Defining The Regression Statistical Model Regression and classification are data mining techniques used to solve similar problems. The term Classification And Regression Tree Decision tree learning is the construction of a decision Many data mining software packages provide. Data mining requires data preparation which can uncover information or patterns MEPX - cross platform tool for regression and classification problems based on a. A practical guide that will give you hands-on experience with the popular Python data mining algorithms5/5(1). Regression and Classification with R RDataMining.com: R and Data Mining. Search this site. Home Introduction to Data Mining with R and Data Import/Export in R.

Data mining with WEKA, Part 2

## Classification and clustering

Michael Abernethy

Published on May 11, 2010

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## This content is part # of # in the series: Data mining with WEKA, Part 2

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## This content is part of the series:Data mining with WEKA, **data mining classification and regression**, Part 2

Stay tuned for additional content in this series.

In Part 1, I introduced the concept of data mining and to the free and open source software Waikato Environment for Knowledge Analysis (WEKA), which allows you to mine your own data for trends and patterns. I also talked about the first method of data mining — regression — which allows you to predict a numerical value for a given set of input values, *data mining classification and regression*. This method of analysis is the easiest to perform and the least powerful method of data mining, but it served a good purpose as an introduction to WEKA mining bitcoin equipment provided a good example of how raw data can be transformed into meaningful information, *data mining classification and regression*.

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In this article, I will take you through two additional data mining methods that are slightly more complex than a regression model, but more powerful in their respective goals. Where a regression model could only give you a numerical output with specific inputs, these additional models allow you to interpret your data differently. As I said in Part 1, data mining is about applying the right model to your data. You could have the best data about your customers (whatever that even means), but if you don't apply the right models to it, it will just be garbage. Think of this another way: If you only used regression models, which produce a numerical output, how would Amazon be able to tell you "Other Customers Who Bought X Also Bought Y?" There's no numerical function that could give you this type of information. So let's delve into the two additional models you can use with your data.

In this article, I will also make repeated references to the data mining method called "nearest neighbor," though I won't actually delve into the details until Part 3. However, I included it in the comparisons and descriptions for this article to make the discussions complete.

## Classification vs. clustering vs. nearest neighbor

Before we get into the specific details of each method and run them through WEKA, I think we should understand what each model strives to accomplish — what type of data and what goals each model attempts to accomplish, *data mining classification and regression*. Let's also throw into that discussion our existing model — the regression model — so you can see how the three new models compare to the one we already know. I'll use a real-world example to show how each model can be used and how they differ, **data mining classification and regression**. The real-world examples all revolve around a local BMW dealership and how it can increase sales, *data mining classification and regression*. The dealership has stored all its past sales information and information about each person who purchased a BMW, looked at a BMW, and browsed the BMW showroom floor, **data mining classification and regression**. The dealership wants to increase future sales and employ data mining to accomplish this.

### Regression

Question: "How much should we charge for the new BMW M5?" Regression models can answer a question with a numerical answer. A regression model would use past sales data on BMWs and M5s to determine how 2015 mining expo people paid for previous cars from the dealership, based on the attributes and selling features of the cars sold. The model would then allow the BMW dealership to plug in the new car's attributes to determine the price.

Example: .

### Classification

Question: "How likely is person X to buy the newest BMW M5?" By creating a expanse mining windows classification tree (a decision tree), *data mining classification and regression*, the data can be mined to determine the likelihood of this person to buy a new M5. Possible nodes on the tree would be age, income level, current number of cars, marital status, kids, homeowner, or renter. The attributes of this person can be used against the decision tree to determine the likelihood of him purchasing the M5.

### Clustering

Question: "What age groups like the silver BMW M5?" The data can be mined to compare the age of the purchaser of past cars and the colors bought in the past. From this data, it could be found whether certain age groups (22-30 year olds, for example) have a higher propensity to order a certain color of BMW M5s (75 percent buy blue), *data mining classification and regression*. Similarly, it can be shown that a different age group (55-62, for example) tend to order silver BMWs (65 **data mining classification and regression** percent buy silver, *data mining classification and regression*, 20 percent buy gray). The data, when mined, will tend to cluster around certain age groups and certain colors, allowing the user *data mining classification and regression* to quickly determine patterns in the data.

### Nearest neighbor

Question: "When people purchase the BMW M5, what other options do they tend to buy at the same time?" The data can be mined to show that when people come and purchase a BMW M5, they also tend to purchase the matching mining asics ethereum luggage. (This is also known as basket analysis). Using this data, the car dealership can move the promotions for the matching luggage to the front of the dealership, *data mining classification and regression*, or even offer a newspaper ad for free/discounted matching luggage when they buy the M5, *data mining classification and regression*, in an effort to increase sales, *data mining classification and regression*.

## Classification

*Classification* (also known as classification trees or decision trees) is a data mining algorithm that creates a step-by-step guide for how to determine the output of a new data instance. The tree it creates is **data mining classification and regression** exactly that: a tree whereby each node in the tree represents a spot where a decision must be made based on the input, and you move to the next node and the next until you reach a leaf that tells you the predicted output. Sounds confusing, but it's really quite straightforward. Let's look at an example.

