Use DBSCAN to cluster dataset

This section will quickly outline how to use DBSCAN on the Tachometer and PWM in the dataset. For more details on how DBSCAN works checkout the documentation for DBSCAN

// Create DBSCAN instance

system_models:load("dbscan");

dbscan:generate("tach_pwm");

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// Add Tach and PWM (4,5) to DBSCAN model for all data
// EXCEPT low voltage (which is the outlier we want to
// Identify)
tach_pwm:dbscan_add_data(select [v[4,1],v[5,1]]
                          from Vector v, Integer i, Integer c
                         where v = windowed_stats_1024(i,c)
                           and c != 1);

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If you recall the Tachometer vs PWM graph:

The Low Voltage class was separate from all other classes. That is why we add the c != 1. We want to fit the DBSCAN model on the data that is not Low Voltage. That way can use a failure to classify a point as an indication of Low Voltage.

Fitting the model

One of the hyper parameters of DBSCAN is the min distance between points. To figure out a good min distance one has to do some explorations. One way to get an indication of a good distance is to measure the distance to the closest neighbor for every datapoint:

{'sa_plot': 'Line plot', 'batch':1, 'labels':['Label 1'], 'memory':200};
select d
  from number a, number d
 where a in range(count(extent(#"tach_pwm:datapoints")))
   and d = mean(select dist
                  from number dist, number b
                 where a != b
                   and dist = euclid(tach_pwm:datapoints(a),
                                     tach_pwm:datapoints(b))
                 order by dist asc limit 3)

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Except for some outliers we have a consistent min distance below 30, let's start with that as hyper parameter to DBCSAN. Min points is set to 3.

//Fit the model
tach_pwm:dbscan(30,3)

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Look at the clusters:

{"sa_plot":"Scatter plot",
 "color_axis":"cluster",
 "size_axis": "none",
 "labels": ["cos(x)", "sin(x)","cluster"]};
select Vector of [v[1],v[2],cid]
  from Number cid, Number pid, Vector v
 where pid in tach_pwm:clustered_points(cid)
   and v = tach_pwm:datapoints(pid);

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Testing the fit.

The following query will classify each point in a stream of 1024 stats over the whole training set. Remember that we are only trying to identify Low Voltage as an outlier. That's why we set the label for every other set to 1 (since we only had one cluster in the DBSCAN model).

set :v = (select Vector of [
              v[1],
              tach_pwm:dbscan_classify([tach,pwm],30,1),
              tach,
              pwm
            ]
            from Vector v, Number tach, Number pwm
           where v in merge([widowed_stats_test_stream(1,-1),
                             widowed_stats_test_stream(2,1),
                             widowed_stats_test_stream(3,1),
                             widowed_stats_test_stream(4,1)
                                        ])
             and tach = v[2,4,1]
             and pwm = v[2,5,1]);

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Then we can use cluster_stats which takes a bag of vector where each vector contains [actual, predicted] and calculates Precision, Recall, F-measure, Rand-index:

pp(label_vector(["Precision","Recall","F-measure","Rand-index"],
             cluster_stats(in(:v),1)));

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If you use the same training values as defined here you will see that you get a precision around 0.76 which is not terrible, but not very good either. Let's take a look at the predictions in a scatter plot.

{
  'sa_plot': 'Scatter plot',
  'labels':['label','predict',"tach","pwm"],
  'x_axis': 'tach', 'y_axis': 'pwm', 'color_axis': 'predict',
  'size_axis': 'off'
};
:v

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With some further investigation it was found that the Tachometer was much higher in the test set for class 4 (obstructed) than the rest. That is what you see with the two separate groupings to the right in the graph above.

dbscan:save_model("tach_pwm", "statisitical_analysis","tach_pwm");