JP6244681B2 - Compensation method for accumulated time series data loss - Google Patents
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Description
本発明は、積算型時系列データの欠損補償方法に係わり、電力量計のような積算型の計量機器から数値を収集する監視システム等において、通信異常やシステムの一時停止等の影響で収集している積算型時系列データに欠損が発生した場合に、その欠損データを補填する方法に関するものである。 The present invention relates to a method for compensating loss of accumulated time series data, and is collected in the monitoring system that collects numerical values from accumulated metering devices such as watt hour meters due to the influence of communication abnormality or system suspension. The present invention relates to a method for compensating for missing data when the accumulated time series data is missing.
様々な計量機器のデータを収集する監視システム等では、多くの計測データを時系列データとして蓄えるが、通信異常やシステムの一時停止等の影響で収集している時系列データに欠損が生じることがある。このような欠損データを補填する方法として前回値をそのまま使う、前後の値から線形補填を行うなどの方法があるが、欠損データが連続すると補填値が適当でなくなることから、特許文献１では別の日（特に一週間前）の同時刻データで補填する方法が記載されている。
この方法は監視システム等で計測する時系列データの多くが人の活動に関連して一日周期・一週間周期の変動パターンを持つことから比較的妥当な補填値を得られると考えられる。
In monitoring systems that collect data from various weighing devices, a large amount of measurement data is stored as time-series data. However, time-series data collected due to communication abnormalities or system suspensions may be lost. is there. As a method of compensating for such missing data, there are methods such as using the previous value as it is, or performing linear compensation from previous and subsequent values. However, if missing data continues, the compensation value becomes inappropriate. The method of supplementing with the same time data of the day (especially one week before) is described.
This method is considered to be able to obtain a relatively reasonable compensation value because most of the time-series data measured by a monitoring system or the like has a fluctuation pattern of a daily cycle or a weekly cycle related to human activities.
その他、時系列データの欠損補填方法としては特許文献２に示すように、カオス予測技術を応用して欠損補填できることの記載がある。なおカオス予測方法の一例として特許文献３で示すような局所ファジィ再構成法がある。 In addition, as a method of compensating for a deficiency in time series data, there is a description that a deficiency can be compensated by applying a chaos prediction technique, as shown in Patent Document 2. An example of the chaos prediction method is a local fuzzy reconstruction method as shown in Patent Document 3.
監視システム等で収集する時系列データの中には、電力量計のように積算量の時系列データになっているものがある。このような積算型時系列データは、計量機器の上限値まで単調に増加して上限に達するとリセットされてゼロに戻るが、このリセットは一般的に一日周期でも一週間周期でもないため、特許文献１の方法をそのまま適用することはできない。 Some time-series data collected by a monitoring system or the like is accumulated time-series data such as a watt-hour meter. Such integrated time series data increases monotonically up to the upper limit of the weighing device and resets to zero when the upper limit is reached, but this reset is generally neither a daily cycle nor a weekly cycle, The method of Patent Document 1 cannot be applied as it is.
図１０で示すように、積算型時系列データの差分を取りだして時刻ごとの値に変換し、その差分値に基づいて補填することは可能であるが、積算型時系列データ自体の補填が必要な場合もあり、そのような場合、差分値で補填しても積算型時系列データに問題が発生する可能性がある。すなわち、補填された当日の積算値で示すように、補填期間直後の積算型時系列データ値が、補填期間最後の値よりも小さくなるという積算型時系列データにはありえないはずの逆転が生じる可能性である。このような逆転データを正常値として解釈するとその期間にリセットが発生したと看做すことになり、その時刻の値が非常に大きなことになる。これは明らかに異常でありこのような補填には問題がある。 As shown in FIG. 10, it is possible to take the difference of the integrated time-series data, convert it to a value for each time, and compensate based on the difference value, but it is necessary to compensate the integrated time-series data itself In such a case, there is a possibility that a problem occurs in the integrated time-series data even if the difference value is used for compensation. In other words, as indicated by the integrated value on the day of compensation, there is a possibility of an inversion that is impossible for the integrated time series data in which the integrated time series data value immediately after the compensation period is smaller than the last value of the compensation period. It is sex. If such reverse data is interpreted as a normal value, it will be considered that a reset has occurred during that period, and the value at that time will be very large. This is clearly abnormal and there is a problem with such compensation.
