FRESH: a feature-extraction and feature-significance toolkit
.ml.fresh Feature extraction and significance
.ml.fresh.createFeatures Apply functions to subsets of initial data to create features .ml.fresh.significantFeatures Statistically significant features
Feature extraction and selection are vital components of many machine-learning pipelines. Here we outline an implementation of the FRESH (FeatuRe Extraction and Scalable Hypothesis testing) algorithm.
Feature extraction is the process of building derived, aggregate features from a time-series dataset. The features created are designed to characterize the underlying time series in a way that is easier to interpret and often provides a more suitable input to machine-learning algorithms.
Following feature extraction, statistical significance tests between feature and target vectors can be applied. This allows selection of only those features with relevance (in the form of a p-value) as defined by the user.
Feature selection can improve the accuracy of a machine-learning algorithm by
- Simplifying the models used
- Shortening the training time needed
- Mitigating the curse of dimensionality
- Reducing variance in the dataset to reduce overfitting
Notebook examples of the FRESH algorithm used in different applications
Loading
Load the FRESH library in isolation from the utilities section of the toolkit using
q)\l ml/ml.q
q).ml.loadfile`:fresh/init.q
Data formatting
Data passed to the feature extraction procedure should contain an identifying (ID) column, which groups the time series into subsets from which features can be extracted. The ID column can be inherent to the data or derived for a specific use-case (e.g. applying a sliding window onto the dataset).
Null values in the data should be replaced with derived values most appropriate to the column.
The feature-extraction procedure supports columns of boolean, integer and floating-point types. Other datatypes should not be passed to the extraction procedure.
In particular, data should not contain text (strings or symbols), other than within the ID column. If a text-based feature is thought to be important, one-hot, frequency or lexigraphical encoding can be used to convert the symbolic data to appropriate numerical values.
A range of formatting functions (e.g. null-filling and one-hot encoding) are supplied in the preprocessing section of the toolkit
Calculated features
Feature extraction functions are defined in the script fresh.q and found within the .ml.fresh.feat namespace.
| function | returns |
|---|---|
| absEnergy[data] | Sum of squares |
| absSumChange[data] | Absolute sum of the differences between successive datapoints |
| aggAutoCorr[data] | Aggregation (mean, median, variance and standard deviation) of an autocorrelation over all possible lags (1 - count[x]) |
| aggLinTrend[data;chunkLen] | Slope, intercept and rvalue for the series over aggregated max, min, variance or average for chunks of size chunklen |
| augFuller[data] | Hypothesis test to check for a unit root in series |
| autoCorr[data;lag] | Autocorrelation over specified lag |
| binnedEntropy[data;numBins] | Entropy of the series binned into nbins equidistant bins |
| c3[data;lag] | Measure of the non-linearity of the series lagged by lag |
| changeQuant[data;lowerQuant;upperQuant;isAbs] | Aggregated value of successive changes within corridor specified by lower quantile lowerQuant and upper quantile upperQuant (boolean isAbs defines whether absolute values are considered) |
| cidCe[data;isAbs] | Measure of series complexity based on peaks and troughs in the dataset (boolean isAbs defines whether absolute values are considered) |
| count[data] | Number of values within the series |
| countAboveMean[data] | Number of values in the series with a value greater than the mean |
| countBelowMean[data] | Number of values in the series with a value less than the mean |
| eRatioByChunk[data;numSeg] | Sum of squares of each region of the series split into numsegments segments, divided by the sum of squares for the entire series |
| firstMax[data] | Position of the first occurrence of the maximum value in the series relative to the series length |
| firstMin[data] | Position of the first occurrence of the minimum value in the series relative to the series length |
| fftAggReg[data] | Spectral centroid (mean), variance, skew, and kurtosis of the absolute Fourier-transform spectrum |
| fftCoeff[data;coeff] | Fast-Fourier transform coeff coefficient, given real inputs and extracting real, imaginary, absolute and angular components |
| hasDup[data] | Boolean: the series contains any duplicate values |
| hasDupMax[data] | Boolean: a duplicate of the maximum value exists in the series |
| hasDupMin[data] | Boolean: a duplicate of the minimum value exists in the series |
| indexMassQuantile[data;quantile] | Relative index such that q% of the series' mass lies to the left |
| kurtosis[data] | Adjusted G2 Fisher-Pearson kurtosis of the series |
| largestDev[data;ratio] | Boolean: the standard deviation is ratio times larger than the max - min values of the series |
| lastMax[data] | Position of the last occurrence of the maximum value in the series relative to the series length |
| lastMin[data] | Position of the last occurrence of the minimum value in the series relative to the series length |
