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. Similarity measures computed by the SIMILARITY procedure include: Input sequence scaling performed by the SIMILARITY procedure include the following:Īfter the working input sequence is optionally scaled to the target sequence, similarity measures can be computed. Scaling is useful when you want to compare the input sequence to the target sequence while discounting the variation of the target sequence. Normalizations performed by the SIMILARITY procedure include the following:Īfter each original sequence is optionally normalized, each working input sequence can be scaled to the target sequence prior to similarity analysis. Normalizations are useful when you want to compare the "shape" or "profile" of the time series. The term "working sequence" applies to a version of both the original input and target sequence under investigation.Įach original sequence can be normalized prior to similarity analysis. Throughout the remainder of this chapter, the term "original sequence" applies to both the original input and target sequence. Each of these sequences can be a target sequence, an input sequence, or both a target and an input sequence.
SAS SIMILARITY SERIES
Additional time series transformations can be performed by using various time series transformation and analysis techniques provided by this procedure or other SAS/ETS procedures.Īfter optionally transforming each time series, the accumulated and transformed time series can be stored in an output data set (OUT= data set).Īfter optional accumulation and transformation, each of these time series are the "working series," which can now be analyzed as sequences of numeric data. Transformations performed by the SIMILARITY procedure include the following:Įach time series can be transformed further by using simple differencing or seasonal differencing or both. Transformations are useful when you want to stabilize the time series before computing the similarity measures. After the input and target time series are formed, the two accumulated time series can be compared as two ordered numeric sequences.įor 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. In order to compare the raw input and the raw target time-stamped data, the raw data must be accumulated to a time series format. The "slides" can be by observation index (sliding-sequence similarity measures) or by seasonal index (seasonal-sliding-sequence similarity measures). The SIMILARITY procedure computes similarity measures between an input sequence and a target sequence, in addition to similarity measures that "slide" the target sequence with respect to the input sequence. 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. PROC SIMILARITY computes similarity measures for time-stamped transactional data (transactions) with respect to time by accumulating the data into a time series format, and it computes similarity measures for sequentially ordered numeric data (sequences) by respecting the ordering of the data.
⚡Tip:\(P\) and \(Q\) are the midpoints of \(BC\) and \(EF\).The SIMILARITY procedure computes similarity measures associated with time-stamped data, time series, and other sequentially ordered numeric data. \(AP\) and \(DQ\) are medians in the two triangles respectively. \Ĭhallenge 2:Consider two similar triangles, \(\Delta ABC\) and \(\Delta DEF\): If the equal angle is a non-included angle, then the two triangles may not be similar. The SAS similarity criterion states that If two sides of one triangle are respectively proportional to two corresponding sides of another, and if the included angles are equal, then the two triangles are similar. What's the difference between the two criteria? Think: SAS is a similarity criterion as well as a congruency criterion. However, in order to be sure that two triangles are similar, we do not necessarily need to have information about all sides and all angles.
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