また、一週間前の同時刻データを参照して補填する方法は、人の活動が一日周期・一週間周期の変動パターンを持つことから妥当ではあるが、祝日などの影響で一週間周期が乱れることがあり絶対的ではない。この補填例を、具体的な数値を用いて図１１に示す。 In addition, it is reasonable to compensate by referring to the same time data of a week ago, because human activities have a fluctuation pattern of a daily cycle or a weekly cycle, but the weekly cycle is affected by holidays and other factors. It may be disturbed and not absolute. This compensation example is shown in FIG. 11 using specific numerical values.
図１１において斜線で示した部分が補填対象日の補填対象期間とし、図１１（ａ）が一週間前の時系列データ、補填対象日の正常値が図１１（ｂ）とする。図１１（ａ）で示す補填対象日の前日に該当する一週間前の時系列データは５１８であり、補填対象日当日では５２０で一日の増分値（差分値）は２である。次の日の時系列データは５２２で差分は２、…補填対象日後の時系列データは５２５である。 In FIG. 11, the hatched portion is the compensation target period of the compensation target date, FIG. 11 (a) is the time series data one week before, and the normal value of the compensation target date is FIG. 11 (b). The time-series data one week before corresponding to the day before the compensation date shown in FIG. 11A is 518, and the daily increment value (difference value) is 520 on the compensation date. The time series data for the next day is 522, the difference is 2,... 525 is the time series data after the compensation date.
図１１（ｃ）が一週間前の時系列データに基づいて補填した場合を示したもので、同時刻の前の時間からの差分を補填対象の直前時刻からの差分と同じとして順次補填していくので、補填対象日の時系列データは、２９０、２９２，２９３，２９４と補填される。この最後の値２９４は補填期間後の値２９３より大きく逆転が起きていることが分かる。 FIG. 11 (c) shows a case where compensation is performed based on time-series data of one week before, and the difference from the time before the same time is sequentially compensated as the difference from the previous time to be compensated. Therefore, the time series data of the compensation target date is supplemented with 290, 292, 293, and 294. It can be seen that the last value 294 is larger than the value 293 after the compensation period, and the reverse occurs.
本発明が目的とするとこは、補填対象に逆転現象が生じることのない積算型時系列データの欠損補償方法を提供することにある。 An object of the present invention is to provide a method for compensating for loss of accumulated time series data in which a reverse phenomenon does not occur in a compensation target.
本発明は、積算型計測機器により計測された積算型の時系列データを監視システムに入力し、入力された時系列データに欠損が発生した時、所定期間前の参照期間前後に計測された時系列データを参照し、監視システム内の補填機能部により補填期間当日の時系列データを補填する方法において、
前記参照期間の前後に計測された時系列データから、参照期間における補填期間前後での変動値ｗを求め、
前記変動値ｗがゼロのときは、補填期間当日の補填期間直前の値を補填値とし、
前記変動値ｗが正のときは、前記参照期間直前と参照期間ｎ番目の時刻との変動値ｓに、補填期間当日の補填期間前後での変動値ｖと前記変動値ｗとの比ｖ／ｗを乗算し、該乗算値と補填期間当日の補填期間直前の値とを加算して補填値とすることを特徴としたものである。
The present invention inputs accumulated time series data measured by an integrating measuring instrument to a monitoring system, and when the input time series data is missing, when measured before and after a reference period before a predetermined period. In the method of referring to the series data and supplementing the time series data on the day of the compensation period by the compensation function unit in the monitoring system,
From the time series data measured before and after the reference period, to obtain the fluctuation value w before and after the compensation period in the reference period ,
When the fluctuation value w is zero , the value immediately before the compensation period on the day of the compensation period is taken as the compensation value,
When the fluctuation value w is positive, the fluctuation value s between the time immediately before the reference period and the nth time of the reference period is the ratio v / The multiplication value is multiplied by w and the value immediately before the compensation period of the compensation period is added to obtain a compensation value.
