missing；Sample TiCurrent missing attribute j is not also lacked in T '.
Preferably, the S5 specifically includes the following steps:
Wherein, N is sample TiThe numerical attribute number not lacked, M are sample TiThe categorical attribute number not lacked, I
(Tim, T 'sm) it is indicator function, T is worked as in expressionimWith T 'smIt is 0 when equal, is 1 when unequal.
The present invention is with local k nearest neighbor interpolation and the maximum difference of k nearest neighbor interpolation: k nearest neighbor interpolation is to endless
This interpolation of bulk sample is according to the k nearest neighbor in Complete Sample, and local k nearest neighbor interpolation is lacking of being presently processing according to sample
It loses attribute and does not lack attribute, once projected in entire data set T, then acquire and work as in the data set that projection obtains
The k nearest neighbor of preceding sample finally carries out corresponding interpolation.Compared with k nearest neighbor interpolation, local k nearest neighbor interpolation makes not exclusively
Sample can acquire k nearest neighbor in a bigger sample set, it means that the sample number that k-nearest neighbor can learn is bigger, finds
Neighbour is closer to currently processed fragmentary sample.
For especially k nearest neighbor interpolating method when data set miss rate is larger, the Complete Sample in data set is considerably less, this meaning
Taste, for fragmentary sample, the k nearest neighbor sample calculated in Complete Sample may not be truly at this time
" neighbour ".This will lead to the k nearest neighbor referred to when missing sample interpolation, and actually there are also a certain distance with sample itself, finally
Cause the numerical error of interpolation larger.And local k nearest neighbor interpolation is not rely on Complete Sample, as miss rate increases, throws
The reference data set that shadow obtains significant can't be reduced.Therefore, compared to k nearest neighbor interpolation, local k nearest neighbor interpolation exists
Performance is more preferably in the larger situation of miss rate.
Compared with prior art, the beneficial effect of technical solution of the present invention is:
For local k nearest neighbor interpolation in the case where miss rate is small, performance is slightly better than traditional k nearest neighbor interpolation；In miss rate
In biggish situation, performance outclass traditional k nearest neighbor interpolation.
Detailed description of the invention
Fig. 1 is a kind of overall flow figure of local k nearest neighbor missing values interpolating method provided by the invention.
Fig. 2 is local k nearest neighbor interpolation and k nearest neighbor interpolation, multiple interpolation, in Breast CancerCoimbra number
Compare figure according to the filling capacity collected under upper different miss rates.
Fig. 3 is local k nearest neighbor interpolation and k nearest neighbor interpolation, multiple interpolation, the difference on Parkinsons data set
Filling capacity under miss rate compares figure.
Wherein, LKNNI is local k nearest neighbor interpolation, and KNNI is k nearest neighbor interpolation, and MI is multiple interpolation.
Specific embodiment
Following will be combined with the drawings in the embodiments of the present invention, and technical solution in the embodiment of the present invention carries out clear, complete
Site preparation description, it is clear that described embodiment is only a unit embodiment of the invention, only for illustration, Bu Nengli
Solution is the limitation to this patent.Based on the embodiments of the present invention, those of ordinary skill in the art are not making creative labor
Every other embodiment obtained under the premise of dynamic, shall fall within the protection scope of the present invention.
The following further describes the technical solution of the present invention with reference to the accompanying drawings and examples.
Embodiment 1
The present embodiment provides a kind of local k nearest neighbor missing values interpolation systems, including input module, normalization module, judgement
Module, projection module, data computation module and output module；
The input module is used to input the parameter K of the data set T comprising fragmentary sample and k nearest neighbor；
The normalization module is for being normalized operation to data set T；
The judgment module is used to judge the fragmentary sample T in data set TiMissing attribute, if j be current interpolation
Missing attribute；
The projection module traverses T, finds out the sample set for meeting corresponding requirements in T for projecting to data set T
T ', wherein sample TiIn the attribute that does not lack also do not lacked in T '；Sample TiCurrent missing attribute j is not also lacked in T '；
The data computation module is for calculating fragmentary sample TiWith each sample T ' in sample set T 'sDistance,
Fragmentary sample T is obtained according to the distance of calculatingiK nearest samples TiK；
The logic processing module is used for fragmentary sample TiMissing attribute j analyzed, if fragmentary sample Ti
Missing attribute j be categorical attribute, then by K nearest samples TiKFragmentary sample is incorporated into the mode of the value of attribute j
TiMissing attribute j in；If fragmentary sample TiMissing attribute j be numerical attribute, then by K nearest samples TiKIn attribute
The average of the value of j is incorporated into fragmentary sample TiMissing attribute j in；
The output module is used to export the data set T of interpolation completion.