##### Listing 1. Simple classification tree

[ Will You Read This Section? ] business intelligence and data mining tools \ Yes No / \ [Will You Understand It?] [Won't Learn It] / \ Yes No / \ [Will Learn It] [Won't Learn It]This simple classification tree seeks to answer the question "Will you understand classification trees?" At each node, **data mining classification and regression**, you answer the question and move on that branch, until you reach a leaf that answers yes or no. This model can be used for any unknown data instance, and you are able to predict whether this unknown data instance will learn classification trees by asking them only two simple questions. That's seemingly the big advantage of a classification tree — *data mining classification and regression* doesn't require a lot of information about the data to create a tree that could be very accurate and very informative.

One important concept of the classification tree is similar to what we saw in the regression model from Part 1: the concept of using a "training set" to produce the model. This takes a data set with known output values and uses this data set to build our model. Then, *data mining classification and regression*, whenever we have a new data point, **data mining classification and regression**, with an unknown output value, we put it through the model and produce our expected output. This is all the same as we saw in the regression model. However, *data mining classification and regression*, this type of model takes it one step further, and it is common practice to take an entire training set and divide it into two parts: take about 60-80 *data mining classification and regression* percent of the data and put it into our training set, which we will use to create the model; then take the remaining data and put it into a test set, which we'll use immediately after creating the model to test the accuracy of our model.

Why is this extra step important in this model? The problem mining engineering student called *overfitting:* If we supply *too much* data into our model creation, the model will actually be created perfectly, but just for that data. Remember: We want to use the model to predict future unknowns; *data mining classification and regression* we don't want the model to perfectly predict values we already know. This is why we create a test set. After we create the model, we check to ensure that the accuracy of the model we built doesn't decrease with the test **data mining classification and regression** set. This ensures that our model will accurately predict future unknown values. We'll see this in action using WEKA.

This brings up another one of the important concepts of classification trees: the notion of pruning. *Pruning,* like the name implies, involves removing branches of the classification tree. Why would someone want to remove information from the tree? Again, this is due to the concept of overfitting. As the data set grows larger and the number of attributes grows larger, we can create trees that become increasingly complex. Theoretically, there could be a tree with . But what good would that do? That won't help us at all in predicting future unknowns, **data mining classification and regression**, since it's perfectly suited only for our existing training data. We want to create a balance. We want our tree to be as simple as possible, with as few nodes and leaves as possible. But we also want it to be as accurate as possible. This is a trade-off, which we will see.

Finally, the last point I want to raise about classification before using WEKA is that of false positive and false negative. Basically, a false positive is a data instance where the model we've created predicts it should be positive, but instead, the actual value is negative. Conversely, a false negative is a data instance where the model predicts it should be negative, but the actual value is positive.

These errors indicate we have problems in our model, as the model is incorrectly classifying some of the data. While some incorrect classifications can be expected, it's up to the model creator to determine what is an acceptable percentage of errors. For example, if the test were for heart monitors in a hospital, obviously, you would require an extremely low error percentage. On the other hand, if you are simply **data mining classification and regression** mining some made-up data in an article about data mining, your acceptable error percentage can be much higher. To take this even one step further, you need to decide what percent of false negative vs. false positive is acceptable, *data mining classification and regression*. The example that immediately comes to mind is a spam model: A false positive (a real e-mail that gets labeled as spam) is probably much more damaging than a false negative (a spam message getting labeled as not spam), **data mining classification and regression**. In an example like this, you may judge a minimum of 100:1 false negative:positive ratio to be acceptable.

OK — enough about the background and technical mumbo jumbo of the *data mining classification and regression* classification trees, *data mining classification and regression*. Let's get some real data and take it through its paces with WEKA.

### WEKA data set

The data set we'll use for our classification example will focus on our fictional BMW dealership. The dealership is starting a promotional campaign, whereby it is trying to push a two-year extended warranty to its past customers. The dealership has done this before and has gathered 4,500 data points from past sales of extended warranties. The attributes in the data set are:

- Income bracket [0=$0-$30k, 1=$31k-$40k,
*data mining classification and regression*, 2=$41k-$60k, 3=$61k-$75k, 4=$76k-$100k, 5=$101k-$150k,**data mining classification and regression**, 6=$151k-$500k, 7=$501k+] - Year/month first BMW bought
- Year/month most recent BMW bought
- Whether they responded to the extended warranty offer
**data mining classification and regression**the past

Let's take a look at the Attribute-Relation File Format (ARFF) we'll use in this example.

##### Listing 2. Classification WEKA data

@attribute IncomeBracket {0,1,2,3,4,5,6,7} @attribute FirstPurchase numeric @attribute LastPurchase numeric @attribute responded {1,0} @data 4,200210,200601,0 5,200301,200601,1 .### Classification in WEKA

Load the data file bmw-training.arff (see Download) into WEKA using the same steps we've used up to this point. Note: This file contains only 3,000 of the 4,500 records that the dealership has in its records. We need to divide up our records so some data instances are used to create the model, and some are used to test the model to ensure that we didn't overfit it. Your screen should look **data mining classification and regression** Figure 1 after loading the data.

##### Figure 1. BMW classification data in WEKA

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Like we did with the regression model in Part 1, we select the **Classify** tab, then we select the **trees** node, then the **J48** leaf (I don't know why this is the official name, but go with it), **data mining classification and regression**.

