class LDA extends ClassifierReal
The LDA class implements a Linear Discriminant Analysis 'LDA' classifier.
It places a vector into a group according to its maximal discriminant function.
FIX - currently only works when the number of classes 'k' = 2.
- See also
en.wikipedia.org/wiki/Linear_discriminant_analysis
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- LDA
- ClassifierReal
- Classifier
- Model
- ConfusionFit
- Error
- QoF
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Instance Constructors
-
new
LDA(x: MatriD, y: VectoI, fn_: Strings = null, k: Int = 2, cn_: Strings = null, hparam: HyperParameter = null)
- x
the real-valued training/test data vectors stored as rows of a matrix
- y
the training/test classification vector, where y_i = class for row i of the matrix x
- fn_
the names for all features/variables
- k
the number of classes (k in {0, 1, ...k-1}
- cn_
the names for all classes
- hparam
the hyper-parameters
Value Members
-
def
accuracy: Double
Compute the accuracy of the classification, i.e., the fraction of correct classifications.
Compute the accuracy of the classification, i.e., the fraction of correct classifications. Note, the correct classifications 'tp_i' are in the main diagonal of the confusion matrix.
- Definition Classes
- ConfusionFit
-
def
calcCorrelation: MatriD
Calculate the correlation matrix for the feature vectors 'fea'.
Calculate the correlation matrix for the feature vectors 'fea'. If the correlations are too high, the independence assumption may be dubious.
- Definition Classes
- ClassifierReal
-
def
calcCorrelation2(zrg: Range, xrg: Range): MatriD
Calculate the correlation matrix for the feature vectors of Z (Level 3) and those of X (level 2).
Calculate the correlation matrix for the feature vectors of Z (Level 3) and those of X (level 2). If the correlations are too high, the independence assumption may be dubious.
- zrg
the range of Z-columns
- xrg
the range of X-columns
- Definition Classes
- ClassifierReal
-
def
classify(z: VectoD): (Int, String, Double)
Classify vector 'z' by computing its discriminant function 'f' for each group and return the group index with the maximun value for 'f'.
Classify vector 'z' by computing its discriminant function 'f' for each group and return the group index with the maximun value for 'f'.
- z
the real vector to classify
- Definition Classes
- LDA → Classifier
-
def
classify(xx: MatriD = x): VectoI
Classify all of the row vectors in matrix 'xx'.
Classify all of the row vectors in matrix 'xx'.
- xx
the row vectors to classify (defaults to x)
- Definition Classes
- ClassifierReal
-
def
classify(z: VectoI): (Int, String, Double)
Given a new discrete (integer-valued) data vector 'z', determine which class it belongs to, by first converting it to a vector of doubles.
Given a new discrete (integer-valued) data vector 'z', determine which class it belongs to, by first converting it to a vector of doubles. Return the best class, its name and its relative probability
- z
the vector to classify
- Definition Classes
- ClassifierReal → Classifier
-
def
clearConfusion(): Unit
Clear the total cummulative confusion matrix.
Clear the total cummulative confusion matrix.
- Definition Classes
- ConfusionFit
-
def
confusion(yp: VectoI, yy: VectoI = y): MatriI
Compare the actual class 'y' vector versus the predicted class 'yp' vector, returning the confusion matrix 'cmat', which for 'k = 2' is
Compare the actual class 'y' vector versus the predicted class 'yp' vector, returning the confusion matrix 'cmat', which for 'k = 2' is
yp 0 1 ---------- y 0 | tn fp | 1 | fn tp | ----------
Note: ScalaTion's confusion matrix is Actual × Predicted, but to swap the position of actual 'y' (rows) with predicted 'yp' (columns) simply use 'cmat.t', the transpose of 'cmat'.
- yp
the precicted class values/labels
- yy
the actual class values/labels for full (y) or test (y_e) dataset
- Definition Classes
- ConfusionFit
- See also
www.dataschool.io/simple-guide-to-confusion-matrix-terminology
-
def
contrast(yp: VectoI, yy: VectoI = y): Unit
Contract the actual class 'yy' vector versus the predicted class 'yp' vector.