また、本発明は、積算型計測機器により計測された積算型の時系列データを監視システムに入力し、入力された時系列データに欠損が発生した時、所定期間前の参照期間前後に計測された時系列データを参照し、監視システム内の補填機能部により補填期間当日の時系列データを補填する方法において、
参照期間前後に計測された時系列データを決定的カオスの概念に基づき埋め込み、埋め込み空間での近傍探索による過去の類似データパターンの期間複数個を使い、局所ファジィ再構成法で補填値を作成することを特徴としたものである。
In addition, the present invention inputs integrated time-series data measured by an integrating measuring instrument to a monitoring system, and when a defect occurs in the input time-series data, it is measured before and after a reference period before a predetermined period. In the method of referring to the time-series data and supplementing the time-series data on the day of the compensation period by the compensation function unit in the monitoring system
Time series data measured before and after the reference period are embedded based on the concept of deterministic chaos, and a compensation value is created by local fuzzy reconstruction using multiple periods of past similar data patterns by neighborhood search in the embedded space. It is characterized by that.
以上のとおり、本発明によれば、補填値の上ブレを防ぎ、明らかな異常値となる補填期間後の逆転した補填が防止でき、精度のよい欠損補填が可能となるものである。 As described above, according to the present invention, it is possible to prevent the compensation value from being shaken up, to prevent the reversed compensation after the compensation period in which the abnormal value is apparent, and to perform the accurate defect compensation.
積算型時系列データの補填機能を持つ監視システムの構成例を図２に示す。
監視システム２は、積算型計測器１から定期的に計測データを取得して積算型時系列データ３にデータを追加していく。積算型時系列データ３に欠損が生じた場合は利用者の指示等により補填機能４が補填値を計算して積算型時系列データ３の欠損データを補填する。
FIG. 2 shows a configuration example of a monitoring system having an integration type time series data compensation function.
The monitoring system 2 periodically acquires measurement data from the integrating meter 1 and adds the data to the integrating time series data 3. When the accumulated time series data 3 is missing, the compensation function 4 calculates a compensation value according to a user's instruction or the like to compensate for the missing data of the accumulated time series data 3.
この構成は従来と同様で、本発明は補填機能部４での補填処理方法で、図３で示すように、一週間前の同時刻データをそのまま補填する代わりに、補填期間の直前から補填期間の直後までの変動量と一週間前の対応する時刻間の変動量との比を使い、補填期間直前から各補填時刻までの変動量と一週間前の対応する時刻間の変動量の比が先の比と一致するように補填値を補正するものである。
以下図に基づいて説明する。
This configuration is the same as the conventional one, and the present invention is a compensation processing method in the compensation function unit 4, and as shown in FIG. 3, instead of supplementing the same time data one week ago as it is, the compensation period immediately before the compensation period. Using the ratio of the amount of variation up to immediately after and the amount of variation between the corresponding times one week ago, the ratio of the amount of variation from just before the compensation period to each compensation time and the amount of variation between the corresponding times one week ago is The compensation value is corrected so as to coincide with the previous ratio.
This will be described below with reference to the drawings.
図１は、本発明の第１の実施例を示す補填処理の処理手順をフローチャートである。 FIG. 1 is a flowchart showing the processing procedure of compensation processing according to the first embodiment of the present invention.
ステップＳ１では、補填機能部４において一週間前の補填時刻前後での変動ｗと、補填時刻前後の変動ｖを計算する。ここでdataは積算型時系列データを保持する配列であり、ｔは補填期間の最初の時刻を指す配列インデックス、ｃは補填期間の時刻数、weekは一週間分の時刻数を示す。またmodは剰余計算であり、差が負であればＲを加算し、結果を０〜(Ｒ−１)の範囲にしている。Ｒは積算量がリセットされる上限値である。 In step S1, the compensation function unit 4 calculates the fluctuation w before and after the compensation time one week ago and the fluctuation v before and after the compensation time. Here, data is an array that holds accumulated time series data, t is an array index indicating the first time of the compensation period, c is the number of times in the compensation period, and week is the number of times for one week. Mod is a remainder calculation. If the difference is negative, R is added, and the result is in the range of 0 to (R-1). R is an upper limit value at which the integrated amount is reset.
