Unsupervised Machine Learning

Giorgia Fortuna, Wolfram Research

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Introduction

Supervised Learning

Given some labeled data, find a model that can predict the labels of new points:

dataset =  {->2,->5,->8,->0,->2,->7,->5,->1,->3,->0,->3,->9,->6,->2,->8,->2,->0,->6,->6,->1,->1,->7,->8,->5,->0,->4,->7,->6,->0,->2,->5,->3,->1,->5,->6,->7,->5,->4,->1,->9,->3,->6};

c = Classify[dataset]

c[{,,}]

Unsupervised Learning

inferring a function to describe hidden structure from unlabeled data.

The description of the data could be given in terms of clusters:

->

The description of the data could be given in terms of the distribution that could have generated the data.

This can be used to generate new samples that look like examples in the training set:

({{, , , , }, {, , , , }, {, , , , }, {, , , , }})->

The learned distribution could be used to impute missing values.

({{, }})

The learned distribution could be used to perform anomaly detection.

({{, , , , }, {, , , , }, {, , , , }, {, , , , }, {, , , , }})  -> PDF[] <<1

ClusterClassify and LearnDistribution

ClusterClassify (new in 10.4) can be used to analyze your data in terms of clusters.

SeedRandom[10]
colors = RandomColor[100];
ClusteringTree[colors, "ClusterDissimilarityFunction"->"Centroid"]

Similarly to Classify, it outputs a ClssifierFunction that labels new points.

c = ClusterClassify[colors]

c = ClusterClassify[colors, 5]

c[{, Red,  , Blue, "Green", }]

ClassifierInformation[c]

ClusterClassify in Practice

Breast Cancer

Source “https://archive.ics.uci.edu/ml/machine-learning-databases/breast-cancer-wisconsin/”.

We can use cluster analysis to study if the information we have is relevant for the diagnosis or not.

labels = {"ID Number", "Clump Thickness", "Uniformity of Cell Size", "Uniformity of Cell Shape", 
"Marginal Adhesion", "Single Epithelial Cell Size", " Bare Nuclei", "Bland Chromatin", "Normal Nucleoli", "Mitoses", "Class"};

{2 -> "benign",4-> "malignant"}

dataset (from "https://archive.ics.uci.edu/ml/machine-learning-databases/breast-cancer-wisconsin/")