| linTrend[data] | Slope, intercept and r-value associated with the series |
| longStrikeAboveMean[data] | Length of the longest subsequence in the series greater than the series mean |
| longStrikeBelowMean[data] | Length of the longest subsequence in the series less than the series mean |
| max[data] | Maximum value of the series |
| mean[data] | Mean value of the series |
| meanAbsChange[data] | Mean over the absolute difference between subsequent series values |
| meanChange[data] | Mean over the difference between subsequent series values |
| mean2DerCentral[data] | Mean value of the central approximation of the second derivative of the series |
| med[data] | Median value of the series |
| min[data] | Minimum value of the series |
| numCrossing[data;crossVal] | Number of crossings in the series over the value crossval |
| numCwtPeaks[data;width] | Number of peaks in the series following data smoothing via application of a Ricker wavelet of defined width |
| numPeaks[data;support] | Number of peaks in the series with a specified support |
| partAutoCorrelation[data;lag] | Partial autocorrelation of the series with a specified lag |
| perRecurToAllData[data] | Ratio of count of values occurring more than once to count of different values |
| perRecurToAllVal[data] | Ratio of count of values occurring more than once to count of data |
| quantile[data;quantile] | The value of series greater than the quantile percent of the ordered series |
| rangeCount[data;minVal;maxVal] | The number of values greater than or equal to minval and less than maxval |
| ratioBeyondRSigma[data;r] | Ratio of values more than r*dev[x] from the mean |
| ratioValNumToSeriesLength[data] | Ratio of number of unique values to total number of values |
| skewness[data] | Skew of the series indicating asymmetry within the series |
| spktWelch[data;coeff] | Cross power spectral density of the series at given coeff |
| stdDev[data] | Standard deviation of series |
| sumRecurringDataPoint[data] | Sum of all points present in the series more than once |
| sumRecurringVal[data] | Sum of all the values present within the series more than once |
| sumVal[data] | Sum of values within the series |
| symmetricLooking[data;ratio] | Measure of symmetry in the series |mean(x)-median(x)|-y*(max[x]-min[x]) with y in range 0->1 |
| treverseAsymStat[data;lag] | Measure of asymmetry of the series based on lag |
| valCount[data;val] | Number of occurrences of val within the series |
| var[data] | Variance of the series |
| varAboveStdDev[data] | Boolean: the variance of the dataset is larger than the standard deviation |
Some of the above functions are deprecated
They are still callable but will be removed after version 3.0.
Feature extraction
Feature extraction involves applying a set of aggregations to subsets of the initial input data, with the goal of obtaining information that is more informative to the prediction of the target vector than the raw time series.
The .ml.fresh.createFeatures function applies a set of aggregation functions to derive features. There are 57 such functions callable within the .ml.fresh.feat namespace, although users may select a subset of these based on requirement.
As of version 0.1.3 the creation of features using the function .ml.fresh.createFeatures is invoked at console initialization. If a process is started with $q -s -4 -p 4321, then four processes will automatically be used to process feature creation.
Feature significance
Statistical significance tests can be applied to the derived features to determine how useful each feature is in predicting a target vector. The specific significance test applied, depends on the characteristics of the feature and target. The following table outlines the test applied in each case.
feature type target type significance test
------------------------------------------------
Binary Real Kolmogorov-Smirnov
Binary Binary Fisher-Exact
Real Real Kendall Tau-b
Real Binary Kolmogorov-Smirnov
Each test returns a p-value, which can then be passed to a selection procedure chosen by the user. The feature selection procedures available at present are as follows;
- The Benjamini-Hochberg-Yekutieli (BHY) procedure: determines if the feature meets a defined False Discovery Rate (FDR) level. The recommended input is 5% (0.05).
- K-best features: choose the K features which have the lowest p-values and thus have been determined to be the most important features to allow us to predict the target vector.
- Percentile based selection: set a percentile threshold for p-values below which features are selected.
Each of these procedures can be implemented by modifying parameter input to the following function;
.ml.fresh.createFeatures
Apply functions to subsets of initial data to create features
.ml.fresh.createFeatures[data;idCol;cols2Extract;params]
Where
datais the input data in the form of a simple table.idColis the ID column name (syms).cols2Extractare the column names (syms) on which extracted features will be calculated (these columns should contain only numerical values).paramsis a table containing the functions/parameters to be applied to cols2Extract. This should be a modified version of.ml.fresh.params
returns a table keyed by ID column and containing the features extracted from the subset of the data identified by the ID column.
