Anomaly Detection - Local Outlier Factor

Demonstrates how to implement the Local Outlier Factor (LOF) anomaly detection algorithm in DAX.

 

LOF Measure = 
    VAR __ID = MAX('Table'[ID])
    VAR __Table0 = ALL('Table')
    VAR __Table = 
        FILTER( 
            GENERATE( 
                SELECTCOLUMNS( __Table0,"ID1",[ID] ) , 
                SELECTCOLUMNS( __Table0,"ID2",[ID] ) 
            ), 
            [ID1] <> [ID2]
        )
    VAR __Table1 = 
        ADDCOLUMNS(
            __Table,
            "ID3", IF([ID1] < [ID2], [ID1], [ID2]),
            "ID4", IF([ID1] > [ID2], [ID1], [ID2])
        )
    VAR __Table3 = 
        ADDCOLUMNS(
            DISTINCT( SELECTCOLUMNS( __Table1, "ID1", [ID3], "ID2", [ID4] ) ),
            "MD",
                VAR __ID1 = [ID1]
                VAR __ID2 = [ID2]
                VAR __x1 = MAXX(FILTER(__Table0, [ID] = __ID1), [X])
                VAR __y1 = MAXX(FILTER(__Table0, [ID] = __ID1), [Y])
                VAR __x2 = MAXX(FILTER(__Table0, [ID] = __ID2), [X])
                VAR __y2 = MAXX(FILTER(__Table0, [ID] = __ID2), [Y])
                VAR __Result = ABS(__x1 - __x2) + ABS(__y1 - __y2)
            RETURN
                __Result
        )
    VAR __Table4 = 
        ADDCOLUMNS(
            ADDCOLUMNS(
                SELECTCOLUMNS(
                    __Table0,
                    "ID",[ID],"X",[X],"Y",[Y]
                ),
                "k-MD",
                    VAR __ID = [ID]
                    VAR __Table = FILTER(__Table3, [ID1] = __ID || [ID2] = __ID)
                    VAR __kMD = MAXX(TOPN([k], __Table, [MD],ASC),[MD])
                RETURN
                    __kMD         
            ),
            "K-neighborhood",
                VAR __kMD = [k-MD]
                VAR __ID = [ID]
                VAR __Table = FILTER('Table 2', [ID1] = __ID || [ID2] = __ID)
                VAR __Result = COUNTROWS( FILTER( __Table, [MD] <= __kMD ) )
            RETURN
                __Result
        )
    VAR __Table5 = 
        ADDCOLUMNS(
            __Table4,
            "LRD",
                VAR __kMD = [k-MD]
                VAR __Kneighborhood = [K-neighborhood]
                VAR __ID = [ID]
                VAR __Table = FILTER('Table 2', ( [ID1] = __ID || [ID2] = __ID ) && [MD] <= __kMD )
                VAR __Table1 = 
                    ADDCOLUMNS( 
                        __Table, 
                        "MaxMD", 
                                VAR __LookupValue = IF([ID1] = __ID, [ID2], [ID1])
                                VAR __LookupKMD = MAXX(FILTER(__Table4, [ID] = __LookupValue), [k-MD])
                            RETURN
                            MAX( [MD], __LookupKMD) )
                VAR __Result = DIVIDE( 1, DIVIDE( SUMX( __Table1, [MaxMD] ), __Kneighborhood ))
            RETURN
                __Result
        )
    VAR __Table6 = 
        ADDCOLUMNS(
             __Table5,
             "LOF",
                VAR __kMD = [k-MD]
                VAR __Kneighborhood = [K-neighborhood]
                VAR __LRD = [LRD]
                VAR __ID = [ID]
                VAR __Table = FILTER(__Table3, ( [ID1] = __ID || [ID2] = __ID ) && [MD] <= __kMD )
                VAR __IDs = DISTINCT( FILTER( UNION( SELECTCOLUMNS( __Table, "ID", [ID1] ), SELECTCOLUMNS( __Table, "ID", [ID2] ) ), [ID] <> __ID ) )
                VAR __Table1 = FILTER( __Table5, [ID] IN __IDs )
                VAR __Result = DIVIDE( SUMX( __Table1, [LRD] ), __Kneighborhood ) * DIVIDE(1, __LRD)
            RETURN
                __Result
        )
    VAR __Result = MAXX(FILTER(__Table6, [ID] = __ID), [LOF])
RETURN
    __Result

 

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