association = {\[LeftAssociation]"ID Number"->1000025,"Clump Thickness"->5,"Uniformity of Cell Size"->1,"Uniformity of Cell Shape"->1,"Marginal Adhesion"->1,"Single Epithelial Cell Size"->2," Bare Nuclei"->1,"Bland Chromatin"->3,"Normal Nucleoli"->1,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->1002945,"Clump Thickness"->5,"Uniformity of Cell Size"->4,"Uniformity of Cell Shape"->4,"Marginal Adhesion"->5,"Single Epithelial Cell Size"->7," Bare Nuclei"->10,"Bland Chromatin"->3,"Normal Nucleoli"->2,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->1015425,"Clump Thickness"->3,"Uniformity of Cell Size"->1,"Uniformity of Cell Shape"->1,"Marginal Adhesion"->1,"Single Epithelial Cell Size"->2," Bare Nuclei"->2,"Bland Chromatin"->3,"Normal Nucleoli"->1,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->1016277,"Clump Thickness"->6,"Uniformity of Cell Size"->8,"Uniformity of Cell Shape"->8,"Marginal Adhesion"->1,"Single Epithelial Cell Size"->3," Bare Nuclei"->4,"Bland Chromatin"->3,"Normal Nucleoli"->7,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->1017023,"Clump Thickness"->4,"Uniformity of Cell Size"->1,"Uniformity of Cell Shape"->1,"Marginal Adhesion"->3,"Single Epithelial Cell Size"->2," Bare Nuclei"->1,"Bland Chromatin"->3,"Normal Nucleoli"->1,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->1017122,"Clump Thickness"->8,"Uniformity of Cell Size"->10,"Uniformity of Cell Shape"->10,"Marginal Adhesion"->8,"Single Epithelial Cell Size"->7," Bare Nuclei"->10,"Bland Chromatin"->9,"Normal Nucleoli"->7,"Mitoses"->1,"Class"->4\[RightAssociation],\[LeftAssociation]"ID Number"->1018099,"Clump Thickness"->1,"Uniformity of Cell Size"->1,"Uniformity of Cell Shape"->1,"Marginal Adhesion"->1,"Single Epithelial Cell Size"->2," Bare Nuclei"->10,"Bland Chromatin"->3,"Normal Nucleoli"->1,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID 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Nuclei"->1,"Bland Chromatin"->3,"Normal Nucleoli"->1,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->1036172,"Clump Thickness"->2,"Uniformity of Cell Size"->1,"Uniformity of Cell Shape"->1,"Marginal Adhesion"->1,"Single Epithelial Cell Size"->2," Bare Nuclei"->1,"Bland Chromatin"->2,"Normal Nucleoli"->1,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->1041801,"Clump Thickness"->5,"Uniformity of Cell Size"->3,"Uniformity of Cell Shape"->3,"Marginal Adhesion"->3,"Single Epithelial Cell Size"->2," Bare Nuclei"->3,"Bland Chromatin"->4,"Normal Nucleoli"->4,"Mitoses"->1,"Class"->4\[RightAssociation],\[LeftAssociation]"ID Number"->1043999,"Clump Thickness"->1,"Uniformity of Cell Size"->1,"Uniformity of Cell Shape"->1,"Marginal Adhesion"->1,"Single Epithelial Cell Size"->2," Bare Nuclei"->3,"Bland Chromatin"->3,"Normal Nucleoli"->1,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->1044572,"Clump 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Shape"->1,"Marginal Adhesion"->1,"Single Epithelial Cell Size"->2," Bare Nuclei"->1,"Bland Chromatin"->1,"Normal Nucleoli"->1,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->1253955,"Clump Thickness"->8,"Uniformity of Cell Size"->7,"Uniformity of Cell Shape"->4,"Marginal Adhesion"->4,"Single Epithelial Cell Size"->5," Bare Nuclei"->3,"Bland Chromatin"->5,"Normal Nucleoli"->10,"Mitoses"->1,"Class"->4\[RightAssociation],\[LeftAssociation]"ID Number"->1257366,"Clump Thickness"->3,"Uniformity of Cell Size"->1,"Uniformity of Cell Shape"->1,"Marginal Adhesion"->1,"Single Epithelial Cell Size"->2," Bare Nuclei"->1,"Bland Chromatin"->1,"Normal Nucleoli"->1,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->1260659,"Clump Thickness"->3,"Uniformity of Cell Size"->1,"Uniformity of Cell Shape"->4,"Marginal Adhesion"->1,"Single Epithelial Cell Size"->2," Bare Nuclei"->1,"Bland Chromatin"->1,"Normal Nucleoli"->1,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->1268952,"Clump Thickness"->10,"Uniformity of Cell Size"->10,"Uniformity of Cell Shape"->7,"Marginal Adhesion"->8,"Single Epithelial Cell Size"->7," Bare Nuclei"->1,"Bland Chromatin"->10,"Normal