Multiple Timeseries
======================

    A timeseries represents an ordered collection of values of an event (or item) over time. A multiple timeseries represents the collection of multiple timeseries gathered from multiple items over a particular duration. Depending on the values stored in a series, a multiple timeseries can be broadly classified into two types:

    - Binary multiple timeseries and

    - (non-binary) multiple timeseries .

    Binary Multiple Timeseries

        A binary multiple time series represents the binary data of multiple items split into temporal windows. An example of this series is shown below.

        +-----------+-------------------------------------+
        | windowID  | 	binary sequences                  |
        +===========+=====================================+
        | 1 	    | (a,1) (a,3) (b,2) (b,3) (c,2) (c,3) |
        +-----------+-------------------------------------+
        | 2 	    | (a,1) (b,1) (b,2) (b,3) (c,1)       |
        +-----------+-------------------------------------+
        | 3 	    | (a,1) (a,2) (b,1) (b,3) (c,2)       |
        +-----------+-------------------------------------+
        | 4 	    | (a,1) (b,1) (b,2) (c,3)             |
        +-----------+-------------------------------------+
        | 5 	    | (a,1) (a,3) (b,3) (c,2) (c,2)       |
        +-----------+-------------------------------------+
        | 6 	    | (a,1) (a,2) (b,2) (b,3)             |
        +-----------+-------------------------------------+

    Rules to create a binary multiple time series.

        - First column must contain an integer representing an windowID.

        - Remaining columns must contain items and their timestamps within braces.

        - In the braces, starting from left hand side, the first word/letter represents an item and the other word/letter represents an timestamp.

        - Columns are seperated with a seperator.

        - ‘ Tab space ’ is the default seperator. However, transactional databases can be constructed using other seperators, such as comma and space.

    Format of a binary multiple time series:

        >>>  windowID<sep>(item,timestamp)<sep>(item,timestamp)<sep>...<sep>(item, timestamp)

An example

        +-----+---------------------------------------+
        | 1   | (a,1) (a,3) (b,2) (b,3) (c,2) (c,3)   |
        +=====+=======================================+
        | 2   | (a,1) (b,1) (b,2) (b,3) (c,1)         |
        +-----+---------------------------------------+
        | 3   | (a,1) (a,2) (b,1) (b,3) (c,2)         |
        +-----+---------------------------------------+
        | 4   | (a,1) (b,1) (b,2) (c,3)               |
        +-----+---------------------------------------+
        | 5   | (a,1) (a,3) (b,3) (c,2) (c,2)         |
        +-----+---------------------------------------+
        | 6   | (a,1) (a,2) (b,2) (b,3)               |
        +-----+---------------------------------------+




.. toctree::
   :maxdepth: 1

   MultiplePartialPeriodicPatternMining1