Contract the actual class 'yy' vector versus the predicted class 'yp' vector.
- yp
the predicted class values/labels
- yy
the actual class values/labels for full (y) or test (y_e) dataset
- Definition Classes
- ConfusionFit
-
def
corrected_cov(xc: MatriD): MatriD
Compute the corrected covariance matrix.
Compute the corrected covariance matrix.
- xc
the corrected martix whose corrected covariance matrix is sought
-
def
crossValidate(nx: Int = 10, show: Boolean = false): Array[Statistic]
Test the accuracy of the classified results by cross-validation, returning the Quality of Fit (QoF) measures such as accuracy.
Test the accuracy of the classified results by cross-validation, returning the Quality of Fit (QoF) measures such as accuracy. This method slices out instances/rows to form the test dataset.
- nx
number of folds/crosses and cross-validations (defaults to 10x).
- show
the show flag (show result from each iteration)
- Definition Classes
- ClassifierReal → Classifier
-
def
crossValidateRand(nx: Int = 10, show: Boolean = false): Array[Statistic]
Test the accuracy of the classified results by cross-validation, returning the Quality of Fit (QoF) measures such as accuracy.
Test the accuracy of the classified results by cross-validation, returning the Quality of Fit (QoF) measures such as accuracy. This method randomizes the instances/rows selected for the test dataset.
- nx
number of folds/crosses and cross-validations (defaults to 10x).
- show
the show flag (show result from each iteration)
- Definition Classes
- ClassifierReal → Classifier
-
def
diagnose(e: VectoD, yy: VectoD, yp: VectoD, w: VectoD = null, ym: Double = noDouble): Unit
Diagnose the health of the model by computing the Quality of Fit (QoF) measures, from the error/residual vector and the predicted & actual responses.
Diagnose the health of the model by computing the Quality of Fit (QoF) measures, from the error/residual vector and the predicted & actual responses. For some models the instances may be weighted.
- e
the m-dimensional error/residual vector (yy - yp)
- yy
the actual response vector to use (test/full)
- yp
the predicted response vector (test/full)
- w
the weights on the instances (defaults to null)
- ym
the mean of the actual response vector to use (test/full)
- Definition Classes
- ConfusionFit → QoF
- See also
Regression_WLS
-
def
eval(xx: MatriD, yy: VectoD = null): ClassifierReal
Test the quality of the training with a test dataset and return the fraction of correct classifications.
Test the quality of the training with a test dataset and return the fraction of correct classifications.
- xx
the integer-valued test vectors stored as rows of a matrix
- yy
the classification vector (impl. classes should ignore or default yy to y)
- Definition Classes
- ClassifierReal → Model
-
def
f1_measure(p: Double, r: Double): Double
Compute the F1-measure, i.e., the harmonic mean of the precision and recall.
Compute the F1-measure, i.e., the harmonic mean of the precision and recall.
- p
the precision
- r
the recall
- Definition Classes
- ConfusionFit
-
def
f1v: VectoD
Compute the micro-F1-measure vector, i.e., the harmonic mean of the precision and recall.
Compute the micro-F1-measure vector, i.e., the harmonic mean of the precision and recall.
- Definition Classes
- ConfusionFit
-
def
f_(z: Double): String
Format a double value.
-
def
featureSelection(TOL: Double = 0.01): Unit
Perform feature selection on the classifier.
Perform feature selection on the classifier. Use backward elimination technique, that is, remove the least significant feature, in terms of cross- validation accuracy, in each round.
- TOL
tolerance indicating negligible accuracy loss when removing features
- Definition Classes
- ClassifierReal
-
def
fit: VectoD
Return the Quality of Fit (QoF) measures corresponding to the labels given above in the 'fitLabel' method.