Nucleoli"->10,"Mitoses"->3,"Class"->4\[RightAssociation],\[LeftAssociation]"ID Number"->1275807,"Clump Thickness"->4,"Uniformity of Cell Size"->2,"Uniformity of Cell Shape"->4,"Marginal Adhesion"->3,"Single Epithelial Cell Size"->2," Bare Nuclei"->2,"Bland Chromatin"->2,"Normal Nucleoli"->1,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->1277792,"Clump Thickness"->4,"Uniformity of Cell Size"->1,"Uniformity of Cell Shape"->1,"Marginal Adhesion"->1,"Single Epithelial Cell Size"->2," Bare Nuclei"->1,"Bland Chromatin"->1,"Normal Nucleoli"->1,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->1277792,"Clump Thickness"->5,"Uniformity of Cell Size"->1,"Uniformity of Cell Shape"->1,"Marginal Adhesion"->3,"Single Epithelial Cell Size"->2," Bare Nuclei"->1,"Bland Chromatin"->1,"Normal Nucleoli"->1,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->1285722,"Clump Thickness"->4,"Uniformity of Cell Size"->1,"Uniformity of Cell Shape"->1,"Marginal Adhesion"->3,"Single Epithelial Cell Size"->2," Bare Nuclei"->1,"Bland Chromatin"->1,"Normal Nucleoli"->1,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->1288608,"Clump Thickness"->3,"Uniformity of Cell Size"->1,"Uniformity of Cell Shape"->1,"Marginal Adhesion"->1,"Single Epithelial Cell Size"->2," Bare Nuclei"->1,"Bland Chromatin"->2,"Normal Nucleoli"->1,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->1290203,"Clump Thickness"->3,"Uniformity of Cell Size"->1,"Uniformity of Cell Shape"->1,"Marginal Adhesion"->1,"Single Epithelial Cell Size"->2," Bare Nuclei"->1,"Bland Chromatin"->2,"Normal Nucleoli"->1,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->1294413,"Clump Thickness"->1,"Uniformity of Cell Size"->1,"Uniformity of Cell Shape"->1,"Marginal Adhesion"->1,"Single Epithelial Cell Size"->2," Bare Nuclei"->1,"Bland Chromatin"->1,"Normal Nucleoli"->1,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->1299596,"Clump Thickness"->2,"Uniformity of Cell Size"->1,"Uniformity of Cell Shape"->1,"Marginal Adhesion"->1,"Single Epithelial Cell Size"->2," Bare Nuclei"->1,"Bland Chromatin"->1,"Normal Nucleoli"->1,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->1303489,"Clump Thickness"->3,"Uniformity of Cell Size"->1,"Uniformity of Cell Shape"->1,"Marginal Adhesion"->1,"Single Epithelial Cell Size"->2," Bare Nuclei"->1,"Bland Chromatin"->2,"Normal Nucleoli"->1,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->1311033,"Clump Thickness"->1,"Uniformity of Cell Size"->2,"Uniformity of Cell Shape"->2,"Marginal Adhesion"->1,"Single Epithelial Cell Size"->2," Bare Nuclei"->1,"Bland Chromatin"->1,"Normal Nucleoli"->1,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->1311108,"Clump Thickness"->1,"Uniformity of Cell Size"->1,"Uniformity of Cell Shape"->1,"Marginal Adhesion"->3,"Single Epithelial Cell Size"->2," Bare Nuclei"->1,"Bland Chromatin"->1,"Normal Nucleoli"->1,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->1315807,"Clump Thickness"->5,"Uniformity of Cell Size"->10,"Uniformity of Cell Shape"->10,"Marginal Adhesion"->10,"Single Epithelial Cell Size"->10," Bare Nuclei"->2,"Bland Chromatin"->10,"Normal Nucleoli"->10,"Mitoses"->10,"Class"->4\[RightAssociation],\[LeftAssociation]"ID Number"->1318671,"Clump Thickness"->3,"Uniformity of Cell Size"->1,"Uniformity of Cell Shape"->1,"Marginal Adhesion"->1,"Single Epithelial Cell Size"->2," Bare Nuclei"->1,"Bland Chromatin"->2,"Normal Nucleoli"->1,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->1319609,"Clump Thickness"->3,"Uniformity of Cell Size"->1,"Uniformity of Cell Shape"->1,"Marginal Adhesion"->2,"Single Epithelial Cell Size"->3," Bare Nuclei"->4,"Bland Chromatin"->1,"Normal Nucleoli"->1,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->1323477,"Clump Thickness"->1,"Uniformity of Cell Size"->2,"Uniformity of Cell Shape"->1,"Marginal Adhesion"->3,"Single Epithelial Cell Size"->2," Bare Nuclei"->1,"Bland Chromatin"->2,"Normal Nucleoli"->1,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->1324572,"Clump Thickness"->5,"Uniformity of Cell Size"->1,"Uniformity of Cell Shape"->1,"Marginal Adhesion"->1,"Single