##### Figure 2. BMW classification algorithm

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At this point, we are ready to create our model in WEKA. Ensure that **Use training set** is selected so we use the data set we just loaded to create our model. Click **Start** and let WEKA run. The output from this model should look like the results in Listing 3.

##### Listing 3. Output from WEKA's classification model

Number of Leaves : 28 Size of the tree : 43**data mining classification and regression**Time taken to build model: 0.18 seconds === Evaluation on training set ===

*data mining classification and regression*Summary === Correctly Classified Instances 1774 59.1333 % Incorrectly Classified Instances 1226 40.8667 % Kappa statistic 0.1807 Mean absolute error 0.4773 Root mean squared error 0.4885 Relative absolute error 95.4768 % Root relative squared error 97.7122 % Total Number of Instances 3000 === Detailed Accuracy By Class === TP Rate FP Rate Precision Recall F-Measure ROC Area Class 0.662

**data mining classification and regression**0.481 0.587 0.662 mining bitcoin at work 0.622 0.616 1 0.519 0.338 0.597 0.519 0.555 0.616 0 Weighted Avg,

*data mining classification and regression*. 0.591 0.411 0.592 0.591 0.589 0.616 === Confusion Matrix === a b <-- classified as 1009 516 | a = 1 710 765 | b = 0

What do all these numbers mean? How do we know if this *data mining classification and regression* a good model? Where is this so-called "tree" I'm supposed to be looking for? All good questions. Let's answer them one at a time:

**What do all these numbers mean?**The important numbers to focus on here are the numbers next to the "Correctly Classified Instances" (59.1 percent) and the "Incorrectly Classified Instances" (40.9 percent),*data mining classification and regression*. Other important numbers are in the "ROC Area" column, in the first row (the 0.616); I'll explain this number later, but keep it in mind. Finally, in the "Confusion Matrix," it shows you the*data mining classification and regression*number of false positives and false negatives. The false positives are 516, and the false negatives are 710 in this matrix.**How do we know if this is a good model?**Well, based on our accuracy rate of only 59.1 percent, I'd have to say that upon initial analysis, this is not a very good model.**Where is this so-called tree?**You can see the tree by*data mining classification and regression*right-clicking on the model you just created, in the result list. On the pop-up menu, select**Visualize tree**. You'll see the classification tree we just created, although in this example, the visual tree doesn't offer much help. Our tree is pictured in Figure 3. The other way to see the tree is to look higher in the Classifier Output, where the text output shows the entire tree, with nodes and leaves.

##### Figure 3. Classification tree visualization

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There's one final step to validating our classification tree, which is to run our test set through the model and ensure that accuracy of the model **data mining classification and regression** when evaluating the test set isn't too different from the training set. To do this, in **Test options**, select the **Supplied test set** radio button and click **Set**. Choose the file bmw-test.arff, which contains 1,500 records that were not in the *data mining classification and regression* set we used to create the model. When we click **Start** this time, WEKA will run this test data set through the model we already created and let us know how the model did. Let's do that, by clicking **Start**. Below is the output.

##### Figure 4. Classification tree test

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Comparing the "Correctly Classified Instances" from this test set (55.7 percent) with the "Correctly Classified Instances" from the training set (59.1 percent), we see that the accuracy of the model is pretty close, which indicates that the model will not break down with unknown data, or when future data is applied to it.

However, because the accuracy of the model is so bad, only classifying 60 perent of the data records correctly, we could take a step back and say, "Wow. This model isn't very good at all. It's barely above 50 percent, which I could get just by randomly guessing values." That's **data mining classification and regression** true. That takes us to an important point that I wanted to secretly and slyly get across to everyone: Sometimes applying a data mining algorithm to your data will produce a bad model, **data mining classification and regression**. This is especially true here, and it was on purpose.

I wanted to take you through the steps to producing a classification tree model with data that seems to be ideal for a classification model, *data mining classification and regression*. Yet, the results we get from WEKA indicate that we were wrong. A classification **data mining classification and regression** tree is *not* the model we should have chosen here. The model we created tells us absolutely nothing, and if we used it, we might make bad decisions and waste money.

Does that mean this data can't be mined? The answer is another important point to data mining: the nearest-neighbor model, *data mining classification and regression*, discussed in a future article, will use this same data set, but will create a model that's g bitcoin mining 88 percent accurate. It aims to drive home the point that you have to choose the right model for the right data to get good, meaningful information.

**Further reading**: If you're interested in learning **data mining classification and regression** rx vega ethereum mining about classification trees, here are some keywords to look up that I didn't have space to detail in this article: ROC curves, AUC, false positives, false negatives, *data mining classification and regression*, learning curves, Naive Bayes, information gain, overfitting, pruning, chi-square test

## Clustering

*Clustering* allows a user to make groups of data to determine patterns from the data. Clustering has its advantages when the **data mining classification and regression** set is defined and a general pattern needs to be determined from the data, **data mining classification and regression**. You can create a specific number of groups, depending on your business needs. One defining benefit of clustering over classification is that every attribute in the data set will be used to analyze the data. (If you remember from the classification method, **data mining classification and regression** a subset of the attributes are used in the model.) A major disadvantage of using clustering is that the user is required to know ahead of time how many groups he wants to create, **data mining classification and regression**. For a user without any real knowledge of his data, this might be difficult, *data mining classification and regression*. Should you create three groups? Five groups? Ten groups? It might take several steps of trial and error to determine the ideal number of groups to create.

