# Machine Learning Functions in Expression Language

This pages describes functions and properties that implement the machine learning functionality, such as clustering and prediction, that are part of the expression language. For prediction, the random forest is a supported algorithm. For clustering, the following algorithms are supported: KModes, KMeans and BalancedKMeans.

## Clustering functions

Function Parameters Description
KModes

Matrix to cluster

Performs KModes clustering for a numeric matrix. Implementation uses Accord.NET KModes method (http://accord-framework.net/docs/html/T_Accord_MachineLearning_KModes.htm).

Parameters:

1. Matrix to cluster. Rows (1st dimension) represent data points and columns represent feature values (2nd dimension)
2. Target number of clusters
3. Distance function to be used in the clustering process.

Returns an array having the following elements:

• Element 0: An array of all the cluster labels for all the rows in the input matrix in the same order as they were given in the matrix parameter.
• Element 1: An array of length 2 having the following elements:
• Element 0: Computed final error of the clustering.
• Element 1: Number of iterations performed in the clustering.

Examples:

```KModes([[1, 2], [2, 3], [2, 2]], 2)
Returns (e.g.): [[0, 1, 0], [0, 2]]

KModes([[1, 2], [2, 3], [2, 2]], 3)
Returns (e.g.): [[2, 1, 0], [0, 1]]
```
KMeans
• Matrix to cluster
• Target number of clusters
• Distance function

Performs KMeans clustering for a numeric matrix. Implementation uses Accord.NET KMeans function (http://accord-framework.net/docs/html/T_Accord_MachineLearning_KMeans.htm).

Parameters:

1. Matrix to cluster, where rows (1st dimension) represent data points and columns represent feature values (2nd dimension).
2. Target number of clusters
3. Distance function to be used in the clustering process.
4. Additional parameters: Optional key value pairs. Supported keys and values: ComputeCovariance: If true, the result will include covariance matrices. Default = false.

Returns an array having the following elements:

• Element 0: An array of all the cluster labels for all the rows in the input matrix in the same order as they were given in the matrix parameter.
• Element 1: An array of length 2 having the following elements:
• Element 0: Computed final error of the clustering.
• Element 1: Number of iterations performed in the clustering.
• Element 2: Only returned if computeCovariance is True.

Examples:

```KMeans([[1, 2], [2, 3], [2, 2]], 2)
Returns (e.g.): [[0, 1, 0], [0.16667, 2]]

KMeans([[1, 2], [2, 3], [2, 2]], 3)
Returns (e.g.): [[2, 1, 0], [0, 1]]

KMeans([[1, 2], [2, 3], [2, 2]], 2, "manhattan", true)
Returns (e.g.): [[0, 1, 0], [0.33333, 2], <covariance matrices (k * columns * columns)>]

KMeans(OneHot(Codify([[123, "foo"], [456, "bar"], [456, "foo"]])), 2)
Returns (e.g.): [[0, 1, 0], [0.33333, 2]]
```
BalancedKMeans
• Matrix to cluster
• Target number of clusters
• Distance function

Performs Balanced KMeans clustering for given numeric matrix. Algorithm is based on http://accord-framework.net/docs/html/T_Accord_MachineLearning_BalancedKMeans.htm. Parameters and return value structure is identical to the KMeans function.

Codify Matrix to codify

Encodes all unique column values into unique numeric integer values. Based on Accord.Net codify functionality: http://accord-framework.net/docs/html/T_Accord_Statistics_Filters_Codification.htm. Returns codified matrix of exactly the same dimensions as the input matrix.

Examples:

```Codify([[1,2], [3,4], [1,4]])
Returns: [[0, 0], [1, 1], [0, 1]]

Codify([[123, "foo"], [456, "bar"], [456, "foo"]])
Returns: [[0, 0], [1, 1], [1, 0]]
```
OneHot

Numeric matrix

One-hot encodes all matrix columns. Implementation uses Accord.NET OneHot method (http://accord-framework.net/docs/html/M_Accord_Math_Jagged_OneHot_1.htm)

Returns a matrix consisting of a concatenation of one-hot encoding of each of the input matrix columns. The number of columns in the returned matrix is at least the same as in the input matrix. For each input column, the corresponding one-hot vector will have all the values of 0, except for one which will be 1.