Epithelial Cell Size"->2," Bare Nuclei"->1,"Bland Chromatin"->2,"Normal Nucleoli"->2,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->1324681,"Clump Thickness"->4,"Uniformity of Cell Size"->1,"Uniformity of Cell Shape"->1,"Marginal Adhesion"->1,"Single Epithelial Cell Size"->2," Bare Nuclei"->1,"Bland Chromatin"->2,"Normal Nucleoli"->1,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->1325159,"Clump Thickness"->3,"Uniformity of Cell Size"->1,"Uniformity of Cell Shape"->1,"Marginal Adhesion"->1,"Single Epithelial Cell Size"->2," Bare Nuclei"->1,"Bland Chromatin"->3,"Normal Nucleoli"->1,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->1326892,"Clump Thickness"->3,"Uniformity of Cell Size"->1,"Uniformity of Cell Shape"->1,"Marginal Adhesion"->1,"Single Epithelial Cell Size"->2," Bare Nuclei"->1,"Bland Chromatin"->2,"Normal Nucleoli"->1,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->1330361,"Clump Thickness"->5,"Uniformity of Cell Size"->1,"Uniformity of Cell Shape"->1,"Marginal Adhesion"->1,"Single Epithelial Cell Size"->2," Bare Nuclei"->1,"Bland Chromatin"->2,"Normal Nucleoli"->1,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->1333877,"Clump Thickness"->5,"Uniformity of Cell Size"->4,"Uniformity of Cell Shape"->5,"Marginal Adhesion"->1,"Single Epithelial Cell Size"->8," Bare Nuclei"->1,"Bland Chromatin"->3,"Normal Nucleoli"->6,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->1334015,"Clump Thickness"->7,"Uniformity of Cell Size"->8,"Uniformity of Cell Shape"->8,"Marginal Adhesion"->7,"Single Epithelial Cell Size"->3," Bare Nuclei"->10,"Bland Chromatin"->7,"Normal Nucleoli"->2,"Mitoses"->3,"Class"->4\[RightAssociation],\[LeftAssociation]"ID Number"->1334667,"Clump Thickness"->1,"Uniformity of Cell Size"->1,"Uniformity of Cell Shape"->1,"Marginal Adhesion"->1,"Single Epithelial Cell Size"->2," Bare Nuclei"->1,"Bland Chromatin"->1,"Normal Nucleoli"->1,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->1339781,"Clump Thickness"->1,"Uniformity of Cell Size"->1,"Uniformity of Cell Shape"->1,"Marginal Adhesion"->1,"Single Epithelial Cell Size"->2," Bare Nuclei"->1,"Bland Chromatin"->2,"Normal Nucleoli"->1,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->1339781,"Clump Thickness"->4,"Uniformity of Cell Size"->1,"Uniformity of Cell Shape"->1,"Marginal Adhesion"->1,"Single Epithelial Cell Size"->2," Bare Nuclei"->1,"Bland Chromatin"->3,"Normal Nucleoli"->1,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->13454352,"Clump Thickness"->1,"Uniformity of Cell Size"->1,"Uniformity of Cell Shape"->3,"Marginal Adhesion"->1,"Single Epithelial Cell Size"->2," Bare Nuclei"->1,"Bland Chromatin"->2,"Normal Nucleoli"->1,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->1345452,"Clump Thickness"->1,"Uniformity of Cell Size"->1,"Uniformity of Cell Shape"->3,"Marginal Adhesion"->1,"Single Epithelial Cell Size"->2," Bare Nuclei"->1,"Bland Chromatin"->2,"Normal Nucleoli"->1,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->1345593,"Clump Thickness"->3,"Uniformity of Cell Size"->1,"Uniformity of Cell Shape"->1,"Marginal Adhesion"->3,"Single Epithelial Cell Size"->2," Bare Nuclei"->1,"Bland Chromatin"->2,"Normal Nucleoli"->1,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->1347749,"Clump Thickness"->1,"Uniformity of Cell Size"->1,"Uniformity of Cell Shape"->1,"Marginal Adhesion"->1,"Single Epithelial Cell Size"->2," Bare Nuclei"->1,"Bland Chromatin"->1,"Normal Nucleoli"->1,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->1347943,"Clump Thickness"->5,"Uniformity of Cell Size"->2,"Uniformity of Cell Shape"->2,"Marginal Adhesion"->2,"Single Epithelial Cell Size"->2," Bare Nuclei"->1,"Bland Chromatin"->1,"Normal Nucleoli"->1,"Mitoses"->2,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->1348851,"Clump Thickness"->3,"Uniformity of Cell Size"->1,"Uniformity of Cell Shape"->1,"Marginal Adhesion"->1,"Single Epithelial Cell Size"->2," Bare Nuclei"->1,"Bland Chromatin"->3,"Normal Nucleoli"->1,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->1350319,"Clump Thickness"->5,"Uniformity