Return the Quality of Fit (QoF) measures corresponding to the labels given above in the 'fitLabel' method.
- Definition Classes
- ConfusionFit → QoF
-
def
fitLabel: Seq[String]
Return the labels for the Quality of Fit (QoF) measures.
Return the labels for the Quality of Fit (QoF) measures. Override to add additional QoF measures.
- Definition Classes
- ConfusionFit → QoF
-
def
fitLabel_v: Seq[String]
Return the labels for the Quality of Fit (QoF) measures.
Return the labels for the Quality of Fit (QoF) measures. Override to add additional QoF measures.
- Definition Classes
- ConfusionFit
-
def
fitMap: Map[String, String]
Build a map of quality of fit measures (use of
LinkedHashMapmakes it ordered).Build a map of quality of fit measures (use of
LinkedHashMapmakes it ordered).- Definition Classes
- QoF
-
def
fitMicroMap: Map[String, VectoD]
Return the Quality of Fit (QoF) vector micor-measures, i.e., measures for each class.
Return the Quality of Fit (QoF) vector micor-measures, i.e., measures for each class.
- Definition Classes
- ConfusionFit
-
final
def
flaw(method: String, message: String): Unit
- Definition Classes
- Error
-
def
help: String
Return the help string that describes the Quality of Fit (QoF) measures provided by the
ConfusionFitclass.Return the help string that describes the Quality of Fit (QoF) measures provided by the
ConfusionFitclass. Override to correspond to 'fitLabel'.- Definition Classes
- ConfusionFit → QoF
-
def
hparameter: HyperParameter
Return the model hyper-parameters (if none, return null).
Return the model hyper-parameters (if none, return null). Hyper-parameters may be used to regularize parameters or tune the optimizer.
- Definition Classes
- ClassifierReal → Model
-
def
kappa: Double
Compute Cohen's 'kappa' coefficient that measures agreement between actual 'y' and predicted 'yp' classifications.
Compute Cohen's 'kappa' coefficient that measures agreement between actual 'y' and predicted 'yp' classifications.
- Definition Classes
- ConfusionFit
- See also
en.wikipedia.org/wiki/Cohen%27s_kappa
-
val
modelConcept: URI
An optional reference to an ontological concept
An optional reference to an ontological concept
- Definition Classes
- Model
-
def
modelName: String
An optional name for the model (or modeling technique)
An optional name for the model (or modeling technique)
- Definition Classes
- Model
-
def
p_r_s(): Unit
Compute the micro-precision, micro-recall and micro-specificity vectors which have elements for each class i in {0, 1, ...
Compute the micro-precision, micro-recall and micro-specificity vectors which have elements for each class i in {0, 1, ... k-1}. -------------------------------------------------------------------------- Precision is the fraction classified as true that are actually true. Recall (sensitivity) is the fraction of the actually true that are classified as true. Specificity is the fraction of the actually false that are classified as false. -------------------------------------------------------------------------- Note, for 'k = 2', ordinary precision 'p', recall 'r' and specificity 's' will correspond to the last elements in the 'pv', 'rv' and 'sv' micro vectors.
- Definition Classes
- ConfusionFit
-
def
parameter: VectoD
Return the vector of model parameter vector.
-
def
pseudo_rSq: Double
Compute the Efron's pseudo R-squared value.
Compute the Efron's pseudo R-squared value. Override to McFadden's, etc.
- Definition Classes
- ConfusionFit
-
def
report: String
Return a basic report on the trained model.
Return a basic report on the trained model.
- Definition Classes
- ClassifierReal → Model
-
def
reset(): Unit
Reset method not applicable.
Reset method not applicable.
- Definition Classes
- LDA → Classifier
-
def
setStream(str: Int = 0): Unit
Set the random number 'stream' to 'str'.
Set the random number 'stream' to 'str'. This is useful for testing purposes, since a fixed stream will follow the same sequence each time.
