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Data Applied:Tree Maps
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Data Applied:Tree Maps

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Data Applied:Tree Maps

Data Applied:Tree Maps

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    Data Applied:Tree Maps Data Applied:Tree Maps Presentation Transcript

    • 5
      Data-Applied.com: Tree Maps
    • What are Treemaps?
      Treemaps display hierarchical (tree-structured) data as a set of nested rectangles
      Each branch of the tree is given a rectangle, which is then tiled with smaller rectangles representing sub-branches
       A leaf node's rectangle has an area proportional to a specified dimension on the data
      The leaf nodes are colored to show a separate dimension of the data
    • Standard Treemaps
      The standard Treemaps algorithm just did the transition from hierarchical data to its representation in the rectangular form
      An example:
    • Standard Treemaps pseudo code
      The tree-map algorithm assumes a tree structure in which each node contains a record with its directory or file name (name), the number of children (num_children), and an array of pointers to the next level (child [1..num_children]). The arguments to the tree-map algorithm are:
      root : a pointer to the root of the tree or subtree
      P, Q : arrays of length 2 with (x,y) coordinate pairs of opposite corners of the current rectangle (assume that Q contains the higher coordinates and P the lower coordinates, but this does not affect the correctness of the algorithm, only the order in which rectangles are drawn)
      axis : varies between 0 and 1 to indicate cuts to be made vertically and horizontally
      color: indicates the color to be used for the current rectangle.
    • Standard Treemaps pseudo code
      In addition we need:
      Paint_rectangle : a procedure that paints within the rectangle using a given color, and resets the color variable.
      Size : a function that returns the number of bytes in the node pointed to by the argument. Alternatively, the size could be pre-computed and stored in each node.
      The initial call is:
      Treemap(root, P, Q, 0, color)
      Where P and Q are the upper right and lower left corners of the display. By setting the axis argument to zero the initial partitions are made vertically. It is assumed that arguments P and Q are passed by value (since P, Q are modified within
    • Standard Treemaps pseudo code
      Treemap(root, P[0..1], Q[0..1], axis, color)
      Paint_rectangle(P, Q, color) -- paint full area
      width := Q[axis] - P[axis] -- compute location of next slice
      for i := 1 to num_children do
      Q[axis] := P[axis] + (Size(child[i])/Size(root))*width
      Treemap(child[i], P, Q, 1 - axis, color) -- recur on each slice, flipping axes
      P[axis] := Q[axis];
      endfor 
    • Problem with standard Treemaps
      Treemaps often fall short to visualize the structure of the tree
      Thin, elongated rectangles emerge as a result of the srtaight forward subdivision technique of standard treemaps
      The second problem can be solved by using a modified version of standard treemaps algorithm called: “SquarifiedTreemaps”
    • SquarifiedTreemaps
      Instead of rectangles, in this algorithm we try do reduce the aspect ratio as much as possible and hence squarifytreemaps. Reason being:
      Display space is used more efficiently. The number of pixels to be used for the border is proportional to its circumference. For rectangles this number is minimal if a square is used
      Square items are easier to detect and point at
      Comparison of the size of rectangles is easier when their aspect ratios are similar
    • Squarification in practice
      We initially start with a 6x4 rectangle and add areas 6,6,4,3,2,2,1 to it. At each addition we make sure we have the maximum aspect ratio
      By standard treemaps algorithm:
    • Squarification in practice
      With squarification:
    • Final layer to treemaps
      The squares can be colored to represent an extra dimensions
      The area/size can be represented using any parameter as per the requirement
    • Using the DA-API to execute treemaps
    • Using the DA-API to execute treemaps
      Again to use the API we just need to figure out the correct entity and the message type
      Looking at the specification the entity is RootTreeMapTaskInfo
      The task will be completed in a sequence of multiple messages, as specified on the website
      As the task is used for data visualization so it does not produce any type of result
    • Message sequence
      The steps are:
    • Treemaps using Data Applied’s web interface
    • Step1: Selection of data
    • Step2: Selecting Tree Maps
    • Step3: Result
    • Visit more self help tutorials
      • Pick a tutorial of your choice and browse through it at your own pace.
      • The tutorials section is free, self-guiding and will not involve any additional support.
      • Visit us at www.dataminingtools.net