Overview: SIMILARITY Procedure

The SIMILARITY procedure computes similarity measures associated with time-stamped data, time series, and/or other sequentially ordered numeric data. The procedure computes similarity measures for time-stamped transactional data (transactions) with respect to time by accumulating the data into a time series format (time series). The procedure computes similarity measures for sequentially ordered numeric data (sequences) by respecting the ordering of the data.

Given two ordered numeric sequences (input and target), a similarity measure is a metric that measures the distance between the input and target sequences while taking into account the ordering of the data. The SIMILARITY procedure computes similarity measures between an input sequence and a target sequence, as well as similarity measures that "slide" the target sequence with respect to the input sequence. The "slides" can be by observation index (sliding-sequence similarity measures) or by seasonal index (seasonal-sliding-sequence similarity measures).

In order to compare the raw input and target time-stamped data, the raw data must be accumulated to a time series format. After the input and target time series is formed, the two accumulated time series can be compared as two ordered numeric sequences.

For raw time-stamped data, after the transactional data are accumulated to form time series and any missing values are interpreted, each accumulated time series can be functionally transformed, if desired. Transformations are useful when you want to stabilize the time series before computing the similarity measures. Transformations performed by the SIMILARITY procedure include the following:

• log (LOG)

• square-root (SQRT)

• logistic (LOGISTIC)

• Box-Cox (BOXCOX)

• user-defined transformations

Each time series can be transformed further by using simple and/or seasonal differencing. Additional time series transformations can be performed by using various time series transformation and analysis techniques provided by this procedure or other procedures in SAS/ETS.

After optionally transforming each time series, the accumulated and transformed time series can be stored in an output data set (OUT= data set).

After optional accumulation and transformation, each of these time series are the "working series," which can now be analyzed as sequences of numeric data. Each of these sequences can be a target sequence, an input sequence, or both a target and an input sequence. Throughout the remainder of this chapter, the term "original sequence" applies to both the original input and target sequence. The term "working sequence" applies to a version both the original input and target sequence under investigation.

Each original sequence can be normalized prior to similarity analysis. Normalizations are useful when you want to compare the "shape" or "profile" of the time series. Normalizations performed by the SIMILARITY procedure include the following:

• standard (STANDARD)

• absolute (ABSOLUTE)

• user-defined normalizations

After each original sequence is optionally normalized as described above, each working input sequence can be scaled to the target sequence prior to similarity analysis. Scaling is useful when you want to compare the input sequence to the target sequence while discounting the variation of the target sequence. Input sequence scaling performed by the SIMILARITY procedure include the following:

• standard (STANDARD)

• sbsolute (ABSOLUTE)

• user-defined scaling

Once the working input sequence is optionally scaled to the target sequence as described above, similarity measures can be computed. Similarity measures computed by the SIMILARITY procedure include:

• squared deviation (SQRDEV)

• absolute deviation (ABSDEV)

• mean square deviation (MSQRDEV)

• mean absolute deviation (MABSDEV)

• user-defined similarity measures

In computing the similarity measure between two time series, tasks are needed for transforming time series, normalizing sequences, scaling sequences, and computing metrics or measures. The SIMILARITY procedure provides built-in routines to perform these tasks. The SIMILARITY procedure also provides a facility that allows you to extend the procedure with user-defined routines.

All results of the similarity analysis can be stored in output data sets, printed, or graphed using the Output Delivery System (ODS).

The SIMILARITY procedure can process large amounts of time-stamped transactional data, time series, or sequential data. Therefore, the analysis results are useful for large-scale time series analysis, analogous time series forecasting, new product forecasting, or time series (temporal) data mining.

In SAS/ETS, the EXPAND procedure can be used for frequency conversion and transformations of time series. The TIMESERIES procedure can be used for large-scale time series analysis. In SAS/STAT, the DISTANCE procedure can be used to compute various measures of distance, dissimilarity, or similarity between observations (rows) of a SAS data set.