Exploring Data

Exploring DataA preliminary exploration of the data to better understand its characteristicsKey motivations of data exploration includeHelping to select the right tool for preprocessing or analysisMaking use of humans’ abilities to recognize pattern People can recognize patterns not captured by data analysistools Related to the area of Exploratory Data Analysis (EDA)Created by statistician John Tukey

Contd…In EDA, as originally defined by TukeyThe focus was on visualizationClustering and anomaly detection were viewed as exploratory techniquesIn data mining, clustering and anomaly detection are major areas of interest, and not thought of as just exploratoryIn our discussion of data exploration, we focus onSummary statisticsVisualizationOnline Analytical Processing (OLAP)

Iris Sample Data Set Many of the exploratory data techniques are illustrated with the Iris Plant data set.Three flower types (classes):SetosaVirginicaVersicolourFour (non-class) attributes Sepal width and length Petal width and length

Summary StatisticsSummary statistics are numbers that summarize properties of the dataSummarized properties include frequency, location and spread Examples: location - mean spread - standard deviation

Frequency and ModeThe frequency of an attribute value is the percentage of time the value occurs in the data set For example, given the attribute ‘gender’ and a representative population of people, the gender ‘female’ occurs about 50% of the time.The mode of a an attribute is the most frequent attribute value The notions of frequency and mode are typically used with categorical data

PercentilesFor continuous data, the notion of a percentile is more useful. Given an ordinal or continuous attribute x and a number p between 0 and 100, the pth percentile is a value of x such that p% of the observed values of x are less than . For instance, the 50th percentile is the value such that 50% of all values of x are less than

Measures of Location: Mean and MedianThe mean is the most common measure of the location of a set of points. However, the mean is very sensitive to outliers. Thus, the median or a trimmed mean is also commonly used

Measures of Spread: Range and VarianceRange is the difference between the max and minThe variance or standard deviation is the most common measure of the spread of a set of points

VisualizationVisualization is the conversion of data into a visual or tabular format so that the characteristics of the data and the relationships among data items or attributes can be analyzed or reported.Humans have a well developed ability to analyze large amounts of information that is presented visuallyCan detect general patterns and trendsCan detect outliers and unusual patterns

Visualization techniques-HistogramHistogram Usually shows the distribution of values of a single variableDivide the values into bins and show a bar plot of the number of objects in each bin. The height of each bar indicates the number of objectsShape of histogram depends on the number of bins

Contd….Ex: petal width 10 bins

Visualization Techniques: Box PlotsInvented by J. TukeyAnother way of displaying the distribution of data Following figure shows the basic part of a box plotoutlier75th percentile50th percentile25th percentile10th percentile10th percentile

Visualization Techniques: Scatter PlotsScatter plots Attributes values determine the positionTwo-dimensional scatter plots most common, but can have three-dimensional scatter plotsOften additional attributes can be displayed by using the size, shape, and color of the markers that represent the objects It is useful to have arrays of scatter plots can compactly summarize the relationships of several pairs of attributes

Visualization Techniques: Contour PlotsContour plots Useful when a continuous attribute is measured on a spatial gridThey partition the plane into regions of similar valuesThe contour lines that form the boundaries of these regions connect points with equal values The most common example is contour maps of elevation

Contour Plot Example: SST Dec, 1998

Visualization Techniques: Matrix PlotsMatrix plots Can plot the data matrixThis can be useful when objects are sorted according to classTypically, the attributes are normalized to prevent one attribute from dominating the plot Plots of similarity or distance matrices can also be useful for visualizing the relationships between objectsExamples of matrix plots are p

Visualization of the Iris Data Matrix

Visualization Techniques: Parallel CoordinatesParallel Coordinates Used to plot the attribute values of high-dimensional dataInstead of using perpendicular axes, use a set of parallel axes The attribute values of each object are plotted as a point on each corresponding coordinate axis and the points are connected by a line Thus, each object is represented as a line

Other Visualization TechniquesStar Plots Similar approach to parallel coordinates, but axes radiate from a central pointThe line connecting the values of an object is a polygon

Contd…Chernoff FacesApproach created by Herman ChernoffThis approach associates each attribute with a characteristic of a faceThe values of each attribute determine the appearance of the corresponding facial characteristic Each object becomes a separate faceRelies on human’s ability to distinguish faces

OLAPOn-Line Analytical Processing (OLAP) was proposed by E. F. Codd, the father of the relational database.Relational databases put data into tables, while OLAP uses a multidimensional array representation. Such representations of data previously existed in statistics and other fieldsThere are a number of data analysis and data exploration operations that are easier with such a data representation.

OLAP Operations: Data CubeThe key operation of a OLAP is the formation of a data cubeA data cube is a multidimensional representation of data, together with all possible aggregates.By all possible aggregates, we mean the aggregates that result by selecting a proper subset of the dimensions and summing over all remaining dimensions.For example, if we choose the species type dimension of the Iris data and sum over all other dimensions, the result will be a one-dimensional entry with three entries, each of which gives the number of flowers of each type.

OLAP Operations: Slicing and DicingSlicing is selecting a group of cells from the entire multidimensional array by specifying a specific value for one or more dimensions. Dicing involves selecting a subset of cells by specifying a range of attribute values. This is equivalent to defining a subarray from the complete array. In practice, both operations can also be accompanied by aggregation over some dimensions.

OLAP Operations: Roll-up and Drill-downAttribute values often have a hierarchical structure.Each date is associated with a year, month, and week.A location is associated with a continent, country, state (province, etc.), and city. Products can be divided into various categories, such as clothing, electronics, and furniture.

Contd…Note that these categories often nest and form a tree or latticeA year contains months which contains dayA country contains a state which contains a city

Contd…This hierarchical structure gives rise to the roll-up and drill-down operations.For sales data, we can aggregate (roll up) the sales across all the dates in a month. Conversely, given a view of the data where the time dimension is broken into months, we could split the monthly sales totals (drill down) into daily sales totals.Likewise, we can drill down or roll up on the location or product ID attributes.

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Exploring Data

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Exploring Data