Examples:

```OneHot([[0], [2], [1], [3]])
Returns: [[1, 0, 0, 0], [0, 0, 1, 0], [0, 1, 0, 0], [0, 0, 0, 1]]

OneHot(Codify([[123, "foo"], [456, "bar"], [456, "foo"]]))
Returns: [[1, 0, 1, 0], [0, 1, 0, 1], [0, 1, 1, 0]]
```

## Prediction functions

Function Parameters Description
MLModel
• LM model type (String)

Create a new machine learning model for making predictions. Takes type of the model to create as a parameter. Currently the supported value is randomforest which uses the Accord.NET's RandomForest algorithm. Additional parameters:

• ComputeCovariance: If true, the result will include covariance matrices. Default value is false.
```let myMLModel = MLModel("randomforest", #{"ComputeCovariance": true});
```
Train (MLModel)
• Input data
• Expected outcomes
• Parameters

Trains given MLModel using given input data and expected outcomes. Returns the trained MLModel object.

Parameters:

• input data: Two dimensional array where:
• The first dimension (rows) specifies different data points.
• The second dimension (columns) specifies the feature values.
• expected outcomes: An array of expected outcomes for each row in the input data. Must be in the same order as the rows in the input data.
• parameters: Additional parameters for the MLModel:
• NumberOfTrees: number of trees in the random forest. Default value is 10.
• SampleRatio: Proportion of samples used to train each of the trees in the decision forest Default value is 0.632.
Transform (array)

Input data

Transforms given input data using the MLModel to generating predictions. Takes the input data as a parameter which is a two dimensional array where the first dimension (rows) specifies different data points and the second dimension (columns) specifies the feature values.

Returns an array of predictions. Transformations for each row in the input data can be found at the same index of the returned array.

## MLModel (Machine Learning Model)

These properties are available for the MLModel object.

MLModel properties Description
Type Returns the exact type of the MLModel.

## Examples

Example #1: Train a model using an event log and test its performance by replaying training data itself.

```
Def("GetOneHotColumnInformation", (
Let("el", _),
ToDictionary([
"et": OrderByValue(el.EventTypes),
"at": ToDictionary(ConcatTop(OrderByTop(el.CaseAttributes, Name).[_: Values]))
])
));

Def("GenerateOneHot", "cases", (
Let("columnInformation", _),
cases.(
Let("cas", _),
Flatten(
[
columnInformation.Get("et").(Let("et", _), If(Count(cas.EventsByType(et)) > 0, 1, 0)),
(
Let("atColumns", columnInformation.Get("at")),
OrderByValue(atColumns.Keys).(
Let("key", _),
Let("values", atColumns.Get(key)),
Let("caseValue", cas.Attribute(key)),
values.(If(_ == caseValue, 1, 0))
)
)
]
)
)
));

Let("el", EventLogById(1));
Let("columnInformation", el.GetOneHotColumnInformation());
Let("allCases", el.Cases);
Let("allCasesOH", columnInformation.GenerateOneHot(el.Cases));
Let("trainDataOH", allCasesOH);
Let("outcomes", allCases.(Duration > TimeSpan(24)));
Let("testDataOH", allCasesOH);
Let("predictions",
MLModel("randomforest")
.Train(trainDataOH, outcomes)
.Transform(trainDataOH));
Sum(Zip(outcomes, predictions).(_[0] == _[1] != 0)) / Count(outcomes)
```

Example #2: Train a model using an a 75% sample of an event log and test its performance by using the rest 25% of the event log.

```Def("GetOneHotColumnInformation", (
Let("el", _),
ToDictionary([
"et": OrderByValue(el.EventTypes),
"at": ToDictionary(ConcatTop(OrderByTop(el.CaseAttributes, Name).[_: Values]))
])
));

Def("GenerateOneHot", "cases", (
Let("columnInformation", _),
cases.(
Let("cas", _),
Flatten(
[
columnInformation.Get("et").(Let("et", _), If(Count(cas.EventsByType(et)) > 0, 1, 0)),
(
Let("atColumns", columnInformation.Get("at")),
OrderByValue(atColumns.Keys).(
Let("key", _),
Let("values", atColumns.Get(key)),
Let("caseValue", cas.Attribute(key)),
values.(If(_ == caseValue, 1, 0))
)
)
]
)
)
));

Let("el", EventLogById(1));
Let("columnInformation", el.GetOneHotColumnInformation());
Let("allCases", Shuffle(el.Cases));
Let("lastTrainCaseIndex", 0.75 * CountTop(el.Cases));
Let("trainCases", allCases[NumberRange(0, lastTrainCaseIndex)]);
Let("testCases", allCases[NumberRange(lastTrainCaseIndex + 1, CountTop(el.Cases) - 1)]);
Let("trainDataOH", columnInformation.GenerateOneHot(trainCases));
Let("testDataOH", columnInformation.GenerateOneHot(testCases));
Let("trainOutcomes", trainCases.(Duration > TimeSpan(24)));
Let("testOutcomes", testCases.(Duration > TimeSpan(24)));
Let("predictions",
MLModel("randomforest")
.Train(trainDataOH, trainOutcomes)
.Transform(testDataOH));
Sum(Zip(testOutcomes, predictions).(_[0] == _[1] != 0)) / Count(testOutcomes)
```