of Cell Size"->7,"Uniformity of Cell Shape"->4,"Marginal Adhesion"->1,"Single Epithelial Cell Size"->6," Bare Nuclei"->1,"Bland Chromatin"->7,"Normal Nucleoli"->10,"Mitoses"->3,"Class"->4\[RightAssociation],\[LeftAssociation]"ID Number"->1350423,"Clump Thickness"->5,"Uniformity of Cell Size"->10,"Uniformity of Cell Shape"->10,"Marginal Adhesion"->8,"Single Epithelial Cell Size"->5," Bare Nuclei"->5,"Bland Chromatin"->7,"Normal Nucleoli"->10,"Mitoses"->1,"Class"->4\[RightAssociation],\[LeftAssociation]"ID Number"->1352848,"Clump Thickness"->3,"Uniformity of Cell Size"->10,"Uniformity of Cell Shape"->7,"Marginal Adhesion"->8,"Single Epithelial Cell Size"->5," Bare Nuclei"->8,"Bland Chromatin"->7,"Normal Nucleoli"->4,"Mitoses"->1,"Class"->4\[RightAssociation],\[LeftAssociation]"ID Number"->1353092,"Clump Thickness"->3,"Uniformity of Cell Size"->2,"Uniformity of Cell Shape"->1,"Marginal Adhesion"->2,"Single Epithelial Cell Size"->2," Bare Nuclei"->1,"Bland Chromatin"->3,"Normal Nucleoli"->1,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->1354840,"Clump Thickness"->2,"Uniformity of Cell Size"->1,"Uniformity of Cell Shape"->1,"Marginal Adhesion"->1,"Single Epithelial Cell Size"->2," Bare Nuclei"->1,"Bland Chromatin"->3,"Normal Nucleoli"->1,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->1354840,"Clump Thickness"->5,"Uniformity of Cell Size"->3,"Uniformity of Cell Shape"->2,"Marginal Adhesion"->1,"Single Epithelial Cell Size"->3," Bare Nuclei"->1,"Bland Chromatin"->1,"Normal Nucleoli"->1,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->1355260,"Clump Thickness"->1,"Uniformity of Cell Size"->1,"Uniformity of Cell Shape"->1,"Marginal Adhesion"->1,"Single Epithelial Cell Size"->2," Bare Nuclei"->1,"Bland Chromatin"->2,"Normal Nucleoli"->1,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->1365075,"Clump Thickness"->4,"Uniformity of Cell Size"->1,"Uniformity of Cell Shape"->4,"Marginal Adhesion"->1,"Single Epithelial Cell Size"->2," Bare Nuclei"->1,"Bland Chromatin"->1,"Normal Nucleoli"->1,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->1365328,"Clump Thickness"->1,"Uniformity of Cell Size"->1,"Uniformity of Cell Shape"->2,"Marginal Adhesion"->1,"Single Epithelial Cell Size"->2," Bare Nuclei"->1,"Bland Chromatin"->2,"Normal Nucleoli"->1,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->1368267,"Clump Thickness"->5,"Uniformity of Cell Size"->1,"Uniformity of Cell Shape"->1,"Marginal Adhesion"->1,"Single Epithelial Cell Size"->2," Bare Nuclei"->1,"Bland Chromatin"->1,"Normal Nucleoli"->1,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->1368273,"Clump Thickness"->1,"Uniformity of Cell Size"->1,"Uniformity of Cell Shape"->1,"Marginal Adhesion"->1,"Single Epithelial Cell Size"->2," Bare Nuclei"->1,"Bland Chromatin"->1,"Normal Nucleoli"->1,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->1368882,"Clump Thickness"->2,"Uniformity of Cell Size"->1,"Uniformity of Cell Shape"->1,"Marginal Adhesion"->1,"Single Epithelial Cell Size"->2," Bare Nuclei"->1,"Bland Chromatin"->1,"Normal Nucleoli"->1,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->1369821,"Clump Thickness"->10,"Uniformity of Cell Size"->10,"Uniformity of Cell Shape"->10,"Marginal Adhesion"->10,"Single Epithelial Cell Size"->5," Bare Nuclei"->10,"Bland Chromatin"->10,"Normal Nucleoli"->10,"Mitoses"->7,"Class"->4\[RightAssociation],\[LeftAssociation]"ID Number"->1371026,"Clump Thickness"->5,"Uniformity of Cell Size"->10,"Uniformity of Cell Shape"->10,"Marginal Adhesion"->10,"Single Epithelial Cell Size"->4," Bare Nuclei"->10,"Bland Chromatin"->5,"Normal Nucleoli"->6,"Mitoses"->3,"Class"->4\[RightAssociation],\[LeftAssociation]"ID Number"->1371920,"Clump Thickness"->5,"Uniformity of Cell Size"->1,"Uniformity of Cell Shape"->1,"Marginal Adhesion"->1,"Single Epithelial Cell Size"->2," Bare Nuclei"->1,"Bland Chromatin"->3,"Normal Nucleoli"->2,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->466906,"Clump Thickness"->1,"Uniformity of Cell Size"->1,"Uniformity of Cell Shape"->1,"Marginal Adhesion"->1,"Single Epithelial Cell