次にステップＳ２，Ｓ３〜Ｓ７によりｎが０〜(ｃ−１)までの反復処理を行う。これにより補填期間の全ての補填値を計算する。反復処理の中では、まずステップＳ４により一週間前の補填時刻前後での変動ｗが正の場合とそれ以外で分岐する。ｗが正のとき、ステップＳ５で一週間前の補填時刻直前と補填期間のｎ番目時刻との変動ｓを計算する。そして、補填時刻直前の積算値に、ｓをｖ／ｗで補正した値を加算してmodにより０〜(Ｒ−１)の範囲に調整したものを補填値とする。ｗが正でないとき、ｗはゼロで一週間前の補填時刻前後で変動が全くないので、ステップＳ６で補填期間直前の値をそのまま補填値とする。 Next, iterative processing from n to 0 to (c-1) is performed in steps S2, S3 to S7. As a result, all the compensation values in the compensation period are calculated. In the iterative process, first, in step S4, the process branches depending on whether or not the fluctuation w before and after the compensation time one week ago is positive. When w is positive, in step S5, a change s between immediately before the compensation time one week ago and the nth time of the compensation period is calculated. Then, a value obtained by adding s corrected by v / w to the integrated value immediately before the compensation time and adjusting it to a range of 0 to (R-1) by mod is used as a compensation value. When w is not positive, w is zero and there is no change before and after the compensation time one week before, so the value immediately before the compensation period is used as the compensation value as it is in step S6.
具体的な値を用いた補填例を図４で示す。図４は図１１に示す従来の補填説明に対応するもので、図４（ｃ）が実施例１に基づくものである。図４において、一週間前の補填期間直前と同じ時刻から各時刻までの増分（差分）を補填期間前後の増分で調整して補填する。すなわち、図４（ｂ）で示す補填期間直前の時系列データ２８８と補填期間直後の時系列データ２９３の増分５と、一週間前の補填期間（参照期間）直前の時系列データ５１８と補填期間（参照期間）直後の時系列データ５２５の増分７との比に、補填期間の各日間の増分加算値を乗算することで各日の補填が行われ、結果としての補填値は、２８９，２９１，２９２，２９２となり、図１１（ｃ）で示す補填値より真値に近くなって逆転のない補填となる。 An example of compensation using specific values is shown in FIG. 4 corresponds to the conventional compensation explanation shown in FIG. 11, and FIG. 4C is based on the first embodiment. In FIG. 4, the increase (difference) from the same time to each time immediately before the compensation period one week ago is adjusted by the increments before and after the compensation period to compensate. That is, the increment 5 of the time series data 288 immediately before the compensation period and the time series data 293 immediately after the compensation period shown in FIG. 4B, the time series data 518 immediately before the compensation period (reference period) one week before, and the compensation period Each day's compensation is performed by multiplying the ratio of the time series data 525 immediately after (reference period) with the increment 7 by the incremental addition value for each day of the compensation period, and the resulting compensation values are 289,291. , 292 , 292, which is closer to the true value than the compensation value shown in FIG .
実施例１では一週間前の同時刻データを参照して、その値を補填期間前後の変動量の比で補正して補填したものであるが、実施例２では、参照データの補正方法は実施例１と同様だが、参照データを一週間前の同時刻データでなくカオス方式で探索した過去の類似パターンのデータとしたものである。 In the first embodiment, the same time data of one week ago is referred to, and the value is corrected by the ratio of the fluctuation amount before and after the compensation period. However, in the second embodiment, the reference data correction method is implemented. Although it is the same as that of Example 1, the reference data is not the same time data of one week ago but the data of the past similar pattern searched by the chaos method.
図５で示すように、カオス方式の探索は積算型時系列データそのままではなく、差分値により求めた時刻ごとの値データに対して行う。値データのパターンを遅れ時間座標系による埋め込み空間の点に対応付けし、埋め込み空間の距離での近傍点を近い方から指定個数だけ抽出する。図６は、この補填処理の処理手順を示すフローチャートである。 As shown in FIG. 5, the chaotic search is performed not on the integrated time-series data but on the value data for each time obtained from the difference value. The pattern of the value data is associated with the point of the embedding space by the delay time coordinate system, and a specified number of neighboring points at the distance of the embedding space are extracted. FIG. 6 is a flowchart showing the processing procedure of this compensation processing.
図６で、ステップＳ１０では、先ず差分値の遅れ時間座標系への埋め込みによる距離で近傍探索して近い方からｍ個を抽出して過去の類似パターンのデータｍ個の時系列データ内でのインデックス位置と補填対象との距離を得る。
次にステップＳ１１で類似パターンのデータそれぞれについて実施例１と同様に補填値を計算する。この計算は図１のフローチャートでｔ−weekの部分を類似パターンのインデックス位置で置き換えたものになる。
In FIG. 6, in step S10, first, a neighborhood search is performed using a distance obtained by embedding the difference value in the delay time coordinate system, m is extracted from the closest one, and the past similar pattern data m in the time series data is extracted. Get the distance between the index position and the target.
