Projection K-Means Clustering basic options

Attributes to consider for clustering

Drag and drop the attributes that will be used as profile attributes in the clustering computation.

Label attributes

Drag and drop the attributes that that will be considered as labels in the clustering computation.

Clustering type

Three different approaches for computing cluster centroids are available:

• k-means, where the mean is used to compute the cluster centroid

• k-medians, where the median is used to compute the cluster centroid

• k-medoids, where the point of the dataset closest to the mean is used as the cluster centroid.

Clustering algorithm

Three different clustering algorithms are available:

• Standard, where cluster centroids are recomputed only after all the points have been reassigned;

• Incremental, where cluster centroids are recomputed after each point moving;

• Error-based, where point moving is decided by minimizing the error, instead of the distance from cluster centroid.

Distance method for clustering

The method employed for computing distances between examples.

Possible methods are: Euclidean, Euclidean (normalized), Manhattan, Manhattan (normalized), Pearson.

Details on these methods are provided in the Distance parameter of the Managing Attribute Properties page.

Distance method for evaluation

Select the method required for distance, from the possible values: Euclidean, Euclidean (normalized), Manhattan, Manhattan (normalized), Pearson.

For details on these methods see the Managing Attribute Properties page.

Normalization for ordered variables

Type of normalization adopted when treating ordered (discrete or continuous) variables.

Every attribute can have its own value for this option, which can be set in the Data Manager. Details on these options are provided in the Distance parameter of the Managing Attribute Properties page.

These choices are preserved if Attribute is selected in the present menu; every other value (e.g. Normal) supersedes previous selections for the current task.

Initial assignment for clusters

Procedure adopted for the initial assignment of points to clusters; it may be one of the following:

• Random: very fast, but less accurate; with this choice several executions (see option 4) of the algorithm can be performed (starting from different random initializations) to retrieve a better result;

• Smart: it can be slow, but tries to produce initial clusters having maximum distance from each other;

• Weight-based: cluster are initialized by taking into account weights (if present); in particular, points with high weight are placed into different clusters.

Number of clusters to be generated

The required number of clusters. The number of clusters cannot exceed the number of different examples in the training set.

(Optional) attribute for initial cluster assignment

Optionally select a specific attribute from the drop-down list, which will be used as an initial cluster assignment.

(Optional) attribute for weights

Optionally select an attribute from the drop-down list, which will be used as a weight in the clustering process.

Number of executions

Number of subsequent executions of the clustering process (to be used in conjunction with Random as the Initial assignment for clusters option); the best result among them is retained.

Maximum number of iterations

Maximum number of iterations of the k-means inside each execution of the clustering process.

Minimum decrease in error value

The error value corresponds to the average distance of each point from the respective centroid.

This value, measured at each iteration, should gradually decrease. When the error decrease value (i.e. the difference in error between the current and previous iteration) falls below the threshold specified here, the clustering process stops immediately since it is supposed that no further significant changes in error will occur.

Minimum number of occurrences

Minimum number of examples in the training set that must be characterized by a given tag so that it passes the filtering phase.

Maximum dispersion coefficient

If the profile attribute values present a dispersion coefficient (computed with respect to the desired central value) greater than the value entered here, the record presents an irregular behavior that can deteriorate the results of the clustering procedure, and is consequently discarded.

Initialize random generator with seed

If checked, the positive integer shown in the box is used as an initial seed for the random generator; with this choice two iterations with the same options produce identical results.

Keep attribute roles before clustering

If selected, roles defined in the clustering task (such as profile, labels, weight and cluster id) will be maintained in subsequent tasks in the flow. 

Filter patterns before clustering

If selected, data is filtered, otherwise all the representative records are considered in the clustering process.

Aggregate data before processing

If checked, identical patterns in the training set are considered as a single point in the clustering process.

Append results

Additional attributes produced by previous tasks are maintained at the end of the present one, rather than being overwritten.

Projection K-Means Clustering advanced options

Number of executions

Number of subsequent executions of the clustering process (to be used in conjunction with Random as the Initial assignment for clusters option); the best result among them is retained.

Maximum number of iterations

Maximum number of iterations of the k-means inside each execution of the clustering process.

Minimum decrease in error value

The error value corresponds to the average distance of each point from the respective centroid.

This value, measured at each iteration, should gradually decrease. When the error decrease value (i.e. the difference in error between the current and previous iteration) falls below the threshold specified here, the clustering process stops immediately since it is supposed that no further significant changes in error will occur.

Minimum number of occurrences

Minimum number of examples in the training set that must be characterized by a given tag so that it passes the filtering phase.

Maximum dispersion coefficient

If the profile attribute values present a dispersion coefficient (computed with respect to the desired central value) greater than the value entered here, the record presents an irregular behavior that can deteriorate the results of the clustering procedure, and is consequently discarded.