Size"->2," Bare Nuclei"->1,"Bland Chromatin"->1,"Normal Nucleoli"->1,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->466906,"Clump Thickness"->1,"Uniformity of Cell Size"->1,"Uniformity of Cell Shape"->1,"Marginal Adhesion"->1,"Single Epithelial Cell Size"->2," Bare Nuclei"->1,"Bland Chromatin"->1,"Normal Nucleoli"->1,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->534555,"Clump Thickness"->1,"Uniformity of Cell Size"->1,"Uniformity of Cell Shape"->1,"Marginal Adhesion"->1,"Single Epithelial Cell Size"->2," Bare Nuclei"->1,"Bland Chromatin"->1,"Normal Nucleoli"->1,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->536708,"Clump Thickness"->1,"Uniformity of Cell Size"->1,"Uniformity of Cell Shape"->1,"Marginal Adhesion"->1,"Single Epithelial Cell Size"->2," Bare Nuclei"->1,"Bland Chromatin"->1,"Normal Nucleoli"->1,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->566346,"Clump Thickness"->3,"Uniformity of Cell Size"->1,"Uniformity of Cell Shape"->1,"Marginal Adhesion"->1,"Single Epithelial Cell Size"->2," Bare Nuclei"->1,"Bland Chromatin"->2,"Normal Nucleoli"->3,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->603148,"Clump Thickness"->4,"Uniformity of Cell Size"->1,"Uniformity of Cell Shape"->1,"Marginal Adhesion"->1,"Single Epithelial Cell Size"->2," Bare Nuclei"->1,"Bland Chromatin"->1,"Normal Nucleoli"->1,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->654546,"Clump Thickness"->1,"Uniformity of Cell Size"->1,"Uniformity of Cell Shape"->1,"Marginal Adhesion"->1,"Single Epithelial Cell Size"->2," Bare Nuclei"->1,"Bland Chromatin"->1,"Normal Nucleoli"->1,"Mitoses"->8,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->654546,"Clump Thickness"->1,"Uniformity of Cell Size"->1,"Uniformity of Cell Shape"->1,"Marginal Adhesion"->3,"Single Epithelial Cell Size"->2," Bare Nuclei"->1,"Bland Chromatin"->1,"Normal Nucleoli"->1,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->695091,"Clump Thickness"->5,"Uniformity of Cell Size"->10,"Uniformity of Cell Shape"->10,"Marginal Adhesion"->5,"Single Epithelial Cell Size"->4," Bare Nuclei"->5,"Bland Chromatin"->4,"Normal Nucleoli"->4,"Mitoses"->1,"Class"->4\[RightAssociation],\[LeftAssociation]"ID Number"->714039,"Clump Thickness"->3,"Uniformity of Cell Size"->1,"Uniformity of Cell Shape"->1,"Marginal Adhesion"->1,"Single Epithelial Cell Size"->2," Bare Nuclei"->1,"Bland Chromatin"->1,"Normal Nucleoli"->1,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->763235,"Clump Thickness"->3,"Uniformity of Cell Size"->1,"Uniformity of Cell Shape"->1,"Marginal Adhesion"->1,"Single Epithelial Cell Size"->2," Bare Nuclei"->1,"Bland Chromatin"->2,"Normal Nucleoli"->1,"Mitoses"->2,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->776715,"Clump Thickness"->3,"Uniformity of Cell Size"->1,"Uniformity of Cell Shape"->1,"Marginal Adhesion"->1,"Single Epithelial Cell Size"->3," Bare Nuclei"->2,"Bland Chromatin"->1,"Normal Nucleoli"->1,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->841769,"Clump Thickness"->2,"Uniformity of Cell Size"->1,"Uniformity of Cell Shape"->1,"Marginal Adhesion"->1,"Single Epithelial Cell Size"->2," Bare Nuclei"->1,"Bland Chromatin"->1,"Normal Nucleoli"->1,"Mitoses"->1,"Class"->2\[RightAssociation],\[LeftAssociation]"ID Number"->888820,"Clump Thickness"->5,"Uniformity of Cell Size"->10,"Uniformity of Cell Shape"->10,"Marginal Adhesion"->3,"Single Epithelial Cell Size"->7," Bare Nuclei"->3,"Bland Chromatin"->8,"Normal Nucleoli"->10,"Mitoses"->2,"Class"->4\[RightAssociation],\[LeftAssociation]"ID Number"->897471,"Clump Thickness"->4,"Uniformity of Cell Size"->8,"Uniformity of Cell Shape"->6,"Marginal Adhesion"->4,"Single Epithelial Cell Size"->3," Bare Nuclei"->4,"Bland Chromatin"->10,"Normal Nucleoli"->6,"Mitoses"->1,"Class"->4\[RightAssociation],\[LeftAssociation]"ID Number"->897471,"Clump Thickness"->4,"Uniformity of Cell Size"->8,"Uniformity of Cell Shape"->8,"Marginal Adhesion"->5,"Single Epithelial Cell Size"->4," Bare Nuclei"->5,"Bland Chromatin"->10,"Normal Nucleoli"->4,"Mitoses"->1,"Class"->4\[RightAssociation]};

