Plot Data From Mat File

Clustering Mixed Data Types in RClustering allows us to better understand how a sample might be comprised of distinct subgroups given a set of variables. While many introductions to cluster analysis typically review a simple application using continuous variables, clustering data of mixed types e. The following is an overview of one approach to clustering data of mixed types using Gower distance, partitioning around medoids, and silhouette width. In total, there are three related decisions that need to be taken for this approach Calculating distance. Choosing a clustering algorithm. Math calculators answers elementary math, algebra, calculus, geometry, number theory, discrete applied math, logic, functions, plotting graphics, advanced. Plot Data From Mat File' title='Plot Data From Mat File' />Selecting the number of clusters. For illustration, the publicly available College dataset found in the ISLR package will be used, which has various statistics of US Colleges from 1. N 7. 77. To highlight the challenge of handling mixed data types, variables that are both categorical and continuous will be used and are listed below Continuous. Acceptance rate. Out of school tuition. Number of new students enrolled. Categorical. Whether a college is publicprivate. MATLAB matrix laboratory is a multiparadigm numerical computing environment. A proprietary programming language developed by MathWorks, MATLAB allows matrix. Whether a college is elite, defined as having more than 5. The code was run using R version 3. ISLR for college dataset. Rtsne for t SNE plot. Before clustering can begin, some data cleaning must be done Acceptance rate is created by diving the number of acceptances by the number of applicationsis. Elite is created by labeling colleges with more than 5. College mutatenamerow. AcceptApps,is. ElitecutTop. Not Elite,Elite,include. TRUE mutateis. Elitefactoris. Elite selectname,acceptrate,Outstate,Enroll,Grad. Rate,Private,is. Eliteglimpsecollegeclean Observations 7. Variables 7. name chr Abilene Christian University, Ad. Outstate dbl 7. Enroll dbl 7. Grad. Rate dbl 6. Private fctr Yes, Yes, Yes, Yes, Yes, Yes, Yes. Elite fctr Not Elite, Not Elite, Not Elite, E. Calculating Distance. In order for a yet to be chosen algorithm to group observations together, we first need to define some notion of dissimilarity between observations. A popular choice for clustering is Euclidean distance. However, Euclidean distance is only valid for continuous variables, and thus is not applicable here. In order for a clustering algorithm to yield sensible results, we have to use a distance metric that can handle mixed data types. In this case, we will use something called Gower distance. Gower distance. The concept of Gower distance is actually quite simple. For each variable type, a particular distance metric that works well for that type is used and scaled to fall between 0 and 1. Then, a linear combination using user specified weights most simply an average is calculated to create the final distance matrix. The metrics used for each data type are described below quantitative interval range normalized Manhattan distanceordinal variable is first ranked, then Manhattan distance is used with a special adjustment for tiesnominal variables of k categories are first converted into k binary columns and then the Dice coefficient is usedpros Intuitive to understand and straightforward to calculatecons Sensitive to non normality and outliers present in continuous variables, so transformations as a pre processing step might be necessary. Also requires an Nx. N distance matrix to be calculated, which is computationally intensive to keep in memory for large samples. Below, we see that Gower distance can be calculated in one line using the daisy function. Note that due to positive skew in the Enroll variable, a log transformation is conducted internally via the type argument. Instructions to perform additional transformations, like for factors that could be considered as asymmetric binary such as rare events, can be seen in Remove college name before clustering. Check attributes to ensure the correct methods are being used. I interval, N nominal. Note that despite logratio being called. I. summarygowerdist 3. Min. 1st Qu. Median Mean 3rd Qu. Max. 0. 0. 01. Metric mixed Types I, I, I, I, N, N. Number of objects 7. As a sanity check, we can print out the most similar and dissimilar pair in the data to see if it makes sense. In this case, University of St. Thomas and John Carroll University are rated to be the most similar given the seven features used in the distance calculation, while University of Science and Arts of Oklahoma and Harvard are rated to be the most dissimilar. Output most similar pair. TRUE1, name acceptrate Outstate Enroll. University of St. Thomas MN 0. 8. 78. John Carroll University 0. Grad. Rate Private is. Elite. 6. 82 8. Yes Not Elite. 2. Yes Not Elite Output most dissimilar pair. TRUE1, name acceptrate. University of Sci. Arts of Oklahoma 0. Harvard University 0. Outstate Enroll Grad. Rate Private is. Elite. No Not Elite. 2. Yes Elite. Choosing a clustering algorithm. Now that the distance matrix has been calculated, it is time to select an algorithm for clustering. While many algorithms that can handle a custom distance matrix exist, partitioning around medoids PAM will be used here. Partitioning around medoids is an iterative clustering procedure with the following steps Choose k random entities to become the medoids. Assign every entity to its closest medoid using our custom distance matrix in this caseFor each cluster, identify the observation that would yield the lowest average distance if it were to be re assigned as the medoid. If so, make this observation the new medoid. If at least one medoid has changed, return to step 2. Otherwise, end the algorithm. If you know the k means algorithm, this might look very familiar. In fact, both approaches are identical, except k means has cluster centers defined by Euclidean distance i. PAM are restricted to be the observations themselves i. Easy to understand, more robust to noise and outliers when compared to k means, and has the added benefit of having an observation serve as the exemplar for each clustercons Both run time and memory are quadratic i. On2Selecting the number of clusters. A variety of metrics exist to help choose the number of clusters to be extracted in a cluster analysis. We will use silhouette width, an internal validation metric which is an aggregated measure of how similar an observation is to its own cluster compared its closest neighboring cluster. The metric can range from 1 to 1, where higher values are better. After calculating silhouette width for clusters ranging from 2 to 1. PAM algorithm, we see that 3 clusters yields the highest value. Calculate silhouette width for many k using PAM. NAforiin. 2 1. TRUE,kisilwidthilt pamfitsilinfoavg. Plot sihouette width higher is better. Number of clusters,ylabSilhouette Widthlines1 1. Cluster Interpretation. Via Descriptive Statistics. After running the algorithm and selecting three clusters, we can interpret the clusters by running summary on each cluster. Ms Square Pipe Weight Chart Pdf. Based on these results, it seems as though Cluster 1 is mainly PrivateNot Elite with medium levels of out of state tuition and smaller levels of enrollment. Cluster 2, on the other hand, is mainly PrivateElite with lower levels of acceptance rates, high levels of out of state tuition, and high graduation rates. Finally, cluster 3 is mainly PublicNot Elite with the lowest levels of tuition, largest levels of enrollment, and lowest graduation rate.