In the present embodiment, the normalization operation of the normalization module is as follows:
Wherein, TijIndicate the raw value of the i-th row j column, T 'ijNumerical value after indicating the i-th row j row normalization, Min (Tj)
Indicate the minimum value of jth column, Max (Tj) indicate the maximum value that jth arranges.
In the present embodiment, the data computation module calculates fragmentary sample TiWith sample T ' each in T 'sDistance
The following steps are included:
Wherein, N is fragmentary sample TiThe numerical attribute number not lacked, M are fragmentary sample TiThe classification category not lacked
Property number, I (Tim, T 'sm) it is indicator function, T is worked as in expressionimWith T 'smIt is 0 when equal, is 1 when unequal.
Embodiment 2
The present embodiment provides a kind of local k nearest neighbor missing values interpolating methods, as shown in Figure 1, comprising the following steps:
S1. the parameter K of data set T and k nearest neighbor of the input module input containing missing data；
S2. operation is normalized to the numerical attribute of data set T in normalization module；
S3. judgment module judges the fragmentary sample T in data set TiMissing attribute, if j be current interpolation missing
Attribute；
S4. projection module is projected, and is traversed T, is found out the sample set T ' for meeting corresponding requirements in T
S5. data computation module calculates fragmentary sample TiAt a distance from each sample in sample set T '；According to step
The resulting distance value of S5 obtains K arest neighbors TiK；
S6. logic processing module is to fragmentary sample TiMissing attribute j analyzed, if fragmentary sample TiMissing
Attribute j is categorical attribute, then by K nearest samples TiKFragmentary sample T is incorporated into the mode of the value of attribute jiLack
It loses in attribute j；If fragmentary sample TiMissing attribute j be numerical attribute, then by K nearest samples TiKIn taking for attribute j
The average of value is incorporated into fragmentary sample TiMissing attribute j in；
S7. judgment module judges the complete fragmentary sample T of interpolationiIt whether is still fragmentary sample, it is no if then returning to S3
Then enter S8；
S8. judgment module judges whether data set T contains fragmentary sample, takes another fragmentary sample if then enabling and returns
S3 is returned, S9 is otherwise entered；
S9. the data set T that output module output interpolation is completed.
In the present embodiment, the normalization operation in the S2 is as follows:
Wherein, TijIndicate the raw value of the i-th row j column, T 'ijNumerical value after indicating the i-th row j row normalization, Min (Tj)
Indicate the minimum value of jth column, Max (Tj) indicate the maximum value that jth arranges.
In the present embodiment, in the S4 sample set T ' meet it is claimed below: sample TiIn the attribute that does not lack in T '
In also do not lack；Sample TiCurrent missing attribute j is not also lacked in T '.
In the present embodiment, the S5 specifically includes the following steps:
Wherein, N is sample TiThe numerical attribute number not lacked, M are sample TiThe categorical attribute number not lacked, I
(Tim, T 'sm) it is indicator function, T is worked as in expressionimWith T 'smIt is 0 when equal, is 1 when unequal.
Embodiment 3
The present embodiment is consistent with 1 content of embodiment, and a kind of local k nearest neighbor missing values interpolating method provided in this embodiment is
The performance of accurate evaluation fill method on different data sets, when calculating Measure Indexes, to all numerical attributes into
Row normalized.In balancing method performance, the filling effect of numerical attribute is indicated with mean square error；Categorical attribute then uses
Accuracy indicates.Calculation is as follows:
Wherein, L is the numerical attribute values number always lacked, TlIt is first of raw value data to be filled, T 'lIt is l
A numeric data filled.
Embodiment 4
The present embodiment, in order to measure the similarity between Filling power and actual numerical value, using on UCI
BreastCancerCoimbra and Parkinsons data set, the two is all complete data set.Utilize the method mould of random erasure
Quasi- multivariable missing at random, compares Filling power and original property value again after Missing Data Filling.
The present embodiment by local k nearest neighbor interpolation, with k nearest neighbor interpolation, multiple interpolation,
Carry out interpolation performance on BreastCancerCoimbra and Parkinsons data set under different miss rates compares.In order to protect
Result credibility is tested in confirmation, reduces simulation missing bring error, sample of this experiment to identical interpolating method and identical miss rate
This progress 30 times experiments, use the average value of Measure Indexes as experimental result, as Figure 2-3.
Obviously, the above embodiment of the present invention be only to clearly illustrate example of the present invention, and not be pair
The restriction of embodiments of the present invention.For those of ordinary skill in the art, may be used also on the basis of the above description
To make other variations or changes in different ways.There is no necessity and possibility to exhaust all the enbodiments.It is all this
Made any modifications, equivalent replacements, and improvements etc., should be included in the claims in the present invention within the spirit and principle of invention
Protection scope within.