Example #3: Three sets of cases: training cases, target cases (subset of training cases) and test cases (independent set of cases). Try to predict which cases in the test set will eventually end up becoming a case in target cases.

```Def("GetOneHotColumnInformation", (
Let("el", _),
ToDictionary([
"et": OrderByValue(el.EventTypes),
"at": ToDictionary(ConcatTop(OrderByTop(el.CaseAttributes, Name).[_: Values]))
])
));

Def("GenerateOneHot", "cases", (
Let("columnInformation", _),
cases.(
Let("cas", _),
Flatten(
[
columnInformation.Get("et").(Let("et", _), If(Count(cas.EventsByType(et)) > 0, 1, 0)),
(
Let("atColumns", columnInformation.Get("at")),
OrderByValue(atColumns.Keys).(
Let("key", _),
Let("values", atColumns.Get(key)),
Let("caseValue", cas.Attribute(key)),
values.(If(_ == caseValue, 1, 0))
)
)
]
)
)
));

Let("el", <event log to use>);
Let("trainCases", <cases to use for training>);
Let("targetCases", <cases representing the properties we want to try to predict (subset of traincases)>);
Let("testCases", <cases to use for testing>);
Let("targetCasesDict", ToDictionary(targetCases:true));
Let("outcomes", traincases.(Let("c", _), targetCasesDict.ContainsKey(c) ? 1 : 0));
Let("columnInformation", el.GetOneHotColumnInformation());

Let("mlModel", MLModel("randomforest"));
mlModel.Train(columnInformation.GenerateOneHot(trainCases), outcomes);
mlModel.Transform(columnInformation.GenerateOneHot(testCases));
```

Example #4: Customized version of example #3 using actual event type and attribute names. Three sets of cases: training cases, target cases (subset of training cases) and test cases (independent set of cases). Try to predict which cases in the test set will eventually end up becoming a case in target cases. Generate HTML result ready to be sent out in an email message.

```Def("GenerateOneHot", "cases", { let columnInformation = _;
cases.{ let cas = _;
Flatten( [
{ let etColumns = columnInformation.Get("et"); etColumns.{ let  et = _; If(Count(cas.EventsByType(et)) > 0, 1, 0) } },
{ let atColumns = columnInformation.Get("at"); OrderByValue(atColumns.Keys).{ let key = _; let values = atColumns.Get(key); let caseValue = cas.Attribute(key); values.(If(_ == caseValue, 1, 0)) } }
] )
}
});

// Make predictions for the whole model:
// let el = ModelById(39694).EventLog;

// Make predictions for cases in a particular filter
let el = EventLogById(109773);

let currenttime = now;

let trainCases = el.Cases.Where(Catch(currenttime - EventTimeStampsByType("hs_analytics_last_visit_timestamp")[0] > TimeSpan(30) , true));
let testCases = el.Cases.Where(Catch(currenttime - EventTimeStampsByType("hs_analytics_last_visit_timestamp")[0] < TimeSpan(30) , false));

let targetCasesDict = ToDictionary(targetCases:true);
let outcomes = traincases.{ let c = _; targetCasesDict.ContainsKey(c) ? 1 : 0 };
let columnInformation = ToDictionary([
"et": OrderByValue(el.EventTypes).Where(_.Name.In(["hs_email_last_click_date","first_conversion_date", "hs_analytics_last_visit_timestamp"])),
"at": ToDictionary(ConcatTop(OrderByTop(el.CaseAttributes.Where(_.Name.In(["Lifecycle Stage", "Original Source", "QPR Digest", "Unsubscribed from all email"])) , Name).[_: Values]))
]);
let mlModel = MLModel("randomforest");
mlModel.Train(columnInformation.GenerateOneHot(trainCases), outcomes);

let predictions = mlModel.Transform(columnInformation.GenerateOneHot(testCases));
let predictedCases = ToDataFrame(Zip(testCases, predictions).Where(_[1] == 1) , ["id", "pred"]).id;

let body = "<html><body><table><tr><td>Last visited</td><td>Name</td></tr><tr>" +
StringJoin( "</tr><tr>", "<td>" + predictedCases.EventTimeStampsByType("hs_analytics_last_visit_timestamp")[0] + "</td><td>" + predictedCases.Name + "</td>") +
"</tr></table></body></html>";

body;
```