Introduction:

Dataset with electrical impedance measurements of freshly excised tissue samples from the breast.

Impedance measurements were made at the frequencies: 15.625, 31.25, 62.5, 125, 250, 500, 1000 KHz Impedance measurements of freshly excised breast tissue were made at the follwoing frequencies: 15.625, 31.25, 62.5, 125, 250, 500, 1000 KHz. These measurements plotted in the (real, -imaginary) plane constitute the impedance spectrum from where the breast tissue features are computed. The dataset can be used for predicting the classification of either the original 6 classes or of 4 classes by merging together the fibro-adenoma, mastopathy and glandular classes whose discrimination is not important (they cannot be accurately discriminated anyway).

Attribute Information:

I0 Impedivity (ohm) at zero frequency PA500 phase angle at 500 KHz HFS high-frequency slope of phase angle DA impedance distance between spectral ends AREA area under spectrum A/DA area normalized by DA MAX IP maximum of the spectrum DR distance between I0 and real part of the maximum frequency point P length of the spectral curve Class car(carcinoma), fad (fibro-adenoma), mas (mastopathy), gla (glandular), con (connective), adi (adipose).

Source:

JP Marques de Sá, INEB-Instituto de Engenharia Biomédica, Porto, Portugal; e-mail: jpmdesa ‘@’ gmail.com J Jossinet, inserm, Lyon, France

Breast Tissue Data Set:

## Classes 'tbl_df', 'tbl' and 'data.frame':    106 obs. of  11 variables:
##  $ Case #: num  1 2 3 4 5 6 7 8 9 10 ...
##  $ Class : chr  "car" "car" "car" "car" ...
##  $ I0    : num  525 330 552 380 363 ...
##  $ PA500 : num  0.187 0.227 0.232 0.241 0.201 ...
##  $ HFS   : num  0.0321 0.2653 0.0635 0.2862 0.2443 ...
##  $ DA    : num  229 121 265 138 125 ...
##  $ Area  : num  6844 3163 11888 5402 3290 ...
##  $ A/DA  : num  29.9 26.1 44.9 39.2 26.3 ...
##  $ Max IP: num  60.2 69.7 77.8 88.8 69.4 ...
##  $ DR    : num  220.7 99.1 253.8 105.2 103.9 ...
##  $ P     : num  557 400 657 494 425 ...

Pre_Processing the Data Set:

Independent Training Set

##  num [1:84, 1:10] 0.808 0.683 0.577 0.76 0.731 ...
##  - attr(*, "dimnames")=List of 2
##   ..$ : chr [1:84] "85" "72" "61" "80" ...
##   ..$ : chr [1:10] "Case.." "I0" "PA500" "HFS" ...

Independent Testing Set

##  num [1:22, 1:10] 0 0.0192 0.1058 0.1154 0.2404 ...
##  - attr(*, "dimnames")=List of 2
##   ..$ : chr [1:22] "2" "4" "13" "14" ...
##   ..$ : chr [1:10] "Case.." "I0" "PA500" "HFS" ...

Dependent Training Set

##  num [1:84, 1:7] 0 0 0 0 0 0 0 0 0 0 ...
##  - attr(*, "dimnames")=List of 2
##   ..$ : chr [1:84] "85" "72" "61" "80" ...
##   ..$ : chr [1:7] "1" "2" "3" "4" ...

Dependent Testing Set

##  num [1:22, 1:7] 0 0 0 0 0 0 0 0 0 0 ...
##  - attr(*, "dimnames")=List of 2
##   ..$ : chr [1:22] "2" "4" "13" "14" ...
##   ..$ : chr [1:7] "1" "2" "3" "4" ...

Neural Network Model Architecture:

## ___________________________________________________________________________
## Layer (type)                     Output Shape                  Param #     
## ===========================================================================
## dense_1 (Dense)                  (None, 128)                   1408        
## ___________________________________________________________________________
## dropout_1 (Dropout)              (None, 128)                   0           
## ___________________________________________________________________________
## dense_2 (Dense)                  (None, 7)                     903         
## ===========================================================================
## Total params: 2,311
## Trainable params: 2,311
## Non-trainable params: 0
## ___________________________________________________________________________

Training the Neural Network Model:

## Trained on 67 samples, validated on 17 samples (batch_size=2, epochs=100)
## Final epoch (plot to see history):
## val_loss: 0.15
##  val_acc: 0.9496
##     loss: 0.1067
##      acc: 0.9552

Predict Using the Testing Dataset:

0 1
0 130 7
1 2 15

Evaluate the Model’s Performance:

Accuracy
94.16