Claims (7)
1. a kind of part k nearest neighbor missing values interpolation system, which is characterized in that including input module, normalization module, judge mould
Block, projection module, data computation module and output module；
The input module is used to input the parameter K of the data set T comprising fragmentary sample and k nearest neighbor；
The normalization module is for being normalized operation to data set T；
The judgment module is used to judge the fragmentary sample T in data set TiMissing attribute, if j be current interpolation lack
Lose attribute；
For the projection module for projecting to data set T, traversal T finds out the sample set T ' for meeting corresponding requirements in T,
Wherein sample TiIn the attribute that does not lack also do not lacked in T '；Sample TiCurrent missing attribute j is not also lacked in T '；
The data computation module is for calculating fragmentary sample TiWith each sample T ' in sample set T 'sDistance, according to
The distance of calculating obtains fragmentary sample TiK nearest samples TiK；
The logic processing module is used for fragmentary sample TiMissing attribute j analyzed, if fragmentary sample TiLack
Losing attribute j is categorical attribute, then by K nearest samples TiKFragmentary sample T is incorporated into the mode of the value of attribute ji's
It lacks in attribute j；If fragmentary sample TiMissing attribute j be numerical attribute, then by K nearest samples TiKAttribute j's
The average of value is incorporated into fragmentary sample TiMissing attribute j in；
The output module is used to export the data set T of interpolation completion.
2. a kind of local k nearest neighbor missing values interpolation system according to claim 1, which is characterized in that the normalization
The normalization operation of module is as follows:
Wherein, TijIndicate the raw value of the i-th row j column, T 'ijNumerical value after indicating the i-th row j row normalization, Min (T·j) indicate
The minimum value of jth column, Max (T·j) indicate the maximum value that jth arranges.
3. a kind of local k nearest neighbor missing values interpolation system according to claim 1, which is characterized in that the data meter
It calculates module and calculates fragmentary sample TiWith sample T ' each in T 'sDistance the following steps are included:
Wherein, N is fragmentary sample TiThe numerical attribute number not lacked, M are fragmentary sample TiThe categorical attribute not lacked
Number, I (Tim, T 'sm) it is indicator function, T is worked as in expressionimWith T 'smIt is 0 when equal, is 1 when unequal.
4. a kind of part k nearest neighbor missing values interpolating method, which comprises the following steps:
S1. the parameter K of data set T and k nearest neighbor of the input module input containing missing data；
S2. operation is normalized to the numerical attribute of data set T in normalization module；
S3. judgment module judges the fragmentary sample T in data set TiMissing attribute, if j be current interpolation missing attribute；
S4. projection module is projected, and is traversed T, is found out the sample set T ' for meeting corresponding requirements in T
S5. data computation module calculates fragmentary sample TiAt a distance from each sample in sample set T '；According to obtained by step S5
Distance value obtain K arest neighbors TiK；
S6. logic processing module is to fragmentary sample TiMissing attribute j analyzed, if fragmentary sample TiMissing attribute j
It is categorical attribute, then by K nearest samples TiKFragmentary sample T is incorporated into the mode of the value of attribute jiMissing attribute
In j；If fragmentary sample TiMissing attribute j be numerical attribute, then by K nearest samples TiKAttribute j value it is flat
Mean is incorporated into fragmentary sample TiMissing attribute j in；
S7. judgment module judges the complete fragmentary sample T of interpolationiWhether still be fragmentary sample, if then returning to S3, otherwise into
Enter S8；
S8. judgment module judges whether data set T contains fragmentary sample, takes another fragmentary sample if then enabling and returns
Otherwise S3 enters S9；
S9. the data set T that output module output interpolation is completed.
5. a kind of local k nearest neighbor missing values interpolating method according to claim 4, which is characterized in that in the S2
Normalization operation is as follows:
Wherein, TijIndicate the raw value of the i-th row j column, T 'ijNumerical value after indicating the i-th row j row normalization, Min (T·j) indicate
The minimum value of jth column, Max (T·j) indicate the maximum value that jth arranges.
6. a kind of local k nearest neighbor missing values interpolating method as claimed in claim 4, which is characterized in that sample in the S4
Collection T ' meets claimed below: sample TiIn the attribute that does not lack also do not lacked in T '；Sample TiCurrent missing attribute j is in T '
In also do not lack.
7. a kind of local k nearest neighbor missing values interpolating method according to claim 4, which is characterized in that the S5 is specific
The following steps are included:
Wherein, N is sample TiThe numerical attribute number not lacked, M are sample TiThe categorical attribute number not lacked, I (Tim, T
′sm) it is indicator function, T is worked as in expressionimWith T 'smIt is 0 when equal, is 1 when unequal.
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