In step S11, a compensation value is calculated for each similar pattern data in the same manner as in the first embodiment. This calculation is obtained by replacing the t-week portion with the index position of the similar pattern in the flowchart of FIG.
続いてステップＳ１２で類似パターンの補填対象からの近傍距離により特許文献３で示す局所ファジィ再構成法を用いて重みを計算する。
最後にステップＳ１３で近傍ごとの補填値を局所ファジィ再構成法の重みで加重平均を取ることで最終的な補填値を得る。
Subsequently, in step S12, the weight is calculated using the local fuzzy reconstruction method shown in Patent Document 3 based on the neighborhood distance from the similar pattern to be compensated.
Finally, in step S13, a final compensation value is obtained by taking a weighted average of the compensation values for each neighborhood using the weight of the local fuzzy reconstruction method.
図７は、図６のステップ１０における類似パターンの探索例を示したものである。類似パターンの探索では、補填対象日直前の期間における各時刻の一つ前の時刻からの差分値を使用する。この差分値を直前時刻から埋め込み次元と遅れ時間で決まるパターンで抽出して埋め込みベクトルを作り、この埋め込みベクトルと過去のデータから同様に作成した埋め込みベクトルの距離を計算し、近い埋め込みベクトルからｍ個を取得する。この近い埋め込みベクトルに続く期間を過去の類似パターンとすると、続く期間も類似パターンになる。この実施例２ではこのカオス予測技術を欠損補填に応用している。 FIG. 7 shows an example of searching for similar patterns in step 10 of FIG. In the search for similar patterns, the difference value from the time immediately before each time in the period immediately before the compensation target date is used. This difference value is extracted from the previous time with a pattern determined by the embedding dimension and the delay time to create an embedding vector, and the distance between this embedding vector and the embedding vector similarly created from the past data is calculated. To get. If the period following this close embedding vector is a past similar pattern, the subsequent period also becomes a similar pattern. In the second embodiment, this chaos prediction technique is applied to defect compensation.
図７で示す数値は、埋め込み次元４８、遅れ時間１、類似パターンｍ＝１０個とした事例で、得られた類似パターンと補填対象との距離は近い方から、１５，１６，１８，…２２となっている。なお、類似パターンは何れも補填対象と同じ時間帯で、同じ曜日のものが半数を占め、２番目に近いパターンは１週間前のデータそのものである。このことは、図１１及び実施例１で使用した１週間前のデータを使用して補填する方法と同様となり、カオス補填方式による類似パターン探索が有効であることを示す。 7 is an example in which the embedding dimension is 48, the delay time is 1, and the number of similar patterns is m = 10, and the distance between the obtained similar pattern and the compensation target is 15, 16, 18,... It has become. Note that all the similar patterns are in the same time zone as the target of compensation, and the same day of the week accounts for half, and the second closest pattern is the data itself one week ago. This is the same as the method of compensation using the data of one week before used in FIG. 11 and Example 1, and shows that the similar pattern search by the chaos compensation method is effective.
また、前述のように、単に１週間まえのデータを取ると、祝日や事故などの場合にはズレが生じるが、カオス補填方式で類似パターン探索する方法では、普通でないデータは探索結果から除外されて間違った補填がしにくくなる。また、類似パターンを複数使って補填値を構成することも、間違って入った異常値の影響を軽減して補填誤差を減らす効果がある。 In addition, as described above, if the data is simply taken one week ago, a deviation occurs in the case of a holiday or an accident. However, in the method of searching for similar patterns using the chaos compensation method, unusual data is excluded from the search results. Makes it difficult to make wrong compensation. In addition, configuring a compensation value by using a plurality of similar patterns also has an effect of reducing the compensation error by reducing the influence of an abnormal value that has been entered incorrectly.
具体的な値での補填例を示したものが図４（ｄ）で、一週間前同時刻を含む複数の過去の類似パターンのデータにより、２８９，２９０，２９１，２９２となって真値に近い補填となっている。 FIG. 4 (d) shows an example of compensation with specific values, and 289 , 290, 291 and 292 are obtained as a true value based on a plurality of past similar pattern data including the same time one week ago. Close compensation.