Initialize random generator with seed

If checked, the positive integer shown in the box is used as an initial seed for the random generator; with this choice two iterations with the same options produce identical results.

Keep attribute roles before clustering

If selected, roles defined in the clustering task (such as profile, labels, weight and cluster id) will be maintained in subsequent tasks in the flow. 

Filter patterns before clustering

If selected, data is filtered, otherwise all the representative records are considered in the clustering process.

Aggregate data before processing

If checked, identical patterns in the training set are considered as a single point in the clustering process.

Append results

Additional attributes produced by previous tasks are maintained at the end of the present one, rather than being overwritten.

After having imported the dataset through an Import from Text File task, add a Data Manager task and configure it as follows:

• select the workclass and occupation attributes, open the context menu by right-clicking on the attributes, click Edit and check Label.

• select the Income attribute and check Ignore in the Attributes tab.

Save and compute the task.

Then add a Split Data task to the flow, and split the dataset as follows:

• select 70% of examples for the training set, and

• the remaining 30% for the test set.

Save and compute the task.

Double-click the Projection Clustering (K-means) task, and configure it as follows:

• Drag and drop the age, education-num, capital-gain and hours-per-week attributes onto the Attributes to consider for clustering list

• Drag the workclass and occupation attributes onto the Label attributes area.

• Select Normal in the Normalization for ordered variables drop down list. In this way it is possible to retrieve a correct grouping even when attributes span a very different domain, as is the case for the continuous attributes:

  • capital-gain, which assumes values in the interval [0,99999], and

  • hours-per-week, which varies in the range [1,80]

• Enter 2 as the Number of clusters to be generated for each label, selecting the labels from the drop-down list.

• Clear the Filter patterns before clustering option, so that every tag is included in the clustering process.

The properties of the generated clusters can be viewed in the Monitor tab of the Standard Clustering task.

At the end of the flow the dispersion coefficients of the clusters are distributed as in the screenshot.

A similar histogram can be viewed for the number of elements, by opening the corresponding #Elements tab.

After the execution of the Projection Clustering task we obtain four clusters whose characteristics are displayed in the Clusters panel of the task.

In each row of the spreadsheet the first two fields, called cluster(workclass) and cluster(occupation), refer to a specific tag included in some patterns of the training set, whereas the subsequent 5 columns contain the components of the centroids for the two clusters.

The columns cluster, nelem and disp provide the cluster index, the number of elements and the dispersion coefficient, respectively.

To view information concerning the representative records created by the Projection Clustering (K-means) task, right-click it and select Take a look.

For each sample (row) of the training set we have the following result variables (columns)

1. assign: the initial assignment required by the user for the corresponding representative record; if no variables with role cluster id is included in the original dataset or its assignment is ambiguous (different cluster number for patterns with the same tag), the value in this column is set to missing.

2. weight: the weight of the associated representative record, computed as the sum of the weights associated with the patterns of the training set which have that tag.

3. nocc: the number of patterns in the training set which have the same tag as the considered sample (row).

4. disp: the dispersion coefficient obtained when computing the values of the profile attributes for the representative record.

5. sample: since several patterns may exist, which have the same tag as the current sample, the first occurrence of that tag in the training set is marked by setting the value 1 in the column; all the other occurrences assume the value 0 for this attribute.

6. selected: samples passing the data filtering phase assume the value 1 in this column; if no filtering is performed (by clearing the corresponding option in the Projection Clustering (K-means) task) this variable assumes the value 1 in all patterns.

Executing the Apply Model task creates the index of the cluster to which each pattern in the training and in the test set belongs.

This is obtained by finding the cluster that includes the same tag as the considered sample; the default cluster is selected if that tag was not considered in the clustering process (i.e.~it was not present in the training set).

14 additional result variables have been added to the dataset as can be seen by right clicking the computed task and selecting Take a look.

The first three result variables concern the cluster associated with the current pattern:

• pred(Output): the index of the cluster.

• conf(Output): the confidence of the association between cluster and pattern, given by 1−0.5∗d₁/d₂, where d₁ and d₂ are the distances from the nearest and the second nearest centroid, respectively. Since d₁<d₂ the confidence always lies in the interval [0.5,1]. 

• clust(Output): the row of the Clusters tab in the Projection Clustering task containing the associated cluster.

The subsequent five result variables report the values of the profile attributes for the centroid of the associated cluster: pred(age), pred(education-num), etc. 

The remaining six result variables concern the error generated when these values are employed as a forecast for the actual profile attributes of the pattern. In particular, the first of these result variables (error) provides the total error, whereas the others (err(age), err(education-name) etc.) provide the error for each attribute.

Corresponding values for the patterns of the test set can be displayed by selecting Test set from the Modeling Sets menu on the top-right corner.