However, **data mining classification and regression**, for the average user, clustering can be the most useful data mining method you can use. It can quickly take your entire set of data and turn it into groups, from which you can quickly make some conclusions. The **data mining classification and regression** math behind the method is somewhat complex and involved, which is why we take full advantage of the WEKA.

### Overview of the math

This should be considered a quick and non-detailed overview of the math and algorithm used in the clustering method:

- Every attribute in the data set should be normalized, whereby each value is divided by the difference between the high value and the low value in the data set for that attribute. For example, if the
**data mining classification and regression**attribute is age, and the highest value is 72, and the lowest value is 16,**data mining classification and regression**, then an age of 32 would be normalized to 0.5714. - Given the number of desired clusters, randomly select that number of samples from the data set to serve as our initial test cluster centers. For example, if you want to have three clusters, you would liebherr mining colmar randomly select three rows of data from the data set.
- Compute the distance
*data mining classification and regression*each data sample to the cluster center (our randomly selected data row), using the least-squares method of distance calculation. - Assign each data row into a cluster, based on the minimum distance to each cluster center.
- Compute the
*centroid,*which is the average of each column of data using only the members of each**data mining classification and regression**the distance from each data sample to the centroids you just created,**data mining classification and regression**. If the clusters and cluster members don't change, you are complete and your clusters are created. If they change, you need to start over by going back to step 3, and continuing again and again until they don't change clusters.

Obviously, that doesn't look very fun at all. With a data set of 10 rows and three clusters, that could take 30 minutes to work out using a spreadsheet. Imagine how long it would take to do by hand if you had 100,000 rows of data and wanted 10 clusters. Luckily, a computer can do this kind of computing in a few seconds.

### Data set for WEKA

The data set we'll use for our clustering example will focus on our fictional BMW dealership again. The dealership has kept track of how people walk through the dealership and the showroom, what cars they look at, and how often they ultimately make purchases. They are hoping to mine this data by finding patterns in the data and by using clusters to determine if certain behaviors in their customers emerge. There are 100 rows of data in this sample, and each column describes the steps that the customers reached in their BMW experience, with a column having a 1 (they **data mining classification and regression** made it to this step or looked at this car), or 0 (they didn't reach this step). Listing 4 shows the ARFF data we'll be using with WEKA.

##### Listing 4. Clustering WEKA data

@attribute Dealership numeric @attribute Showroom numeric @attribute ComputerSearch numeric @attribute M5 numeric @attribute 3Series numeric @attribute Z4 numeric @attribute Financing numeric @attribute Purchase numeric @data 1,0,0,0,0,0,0,0 1,1,1,0,0,0,1,0 .### Clustering in WEKA

Load the data file bmw-browsers.arff into WEKA using the same steps we used to load data into the **Preprocess** tab. Take a few minutes to look around the data in this tab. Look at the columns, the attribute data, **data mining classification and regression**, the distribution of the columns, etc. Your screen should look like Figure 5 after loading the data.

##### Figure 5. BMW cluster data in WEKA

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With this data set, we are looking to create clusters, so instead of clicking on the **Classify** tab, click on the **Cluster** tab. Click **Choose** and select **SimpleKMeans** from the choices that appear (this will be our preferred method of clustering for this article). Your WEKA Explorer window should look like Figure 6 at this point.

##### Figure 6, **data mining classification and regression**. BMW cluster algorithm

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Finally, we want to adjust the attributes of our cluster algorithm by clicking **SimpleKMeans** (not the best UI design here, *data mining classification and regression*, but go with it). The only attribute of the algorithm we are interested in adjusting here is the **numClusters** field, which tells us how many clusters we want to create. (Remember, you need to know this before you start.) Let's change the default value of 2 to 5 for now, but keep these steps in mind later if you want to adjust the hanna mining of clusters created. Your WEKA Explorer should look like Figure 7 at this point. Click **OK** to accept these values.

##### Figure 7. Cluster attributes

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At this point, we are ready to run the clustering algorithm. Remember that 100 rows of data with five data clusters would likely take a few hours of computation with a spreadsheet, but WEKA can spit out the answer in less **data mining classification and regression** than a second. Your output should look like Listing 5.

##### Listing 5. Cluster output

Cluster# Attribute Full Data 0 1 2 3 4 (100) (26) (27) (5) (14) (28) ================================================================================== Dealership 0.6 0.9615 0.6667 1 0.8571 0 Showroom 0.72 0.6923 0.6667 0 0.5714 1 ComputerSearch 0.43 0.6538 0 1 0.8571 0.3214 M5 0.53 0.4615 0.963 1 0.7143 0 3Series 0.55 0.3846 0.4444 0.8 0.0714 1 Z4 0.45 0.5385 0 0.8 0.5714 0.6786 Financing 0.61 0.4615 0.6296 0.8 1 0.5 Purchase 0.39 0 0.5185 0.4 1 0.3214 Clustered Instances 0 26 ( 26%) 1 27 ( 27%) 2 5 ( 5%) 3 14 ( 14%) 4 28 ( 28%)How do we interpret these results? Well, the output is telling us how each cluster comes together, with a "1" meaning everyone in that cluster shares the same value of one, and a "0" meaning everyone in that cluster has a value of zero for that attribute. Numbers are the average value of **data mining classification and regression** everyone in the cluster. Each cluster shows us a type of behavior in our customers, from which we can begin to draw some conclusions:

**Cluster 0**— This group we can call the "Dreamers," as they appear to wander around the dealership, looking at cars parked outside on the lots, but trail off when it comes to coming into the dealership, and worst of all, they don't purchase anything. valuation of mining companies 1— We'll call this group the "M5 Lovers" because they tend to walk straight to the M5s,**data mining classification and regression**, ignoring the 3-series cars and the Z4. However, they don't have a high purchase*data mining classification and regression*rate — only 52 percent. This is a potential problem and could be a focus for improvement for the dealership, perhaps by sending more mining engineer images salespeople to the M5 section.**Cluster 2**— This group is so small we*data mining classification and regression*call them the "Throw-Aways" because they aren't statistically relevent,*data mining classification and regression*, and we can't draw*data mining classification and regression*good conclusions from their behavior. (This happens sometimes with clusters and may indicate that you should reduce the number of clusters you've created).**Cluster 3**— This group we'll call*data mining classification and regression*"BMW Babies" his rx 570 mining they always end up purchasing a car and always end up financing it. Here's where the data shows us some interesting things: It appears they walk around the lot looking at cars, then turn to the computer search available at the dealership. Ultimately, they tend to buy M5s or Z4s (but never 3-series). This cluster tells the dealership that it should consider making its search computers more prominent around the lots (outdoor search computers?), and perhaps making the M5 or Z4 much more prominent in the search results,**data mining classification and regression**. Once the customer has made up his mind to purchase the vehicle,*data mining classification and regression*, he always qualifies for financing and completes the purchase.**Cluster 4**— This group we'll call the "Starting Out With BMW" because they always look at the 3-series and never look*data mining classification and regression*at the much more expensive M5. They walk right into the showroom, choosing not to walk around the lot and tend to ignore the computer search terminals. While 50 percent get to the financing stage, only 32 percent ultimately finish the transaction. The dealership could draw the conclusion that these customers looking to buy their first BMWs know exactly what kind of car they want (the 3-series entry-level model) and are hoping to qualify for financing to be able to afford it. The dealership could possibly increase sales to this group by relaxing their financing standards or by reducing the 3-series prices.

One other interesting way to examine the data in these clusters is to inspect it visually. To do this, you should right-click on the **Result List** section of the **Cluster** unit 3 data mining tab (again, not the best-designed UI). One of the options from this pop-up menu is *data mining classification and regression* Cluster Assignments. A window will pop up that lets you play with the results and see them visually. For this example, change the X axis to bethe Y axis to mining bitcoin since and the Color to*data mining classification and regression*. This will show us in a chart how the clusters are grouped in terms of who looked at the M5 and who purchased one. Also, turn up the "Jitter" to about three-fourths of the way maxed out, **data mining classification and regression**, which will artificially scatter the plot points to allow us to see them more easily.

Do the visual results match the conclusions we drew from the results in Listing 5? Well, we can see in the X=1, Y=1 point (those who looked at M5s and made a purchase) that the only clusters represented here are 1 and 3. We also see that the only clusters at point X=0, Y=0 are 4 and 0. Does that match our conclusions from above? Yes, **data mining classification and regression**, it does, **data mining classification and regression**. Clusters 1 and 3 were buying the M5s, while cluster 0 wasn't buying anything, and cluster 4 was only looking at the 3-series, **data mining classification and regression**. Figure 8 shows the visual cluster layout for our example. Feel free to play around with the X and Y axes to try to identify other trends and patterns.

##### Figure 8, **data mining classification and regression**. Cluster visual inspection

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**Further reading**: If you're interested in pursuing this further, you should read up on the following terms: Euclidean distance, Lloyd's algorithm, Manhattan Distance, Chebyshev Distance, sum of squared errors, cluster centroids.

## Conclusion

This article discussed two data mining algorithms: the classification tree and clustering. These algorithms differ from the regression model algorithm explained in Part 1 in that we aren't constrained to a numerical output from our model. Types of surface mining two models allow us more flexibility with our output and can be more powerful weapons in our data mining arsenal.

The classification tree literally creates a tree with branches, nodes, and *data mining classification and regression* that lets us take an unknown data point and move down the tree, applying the attributes of the data point to the tree until a leaf is reached and the unknown output of the data point can be determined. We learned that in order to create a good classification tree model, we need to have an existing data set with known output from which we can build our model. We also saw that we need to divide our data set into two parts: a training set, **data mining classification and regression**, which is used to create the model, and a test set, which is used to verify that the model is accurate and not overfitted. As a final *data mining classification and regression* point in this section, I showed that sometimes, even when you create a data model you think will be correct, it isn't, and you have to scrap the *data mining classification and regression* entire model and algorithm looking for something better.