図８，９は特許文献１等を用いた従来の手法と、本発明の実施例１と実施例２による欠損補填の誤差評価の比較結果を示したものである。実際に、５つの積算電力量計（Ａ〜Ｅ）による３０分ごと１年分の時系列データについてランダムに補填対象期間を作って補填値を比較した。積算電力量計は０〜９９９の範囲で積算され、計測間隔（３０分）の間に０〜１０程度増加する。補填対象は最初の１０日分を除く範囲で１〜２４回連続の期間をランダムに作り、その期間の補填値と真値との誤差の平均と最大を計算する。この試行を１０００回繰り返して誤差の平均と最大を集計した。その結果が図８、図９のグラフで、従来手法に比べて本発明では平均誤差・最大誤差とも大きく改善していることが分かる。また実施例２の方法は実施例１の方法と比べても改善しており、特に最大誤差の改善が大きくなっている。 FIGS. 8 and 9 show comparison results of error estimation for defect compensation according to the conventional method using Patent Document 1 and the like and Example 1 and Example 2 of the present invention. Actually, a compensation target period was randomly created for time series data for one year every 30 minutes by five integrated watt-hour meters (A to E), and the compensation values were compared. The integrated watt-hour meter is integrated in the range of 0 to 999, and increases by about 0 to 10 during the measurement interval (30 minutes). The compensation target is randomly created a period of 1 to 24 times in a range excluding the first 10 days, and the average and maximum error between the compensation value and the true value for that period are calculated. This trial was repeated 1000 times, and the average and maximum error were counted. The results are shown in the graphs of FIGS. 8 and 9, and it can be seen that both the average error and the maximum error are greatly improved in the present invention as compared with the conventional method. Further, the method of the second embodiment is improved as compared with the method of the first embodiment, and the improvement of the maximum error is particularly great.
１… 積算型計測機器
２… 監視システム
３… 積算型データ
４… 補填機能部
DESCRIPTION OF SYMBOLS 1 ... Integration type measuring device 2 ... Monitoring system 3 ... Integration type data 4 ... Compensation function part
Claims (2)
前記参照期間の前後に計測された時系列データから、参照期間における補填期間前後での変動値ｗを求め、
前記変動値ｗがゼロのときは、補填期間当日の補填期間直前の値を補填値とし、
前記変動値ｗが正のときは、前記参照期間直前と参照期間ｎ番目の時刻との変動値ｓに、補填期間当日の補填期間前後での変動値ｖと前記変動値ｗとの比ｖ／ｗを乗算し、該乗算値と補填期間当日の補填期間直前の値とを加算して補填値とすることを特徴とする積算型時系列データの欠損補償方法。 Accumulated time series data measured by an integrating measuring instrument is input to the monitoring system, and when the input time series data is lost, refer to the time series data measured before and after the reference period before the specified period. In the method of supplementing time series data on the compensation period day by the compensation function unit in the monitoring system,
From the time series data measured before and after the reference period, to obtain the fluctuation value w before and after the compensation period in the reference period ,
When the fluctuation value w is zero , the value immediately before the compensation period on the day of the compensation period is taken as the compensation value,
When the fluctuation value w is positive, the fluctuation value s between the time immediately before the reference period and the nth time of the reference period is the ratio v / A deficiency compensation method for accumulated time-series data, characterized by multiplying w and adding the multiplied value and a value immediately before the compensation period on the compensation period to obtain a compensation value.
参照期間前後に計測された時系列データを決定的カオスの概念に基づき埋め込み、埋め込み空間での近傍探索による過去の類似データパターンの期間複数個を使い、局所ファジィ再構成法で補填値を作成することを特徴とする積算型時系列データの欠損補償方法。 Accumulated time series data measured by an integrating measuring instrument is input to the monitoring system, and when the input time series data is lost, refer to the time series data measured before and after the reference period before the specified period. In the method of supplementing time series data on the compensation period day by the compensation function unit in the monitoring system,
Time series data measured before and after the reference period are embedded based on the concept of deterministic chaos, and a compensation value is created by local fuzzy reconstruction using multiple periods of past similar data patterns by neighborhood search in the embedded space. A deficiency compensation method for accumulated time series data, characterized in that:
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