- str
the new fixed random number stream
- Definition Classes
- Classifier
-
def
size: Int
Return the number of data vectors in training/test-set (# rows).
Return the number of data vectors in training/test-set (# rows).
- Definition Classes
- ClassifierReal → Classifier
-
def
summary(b: VectoD = null, show: Boolean = false): String
Produce a summary report with diagnostics and the overall quality of fit.
Produce a summary report with diagnostics and the overall quality of fit.
- b
the parameters of the model
- show
flag indicating whether to print the summary
- Definition Classes
- ConfusionFit
-
def
test(xx: MatriD, yy: VectoI): Double
Test the quality of the training with a test-set and return the fraction of correct classifications.
Test the quality of the training with a test-set and return the fraction of correct classifications.
- xx
the real-valued test vectors stored as rows of a matrix
- yy
the test classification vector, where 'yy_i = class for row i of xx'
- Definition Classes
- ClassifierReal
-
def
test(itest: Ints): Double
Test the quality of the training with a test-set and return the fraction of correct classifications.
Test the quality of the training with a test-set and return the fraction of correct classifications.
- itest
indices of the instances considered test data
- Definition Classes
- ClassifierReal → Classifier
-
def
test(testStart: Int, testEnd: Int): Double
Test the quality of the training with a test dataset and return the fraction of correct classifications.
Test the quality of the training with a test dataset and return the fraction of correct classifications. Can be used when the dataset is randomized so that the testing/training part of a dataset corresponds to simple slices of vectors and matrices.
- testStart
the beginning of test region (inclusive).
- testEnd
the end of test region (exclusive).
- Definition Classes
- Classifier
-
def
tn_fp_fn_tp(con: MatriI = cmat): (Double, Double, Double, Double)
Return the confusion matrix for 'k = 2' as a tuple (tn, fp, fn, tp).
Return the confusion matrix for 'k = 2' as a tuple (tn, fp, fn, tp).
- con
the confusion matrix (defaults to cmat)
- Definition Classes
- ConfusionFit
-
def
total_cmat(): MatriI
Return a copy of the total cummulative confusion matrix 'tcmat' and clear 'tcmat'.
Return a copy of the total cummulative confusion matrix 'tcmat' and clear 'tcmat'.
- Definition Classes
- ConfusionFit
-
def
train(itest: Ints): LDA
Train the classifer by computing 'pcovar', 'ipcovar' and 'prior' that are needed to compute the discriminant functions 'f'.
Train the classifer by computing 'pcovar', 'ipcovar' and 'prior' that are needed to compute the discriminant functions 'f'. These are computed in the 'classify' method.
- itest
the indices of the test data - FIX - not used yet
- Definition Classes
- LDA → Classifier
-
def
train(xx: MatriD = null, yy: VectoD = null): Classifier
Train the classifier by computing the probabilities from a training dataset of data vectors and their classifications.
Train the classifier by computing the probabilities from a training dataset of data vectors and their classifications. Must be implemented in any extending class. Can be used when the whole dataset is used for training.
- xx
the data/input matrix (impl. classes should ignore or default xx to x)
- yy
the response/classification vector (impl. classes should ignore or default yy to y)
- Definition Classes
- Classifier → Model
-
def
train(testStart: Int, testEnd: Int): Classifier
Train the classifier by computing the probabilities from a training dataset of data vectors and their classifications.
Train the classifier by computing the probabilities from a training dataset of data vectors and their classifications. Must be implemented in any extending class. Can be used when the dataset is randomized so that the training part of a dataset corresponds to simple slices of vectors and matrices.
- testStart
starting index of test region (inclusive) used in cross-validation
- testEnd
ending index of test region (exclusive) used in cross-validation
- Definition Classes
- Classifier
-
def
vc_default: Array[Int]
Return default values for binary input data (value count 'vc' set to 2).
Return default values for binary input data (value count 'vc' set to 2). Also may be used for binning into two categories.
- Definition Classes
- ClassifierReal