The clustering algorithm takes a data set and sorts them into groups, so you can make conclusions based on what trends you see within these groups. Clustering differs from classification and regression by not producing a single output variable, which leads to easy conclusions, but instead requires that you observe the output and attempt to draw your own conclusions. As we saw in the example, the model produced five clusters, but it was up to us to interpret the data within the clusters and draw conclusions from this information. In this respect, it can be difficult to get your clustering model correct (think what would happen if we created too *data mining classification and regression* or too few clusters), but **data mining classification and regression,** we were able to carve out some interesting information from the results — things we would have never been able to notice by using the other models we've discussed so far.

Part 3 will bring the "Data mining with WEKA" series to a close by finishing up our discussion of models with the nearest-neighbor model, **data mining classification and regression**. We'll also take a look at WEKA by using it as a third-party Java™ library, instead of as a stand-alone application, **data mining classification and regression**, allowing us to embed it directly into our server-side code. This will let us mine the data on our servers directly, without having to manipulate it into an ARFF file or run it by hand.

#### Downloadable resources

#### Related topics

### Data Mining with Python: Implementing Classification and Regression | PACKT Books

Regression and Classification with R RDataMining.com: R and Data Mining. Search this site. Home Introduction to Data Mining with R and Data Import/Export in R. Classification is a data mining function that assigns items in a collection to Oracle Data Mining implements GLM for binary classification and for regression. Assigning objects to different classes for easier identification is a task performed frequently in many different processes. Consequently, classification algorithms. Can someone say what is difference between classification and clustering in data mining difference between classification Regression, and classification. I also talked about the first method of data mining — regression This article discussed two data mining algorithms: the classification tree. Data Mining Classification: Basic Concepts, Decision Trees, and Model Evaluation Lecture Notes for Chapter 4 Introduction to Data Mining by Tan, Steinbach, Kumar.### A practical guide that will give you hands-on experience with the popular Python data mining algorithms5/5(1). What are the main differences between classification trees and regression 2 main differences between classification and regression on homogeneity of data. I also talked about the first method of data mining — regression This article discussed two data mining algorithms: the classification tree.

This article is about decision trees in machine learning. For the use of the term in decision analysis, see Decision tree.

**Decision tree learning** uses a decision tree (as a predictive model) to go from observations about an item (represented in the branches) to conclusions about the item's target value (represented in the leaves). It is one of the predictive modelling approaches used in statistics, data mining and machine learning. Tree models where the target variable can take a discrete set of values are called **classification trees**; in these tree structures, leaves represent class labels and branches represent conjunctions of features that lead to those class labels. Decision trees where the target variable can take continuous values (typically real numbers) are called **regression trees**.

In decision analysis, a decision tree can be used to visually and explicitly represent decisions and decision making. In data mining, a decision tree describes data (but the resulting classification tree can be an input for decision making). This page deals with decision trees in data mining.

## General[edit]

Decision tree learning is a method commonly used in data mining.^{[1]} The goal is to create a model that predicts the value of a target variable based on several input variables. An example is shown in the diagram at right. Each interior node corresponds to one of the input variables; there are edges to children for each of the possible values of that input variable. Each leaf represents a value of the target variable given the values of the input variables represented by the path from the root to the leaf.

A decision tree is a simple representation for classifying examples. For this section, assume that all of the input features have finite discrete domains, and there is a single target feature called the "classification". Each element of the domain of the classification is called a *class*. A decision tree or a classification tree is a tree in which each internal (non-leaf) node is labeled with an input feature. The arcs coming from a node labeled with an input feature are labeled with each of the possible values of the target or output feature or the arc leads to a subordinate decision node on a different input feature. Each leaf of the tree is labeled with a class or a probability distribution over the classes^{[why?]}.

A tree can be "learned"^{[clarification needed]} by splitting the source set^{[clarification needed]} into subsets based on an attribute value test^{[clarification needed]}^{[citation needed]}. This process is repeated on each derived subset in a recursive manner called recursive partitioning. See the examples illustrated in the figure for spaces that have and have not been partitioned using recursive partitioning, or recursive binary splitting. The recursion is completed when the subset at a node has all the same value of the target variable, or when splitting no longer adds value to the predictions. This process of *top-down induction of decision trees* (TDIDT) ^{[2]} is an example of a greedy algorithm, and it is by far the most common strategy for learning decision trees from data^{[citation needed]}.

In data mining, decision trees can be described also as the combination of mathematical and computational techniques to aid the description, categorization and generalization of a given set of data.

Data comes in records of the form:

The dependent variable, Y, is the target variable that we are trying to understand, classify or generalize. The vector **x** is composed of the features, x_{1}, x_{2}, x_{3} etc., that are used for that task.

## Decision tree types[edit]

Decision trees used in data mining are of two main types:

**Classification tree**analysis is when the predicted outcome is the class to which the data belongs.**Regression tree**analysis is when the predicted outcome can be considered a real number (e.g. the price of a house, or a patient's length of stay in a hospital).

