Data Applied:Tree Maps
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Treemaps are a visualization technique that displays hierarchical data as a set of nested rectangles. Each branch of the tree is represented by a rectangle, with smaller rectangles representing sub-branches. Leaf nodes are sized proportionally and colored to show additional data dimensions. Standard treemaps can result in thin, elongated rectangles. Squarified treemaps aim to reduce the aspect ratio and "squarify" the rectangles for a more efficient use of space and easier comparisons. The Data-Applied API supports executing treemaps using the RootTreeMapTaskInfo entity and a sequence of messages.
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This document introduces Matlab and how it can be used for computer vision and image processing tasks. Matlab is a useful language for these applications because images can be represented as matrices and many vision algorithms are naturally implemented using matrix operations in Matlab. The document provides examples of reading image files in common formats like PGM and PPM, and demonstrates basic Matlab operations for creating, accessing, and manipulating image matrices.
M tree
The document proposes an extension to the M-tree family of index structures called M*-tree. M*-tree improves upon M-tree by maintaining a nearest-neighbor graph within each node. The nearest-neighbor graph stores, for each entry in a node, a reference and distance to its nearest neighbor among the other entries in that node. This additional structure allows for more efficient filtering of non-relevant subtrees during search queries through the use of "sacrifice pivots". The experiments showed that M*-tree can perform searches significantly faster than M-tree while keeping construction costs low.
Pandas,scipy,numpy cheatsheet
ref: https://s3.amazonaws.com/quandl-static-content/Documents/Quandl+-+Pandas,+SciPy,+NumPy+Cheat+Sheet.pdf
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This document discusses algorithms that can be implemented using MapReduce, including sorting, searching, TF-IDF, breadth-first search, PageRank, and more advanced algorithms. It provides details on how sorting, searching, TF-IDF, breadth-first search, and PageRank algorithms work in MapReduce, including explaining the map and reduce phases. It also discusses graph representations that can be used for algorithms like breadth-first search and PageRank and how the algorithms are distributed across parallel tasks in MapReduce.
statistical computation using R- an intro..
This presentation deals with some basics of R language. It is very useful for benners in R. It describes the basics in a very easy manner, so those who are not familiar with R it would be very helpful.
Raster data analysis
Raster data is represented by a grid of cells, where each cell contains numeric or qualitative values. Raster data comes from sources like images, maps, and satellite imagery. Common analyses of raster data include buffering, reclassification, hillshades, interpolation, and surface calculation. Buffering assigns "in" and "out" values to cells based on their distance from a feature. Reclassification reassigns cell values. Hillshades create shaded relief maps from elevation data. Interpolation estimates values between known data points. Surface calculation performs cell-by-cell mathematical functions on rasters.
Chart and graphs in R programming language
This slide contains basics of charts and graphs in R programming language. I also focused on practical knowledge so I tried to give maximum example to understand the concepts.
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Svm Presentation
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Data Manipulation with Numpy and Pandas in PythonStarting with N
Data Manipulation with Numpy and Pandas in Python
Starting with Numpy
#load the library and check its version, just to make sure we aren't using an older version
import numpy as np
np.__version__
'1.12.1'
#create a list comprising numbers from 0 to 9
L = list(range(10))
#converting integers to string - this style of handling lists is known as list comprehension.
#List comprehension offers a versatile way to handle list manipulations tasks easily. We'll learn about them in future tutorials. Here's an example.
[str(c) for c in L]
['0', '1', '2', '3', '4', '5', '6', '7', '8', '9']
[type(item) for item in L]
[int, int, int, int, int, int, int, int, int, int]
Creating Arrays
Numpy arrays are homogeneous in nature, i.e., they comprise one data type (integer, float, double, etc.) unlike lists.
#creating arrays
np.zeros(10, dtype='int')
array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0])
#creating a 3 row x 5 column matrix
np.ones((3,5), dtype=float)
array([[ 1., 1., 1., 1., 1.],
[ 1., 1., 1., 1., 1.],
[ 1., 1., 1., 1., 1.]])
#creating a matrix with a predefined value
np.full((3,5),1.23)
array([[ 1.23, 1.23, 1.23, 1.23, 1.23],
[ 1.23, 1.23, 1.23, 1.23, 1.23],
[ 1.23, 1.23, 1.23, 1.23, 1.23]])
#create an array with a set sequence
np.arange(0, 20, 2)
array([0, 2, 4, 6, 8,10,12,14,16,18])
#create an array of even space between the given range of values
np.linspace(0, 1, 5)
array([ 0., 0.25, 0.5 , 0.75, 1.])
#create a 3x3 array with mean 0 and standard deviation 1 in a given dimension
np.random.normal(0, 1, (3,3))
array([[ 0.72432142, -0.90024075, 0.27363808],
[ 0.88426129, 1.45096856, -1.03547109],
[-0.42930994, -1.02284441, -1.59753603]])
#create an identity matrix
np.eye(3)
array([[ 1., 0., 0.],
[ 0., 1., 0.],
[ 0., 0., 1.]])