q)m:30;n:100
q)tab:([]date:raze m#'"d"$til n;
time:(m*n)#"t"$til m;
col1:50*1+(m*n)?20;
col2:(m*n)?1f )
q)10#tab
date time col1 col2
----------------------------------------
2000.01.01 00:00:00.000 450 0.6859514
2000.01.01 00:00:00.001 150 0.009530776
2000.01.01 00:00:00.002 500 0.3867134
2000.01.01 00:00:00.003 750 0.04674769
2000.01.01 00:00:00.004 1000 0.06310223
2000.01.01 00:00:00.005 200 0.5888565
2000.01.01 00:00:00.006 250 0.302542
2000.01.01 00:00:00.007 1000 0.7859634
2000.01.01 00:00:00.008 250 0.9453783
2000.01.01 00:00:00.009 650 0.9575708
q)show params:.ml.fresh.params / truncated for documentation purposes
f | pnum pnames pvals valid
-------------------| ------------------------------------------
absEnergy | 0 () () 1
absSumChange | 0 () () 1
aggAutoCorr | 0 () () 1
augFuller | 0 () () 1
count | 0 () () 1
countAboveMean | 0 () () 1
countBelowMean | 0 () () 1
sumVal | 0 () () 1
var | 0 () () 1
varAboveStdDev | 0 () () 1
aggLinTrend | 1 ,`chunkLen ,5 10 50 1
autoCorr | 1 ,`lag ,0 1 2 3 4 5 6 7 8 9 1
binnedEntropy | 1 ,`numBins ,2 5 10 1
c3 | 1 ,`lag ,1 2 3 1
q)5#feats:.ml.fresh.createFeatures[tab;`date;2_ cols tab;params]
date | col1_absEnergy col1_absSumChange col1_count col1_..
----------| -------------------------------------------------..
2000.01.01| 1.1385e+07 11400 30 16 ..
2000.01.02| 1.0455e+07 9500 30 15 ..
2000.01.03| 1.31825e+07 9500 30 17 ..
2000.01.04| 1.1515e+07 10600 30 13 ..
2000.01.05| 9492500 8800 30 16 ..
q)count 1_cols feats / 595 features have been produced from 2 columns
566
// Update ptab to exclude hyperparameter-dependent functions
q)paramsNew:update valid:0b from params where pnum>0
q)5#featsNew:.ml.fresh.createFeatures[tab;`date;2_ cols tab;paramsNew]
date | col1_absEnergy col1_absSumChange col1_count col1_..
----------| -------------------------------------------------..
2000.01.01| 1.1385e+07 11400 30 16 ..
2000.01.02| 1.0455e+07 9500 30 15 ..
2000.01.03| 1.31825e+07 9500 30 17 ..
2000.01.04| 1.1515e+07 10600 30 13 ..
2000.01.05| 9492500 8800 30 16 ..
// Less columns now being created via a subset of initial functions
q)count 1_cols featsNew
92
Deprecated
This function was previously defined as .ml.fresh.createfeatures.
That is still callable but will be removed after version 3.0.
The following functions contain some Python dependency.
funcs:`aggAutoCorr`augFuller`fftAggReg`fftCoeff`numCwtPeaks`partAutoCorrelation`spktWelch
If only q-dependent functions are to be applied, run the following update
command on the .ml.fresh.params table.
q)update valid:0b from `.ml.fresh.params where f in funcs
Modifications to the file hyperparameters.json within the FRESH folder allows fine tuning of the number and variety of calculations to be made. Users can create their own features by defining a function within the .ml.fresh.feat namespace within feat.q and, if necessary, providing relevant hyperparameters in .ml.fresh.params.
.ml.fresh.significantFeatures
Statistically significant features based on defined selection procedure
.ml.fresh.significantFeatures[tab;target;func]
Where
tabis the value side of a table of created featurestargetis a list of targets corresponding to the rows of tabletabfuncis a projection with example syntax.ml.fresh.kSigFeat 10
returns a list of features deemed statistically significant according to the user defined procedure within parameter func.
// Combination of col avgs
q)target:value exec avg col2+.001*col2 by date from tab
// BHY procedure with a FDR level of 0.05
q)show sigBH:.ml.fresh.significantFeatures[value feats;target;.ml.fresh.benjhoch 0.05]
`col2_mean`col2_sumVal`col2_fftCoeff_coeff_10_coeff_0_real`col2_fftCoeff_coef..
// Extract the top 20 best features
q)show sigK:.ml.fresh.significantFeatures[value feats;target;.ml.fresh.kSigFeat 20]
`col2_mean`col2_sumVal`col2_fftCoeff_coeff_10_coeff_0_real`col2_fftCoeff_coef..
// Extract the top 5th percentile of created features
q)show sigP:.ml.fresh.significantFeatures[value feats;target;.ml.fresh.percentile 0.05]
`col2_absEnergy`col2_mean`col2_med`col2_skewness`col2_sumVal`col2_c3_lag_1`co..
// Check the count of each method to show differences in outputs
q)count each (sigBH;sigK;sigP)
30 20 22
Deprecated
Earlier versions of this function were defined as .ml.fresh.significantfeatures and .ml.fresh.ksigfeat.
They are still callable but will be removed after version 3.0.