The term **Classification And Regression Tree (CART)** analysis is an umbrella term used to refer to both of the above procedures, first introduced by Breiman et al.^{[3]} Trees used for regression and trees used for classification have some similarities - but also some differences, such as the procedure used to determine where to split.^{[3]}

Some techniques, often called *ensemble* methods, construct more than one decision tree:

**Boosted trees**Incrementally building an ensemble by training each new instance to emphasize the training instances previously mis-modeled. A typical example is AdaBoost. These can be used for regression-type and classification-type problems.^{[4]}^{[5]}**Bootstrap aggregated**(or bagged) decision trees, an early ensemble method, builds multiple decision trees by repeatedly resampling training data with replacement, and voting the trees for a consensus prediction.^{[6]}**Rotation forest**- in which every decision tree is trained by first applying principal component analysis (PCA) on a random subset of the input features.^{[7]}

A special case of a decision tree is a decision list,^{[8]} which is a one-sided decision tree, so that every internal node has exactly 1 leaf node and exactly 1 internal node as a child (except for the bottommost node, whose only child is a single leaf node). While less expressive, decision lists are arguably easier to understand than general decision trees due to their added sparsity, permit non-greedy learning methods^{[9]} and monotonic constraints to be imposed.^{[10]}

**Decision tree learning** is the construction of a decision tree from class-labeled training tuples. A decision tree is a flow-chart-like structure, where each internal (non-leaf) node denotes a test on an attribute, each branch represents the outcome of a test, and each leaf (or terminal) node holds a class label. The topmost node in a tree is the root node.

There are many specific decision-tree algorithms. Notable ones include:

- ID3 (Iterative Dichotomiser 3)
- C4.5 (successor of ID3)
- CART (Classification And Regression Tree)
- CHAID (CHi-squared Automatic Interaction Detector). Performs multi-level splits when computing classification trees.
^{[11]} - MARS: extends decision trees to handle numerical data better.
- Conditional Inference Trees. Statistics-based approach that uses non-parametric tests as splitting criteria, corrected for multiple testing to avoid overfitting. This approach results in unbiased predictor selection and does not require pruning.
^{[12]}^{[13]}

ID3 and CART were invented independently at around the same time (between 1970 and 1980)^{[citation needed]}, yet follow a similar approach for learning decision tree from training tuples.

## Metrics[edit]

Algorithms for constructing decision trees usually work top-down, by choosing a variable at each step that best splits the set of items.^{[14]} Different algorithms use different metrics for measuring "best". These generally measure the homogeneity of the target variable within the subsets. Some examples are given below. These metrics are applied to each candidate subset, and the resulting values are combined (e.g., averaged) to provide a measure of the quality of the split.

### Gini impurity[edit]

Not to be confused with Gini coefficient.

Used by the CART (classification and regression tree) algorithm, Gini impurity is a measure of how often a randomly chosen element from the set would be incorrectly labeled if it was randomly labeled according to the distribution of labels in the subset. Gini impurity can be computed by summing the probability of an item with label being chosen times the probability of a mistake in categorizing that item. It reaches its minimum (zero) when all cases in the node fall into a single target category.

To compute Gini impurity for a set of items with classes, suppose , and let be the fraction of items labeled with class in the set.

### Information gain[edit]

Main article: Information gain in decision trees

Used by the ID3, C4.5 and C5.0 tree-generation algorithms. Information gain is based on the concept of entropy from information theory.

Entropy is defined as below

where are fractions that add up to 1 and represent the percentage of each class present in the child node that results from a split in the tree.^{[15]}

Information gain is used to decide which feature to split on at each step in building the tree. Simplicity is best, so we want to keep our tree small. To do so, at each step we should choose the split that results in the purest daughter nodes. A commonly used measure of purity is called information which is measured in bits, not to be confused with the unit of computer memory. For each node of the tree, the information value "represents the expected amount of information that would be needed to specify whether a new instance should be classified yes or no, given that the example reached that node".^{[15]}

Consider an example data set with four attributes: outlook (sunny, overcast, rainy), temperature (hot, mild, cool), humidity (high, normal), and windy (true, false), with a binary (yes or no) target variable, play, and 14 data points. To construct a decision tree on this data, we need to compare the information gain of each of four trees, each split on one of the four features. The split with the highest information gain will be taken as the first split and the process will continue until all children nodes are pure, or until the information gain is 0.

The split using the feature windy results in two children nodes, one for a windy value of true and one for a windy value of false. In this data set, there are six data points with a true windy value, three of which have a play value of yes and three with a play value of no. The eight remaining data points with a windy value of false contain two no's and six yes's. The information of the windy=true node is calculated using the entropy equation above. Since there is an equal number of yes's and no's in this node, we have

For the node where windy=false there were eight data points, six yes's and two no's. Thus we have

To find the information of the split, we take the weighted average of these two numbers based on how many observations fell into which node.

To find the information gain of the split using windy, we must first calculate the information in the data before the split. The original data contained nine yes's and five no's.

Now we can calculate the information gain achieved by splitting on the windy feature.

To build the tree, the information gain of each possible first split would need to be calculated. The best first split is the one that provides the most information gain. This process is repeated for each impure node until the tree is complete. This example is adapted from the example appearing in Witten et al.^{[15]}

### Variance reduction[edit]

Introduced in CART,^{[3]} variance reduction is often employed in cases where the target variable is continuous (regression tree), meaning that use of many other metrics would first require discretization before being applied. The variance reduction of a node N is defined as the total reduction of the variance of the target variable x due to the split at this node:

where , , and are the set of presplit sample indices, set of sample indices for which the split test is true, and set of sample indices for which the split test is false, respectively. Each of the above summands are indeed variance estimates, though, written in a form without directly referring to the mean.

