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Clusters are collections of data based on similarity."
Data points clustered together in a graph can often be classified into clusters.
In the graph below we can distinguish 3 different clusters:
Clusters can hold a lot of valuable information, but clusters come in all sorts of shapes, so how can we recognize them?
The two main methods are:
Clustering is trying to:
The Density Method considers points in a dense regions to have more similarities
and differences than points in a lower dense region.
The density method has a good accuracy. It also has the ability to merge clusters.
Two common algorithms are DBSCAN and OPTICS.
The Hierarchical Method forms the clusters in a tree-type structure.
New clusters are formed using previously formed clusters.
Two common algorithms are CURE and BIRCH.
The Grid-based Method formulates the data into a finite number of cells that form a grid-like structure.
Two common algorithms are CLIQUE and STING
The Partitioning Method partitions the objects into k clusters and each partition forms one cluster.
One common algorithm is CLARANS.
The Correlation Coefficient (r) describes the strength and direction of a linear relationship and x/y variables on a scatterplot.
The value of r is always between -1 and +1:
| -1.00 | Perfect downhill | Negative linear relationship. |
| -0.70 | Strong downhill | Negative linear relationship. |
| -0.50 | Moderate downhill | Negative linear relationship. |
| -0.30 | Weak downhill | Negative linear relationship. |
| 0 | No linear relationship. | |
| +0.30 | Weak uphill | Positive linear relationship. |
| +0.50 | Moderate uphill | Positive linear relationship. |
| +0.70 | Strong uphill | Positive linear relationship. |
| +1.00 | Perfect uphill | Positive linear relationship. |
Perfect Uphill +1.00:
Perfect Downhill -1.00:
Strong Uphill +0.61:
No Relationship:
// Create a Plotter let myPlotter = new XYPlotter("myCanvas1"); myPlotter.transformXY(); // Create some XY Points numPoints = 500; let xPoints = []; let yPoints = []; for (let i = 0; i < numPoints; i+=10) { xPoints[i] = Math.random() * myPlotter.xMax; yPoints[i] = Math.random() * myPlotter.yMax; } // Plot the Points myPlotter.plotPoints(numPoints, xPoints, yPoints, "blue"); myPlotter.plotLine(0, 0, myPlotter.xMax-100, myPlotter.yMax, "blue"); myPlotter = new XYPlotter("myCanvas2"); myPlotter.transformXY(); xPoints = []; yPoints = []; for (let i = 0; i < numPoints; i+=10) { xPoints[i] = Math.random() * myPlotter.xMax; yPoints[i] = xPoints[i] * 1.3; } myPlotter.plotPoints(numPoints, xPoints, yPoints, "blue"); myPlotter = new XYPlotter("myCanvas3"); xPoints = []; yPoints = []; for (let i = 0; i < numPoints; i+=10) { xPoints[i] = i; yPoints[i] = xPoints[i] * 1.2 + 50; } myPlotter.plotPoints(numPoints, xPoints, yPoints, "red"); numPoints = 11; myPlotter = new XYPlotter("myCanvas4"); myPlotter.transformXY(); xPoints = [50,60,70,80,90,100,110,120,130,140,150]; yPoints = [7,8,8,9,9,9,9,10,11,14,14,15]; for (let i = 0; i < numPoints; i++) { xPoints[i] = xPoints[i] * 2.8 - 130; yPoints[i] = yPoints[i] * 30 - 150; } myPlotter.plotPoints(numPoints, xPoints, yPoints, "blue"); myPlotter.plotLine(xPoints[0], yPoints[0], xPoints[10], yPoints[10], "red"); // Create a Plotter xPoints = []; yPoints = []; let myPlotter1 = new XYPlotter("myCanvas11"); let myPlotter2 = new XYPlotter("myCanvas12"); myPlotter1.transformXY(); myPlotter2.transformXY(); xMax = myPlotter1.xMax; yMax = myPlotter1.yMax // Create some XY Points numPoints = 40; for (let i = 0; i < numPoints; i++) { xPoints[i] = Math.random() * xMax; yPoints[i] = Math.random() * yMax; } myPlotter1.plotPoints(numPoints, xPoints, yPoints, "black", 2); myPlotter2.plotPoints(numPoints, xPoints, yPoints, "black", 2); for (let i = 0; i < numPoints; i++) { xPoints[i] = Math.random() * xMax/4 + xMax/50; yPoints[i] = Math.random() * yMax/4 + yMax/2;; } myPlotter1.plotPoints(numPoints, xPoints, yPoints, "black", 2); myPlotter2.plotPoints(numPoints, xPoints, yPoints, "red"); for (let i = 0; i < numPoints; i++) { xPoints[i] = Math.random() * xMax/4 + xMax/2.5; yPoints[i] = Math.random() * yMax/3 + yMax/4; } myPlotter1.plotPoints(numPoints, xPoints, yPoints, "black", 2); myPlotter2.plotPoints(numPoints, xPoints, yPoints, "green"); for (let i = 0; i < numPoints; i++) { xPoints[i] = Math.random() * xMax/4 + xMax/1.4; yPoints[i] = Math.random() * yMax/4 + yMax/2; } myPlotter1.plotPoints(numPoints, xPoints, yPoints, "black", 2); myPlotter2.plotPoints(numPoints, xPoints, yPoints, "blue");