#set a random seed
np.random.seed(0)
x1 = np.random.randint(10, size=6) #one dimension
x2 = np.random.randint(10, size=(3,4)) #two dimension
x3 = np.random.randint(10, size=(3,4,5)) #three dimension
print("x3 ndim:", x3.ndim)
print("x3 shape:", x3.shape)
print("x3 size: ", x3.size)
('x3 ndim:', 3)
('x3 shape:', (3, 4, 5))
('x3 size: ', 60)
Array Indexing
The important thing to remember is that indexing in python starts at zero.
x1 = np.array([4, 3, 4, 4, 8, 4])
x1
array([4, 3, 4, 4, 8, 4])
#assess value to index zero
x1[0]
4
#assess fifth value
x1[4]
8
#get the last value
x1[-1]
4
#get the second last value
x1[-2]
8
#in a multidimensional array, we need to specify row and column index
x2
array([[3, 7, 5, 5],
[0, 1, 5, 9],
[3, 0, 5, 0]])
#1st row and 2nd column value
x2[2,3]
0
#3rd row and last value from the 3rd column
x2[2,-1]
0
#replace value at 0,0 index
x2[0,0] = 12
x2
array([[12, 7, 5, 5],
[ 0, 1, 5, 9],
[ 3, 0, 5, 0]])
Array Slicing
Now, we'll learn to access multiple or a range of elements from an array.
x = np.arange(10)
x
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
#from start to 4th position
x[: ...
Optimizing spatial database
The document discusses optimizing spatial databases by using spatial indexes like R-trees and quadtrees. It provides an overview of different spatial indexing structures including R-trees, quadtrees, grid indexes and others. It also compares R-trees and quadtrees, and provides examples of implementing spatial indexes in Oracle Spatial.
Clique and sting
CLIQUE is an algorithm for subspace clustering of high-dimensional data. It works in two steps: (1) It partitions each dimension of the data space into intervals of equal length to form a grid, (2) It identifies dense units within this grid and finds clusters as maximal sets of connected dense units. CLIQUE efficiently discovers clusters by identifying dense units in subspaces and intersecting them to obtain candidate dense units in higher dimensions. It automatically determines relevant subspaces for clustering and scales well with large, high-dimensional datasets.
Pandas.pptx
Introduction to pandas, Library Architecture, Features, Applications, Data Structures: Series, DataFrame, Index Objects, Essential Functionality, Reindexing, Dropping Entries (from an axis, Indexing, selection, and filtering), Sorting, Ranking, Summarizing and Computing Descriptive Statistics, Unique Values, Value Counts, Handling Missing Data, Filtering out missing data.
pandas-221217084954-937bb582.pdf
Pandas is an open-source Python library that provides high-performance data manipulation and analysis tools using powerful data structures like DataFrame. It allows users to load, prepare, manipulate, model, and analyze data regardless of its source through these five typical steps of data processing. Pandas contains data structures like Series and DataFrame, and methods for data loading, merging, sorting, filtering and handling missing data.
MODULE III.pptx
This document provides an overview of simple graphics using Turtle and image processing concepts. It discusses Turtle graphics, which were developed for the Logo programming language. A Turtle has attributes like position and heading that define its state. Methods can modify these attributes to draw shapes. The document also covers basic image processing concepts like analog vs. digital images, sampling, file formats, compression techniques, and common operations like filtering and resizing.
2.4 Scatterplots, correlation, and regression
This document discusses scatterplots, correlation, and regression. It defines key terms like scatterplot, correlation, linear correlation, and regression line. Examples are provided to illustrate scatterplots and whether they show correlation between two variables. The linear correlation coefficient r is introduced as a measure of the strength of linear correlation between -1 and 1. Interpreting the p-value is also discussed, with a small p-value providing evidence of a linear correlation. Regression finds the straight line that best fits a set of paired sample data.
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- 1. 5 Data-Applied.com: Tree Maps
- 2. 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
- 3. Standard Treemaps The standard Treemaps algorithm just did the transition from hierarchical data to its representation in the rectangular form An example:
- 4. 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.
- 5. 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
- 6. 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
- 7. 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”
- 8. 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
- 9. 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:
- 10. Squarification in practice With squarification:
- 11. 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
- 12. Using the DA-API to execute treemaps
- 13. 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
- 14. Message sequence The steps are:
- 15. Treemaps using Data Applied’s web interface
- 16. Step1: Selection of data
- 17. Step2: Selecting Tree Maps
- 18. Step3: Result
- 20. The tutorials section is free, self-guiding and will not involve any additional support.
- 21. Visit us at www.dataminingtools.net