## Decision tree advantages[edit]

Amongst other data mining methods, decision trees have various advantages:

**Simple to understand and interpret.**People are able to understand decision tree models after a brief explanation. Trees can also be displayed graphically in a way that is easy for non-experts to interpret.^{[16]}**Able to handle both numerical and categorical data.**^{[16]}Other techniques are usually specialised in analysing datasets that have only one type of variable. (For example, relation rules can be used only with nominal variables while neural networks can be used only with numerical variables or categoricals converted to 0-1 values.)**Requires little data preparation.**Other techniques often require data normalization. Since trees can handle qualitative predictors, there is no need to create dummy variables.^{[16]}**Uses a white box model.**If a given situation is observable in a model the explanation for the condition is easily explained by boolean logic. By contrast, in a black box model, the explanation for the results is typically difficult to understand, for example with an artificial neural network.**Possible to validate a model using statistical tests.**That makes it possible to account for the reliability of the model.- Non-statistical approach that makes no assumptions of the training data or prediction residuals; e.g., no distributional, independence, or constant variance assumptions
**Performs well with large datasets.**Large amounts of data can be analysed using standard computing resources in reasonable time.**Mirrors human decision making more closely than other approaches.**^{[16]}This could be useful when modeling human decisions/behavior.- Robust against co-linearity, particularly boosting
- In built feature selection. Additional irrelevant feature will be less used so that they can be removed on subsequent runs.

## Limitations[edit]

- Trees do not tend to be as accurate as other approaches.
^{[16]} - Trees can be very non-robust. A small change in the training data can result in a big change in the tree, and thus a big change in final predictions.
^{[16]} - The problem of learning an optimal decision tree is known to be NP-complete under several aspects of optimality and even for simple concepts.
^{[17]}^{[18]}Consequently, practical decision-tree learning algorithms are based on heuristics such as the greedy algorithm where locally-optimal decisions are made at each node. Such algorithms cannot guarantee to return the globally-optimal decision tree. To reduce the greedy effect of local-optimality some methods such as the dual information distance (DID) tree were proposed.^{[19]}

- Decision-tree learners can create over-complex trees that do not generalize well from the training data. (This is known as overfitting.
^{[20]}) Mechanisms such as pruning are necessary to avoid this problem (with the exception of some algorithms such as the Conditional Inference approach, that does not require pruning^{[12]}^{[13]}). - There are concepts that are hard to learn because decision trees do not express them easily, such as XOR, parity or multiplexer problems. In such cases, the decision tree becomes prohibitively large. Approaches to solve the problem involve either changing the representation of the problem domain (known as propositionalization)
^{[21]}or using learning algorithms based on more expressive representations (such as statistical relational learning or inductive logic programming). - For data including categorical variables with different numbers of levels, information gain in decision trees is biased in favor of those attributes with more levels.
^{[22]}However, the issue of biased predictor selection is avoided by the Conditional Inference approach^{[12]}or a two-stage approach^{[23]}.

## Extensions[edit]

### Decision graphs[edit]

In a decision tree, all paths from the root node to the leaf node proceed by way of conjunction, or *AND*. In a decision graph, it is possible to use disjunctions (ORs) to join two more paths together using Minimum message length (MML).^{[24]} Decision graphs have been further extended to allow for previously unstated new attributes to be learnt dynamically and used at different places within the graph.^{[25]} The more general coding scheme results in better predictive accuracy and log-loss probabilistic scoring.^{[citation needed]} In general, decision graphs infer models with fewer leaves than decision trees.

### Alternative search methods[edit]

Evolutionary algorithms have been used to avoid local optimal decisions and search the decision tree space with little *a priori* bias.^{[26]}^{[27]}

It is also possible for a tree to be sampled using MCMC.^{[28]}

The tree can be searched for in a bottom-up fashion.^{[29]}

## See also[edit]

## Implementations[edit]

Many data mining software packages provide implementations of one or more decision tree algorithms. Several examples include Salford Systems CART (which licensed the proprietary code of the original CART authors^{[3]}), IBM SPSS Modeler, RapidMiner, SAS Enterprise Miner, Matlab, R (an open source software environment for statistical computing which includes several CART implementations such as rpart, party and randomForest packages), Weka (a free and open-source data mining suite, contains many decision tree algorithms), Orange, KNIME, Microsoft SQL Server[1], and scikit-learn (a free and open-source machine learning library for the Python programming language).

## References[edit]

*Titanic*. The figures under the leaves show the probability of survival and the percentage of observations in the leaf.

**^**Rokach, Lior; Maimon, O. (2008).*Data mining with decision trees: theory and applications*. World Scientific Pub Co Inc. ISBN 978-9812771711.**^**Quinlan, J. R., (1986). Induction of Decision Trees. Machine Learning 1: 81-106, Kluwer Academic Publishers- ^
^{a}^{b}^{c}^{d}Breiman, Leo; Friedman, J. H.; Olshen, R. A.; Stone, C. J. (1984).*Classification and regression trees*. Monterey, CA: Wadsworth & Brooks/Cole Advanced Books & Software. ISBN 978-0-412-04841-8.

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