Dataset[association]

Select a subset of features and cluster them:

patientsData = association[[All, { "Clump Thickness", "Uniformity of Cell Size", "Uniformity of Cell Shape", 
"Marginal Adhesion", "Single Epithelial Cell Size", " Bare Nuclei", "Bland Chromatin", "Normal Nucleoli", "Mitoses"}]];

classifier = ClusterClassify[patientsData]

ClassifierInformation[classifier, "MethodDescription"]

labels = classifier[patientsData];

The classifier was able to separate patients with benign tumors

Pick[association,labels , 1][[All, "Class"]];

Pick[association, labels, 2][[All, "Class"]];

classifier[\[LeftAssociation]"Clump Thickness"->2,"Uniformity of Cell Size"->9,"Uniformity of Cell Shape"->1,"Marginal Adhesion"->2,"Single Epithelial Cell Size"->9," Bare Nuclei"->2,"Bland Chromatin"->7,"Normal Nucleoli"->9,"Mitoses"->2\[RightAssociation], "Probabilities"]

Visualize the data:

ListPointPlot3D[Pick[DimensionReduce[Values/@patientsData, 3], labels, #]&/@{1,2}]

Seeds

Source: “https://archive.ics.uci.edu/ml/datasets/seeds”

labelsSeeds ={"area", "perimeter", "compactness", "length of kernel", " width of kernel" , "asymmetry coefficient", "length of kernel groove"};

dataset

datasetKernels =RandomSample@ {\[LeftAssociation]"area"->15.26`,"perimeter"->14.84`,"compactness"->0.871`,"length of kernel"->5.763`," width of kernel"->3.312`,"asymmetry coefficient"->2.221`,"length of kernel groove"->5.22`\[RightAssociation],\[LeftAssociation]"area"->14.88`,"perimeter"->14.57`,"compactness"->0.8811`,"length of kernel"->5.554`," width of kernel"->3.333`,"asymmetry coefficient"->1.018`,"length of kernel groove"->4.956`\[RightAssociation],\[LeftAssociation]"area"->14.29`,"perimeter"->14.09`,"compactness"->0.905`,"length of kernel"->5.291`," width of kernel"->3.337`,"asymmetry coefficient"->2.699`,"length of kernel groove"->4.825`\[RightAssociation],\[LeftAssociation]"area"->13.84`,"perimeter"->13.94`,"compactness"->0.8955`,"length of kernel"->5.324`," width of kernel"->3.379`,"asymmetry coefficient"->2.259`,"length of kernel groove"->4.805`\[RightAssociation],\[LeftAssociation]"area"->16.14`,"perimeter"->14.99`,"compactness"->0.9034`,"length of kernel"->5.658`," width of kernel"->3.562`,"asymmetry coefficient"->1.355`,"length of kernel groove"->5.175`\[RightAssociation],\[LeftAssociation]"area"->14.38`,"perimeter"->14.21`,"compactness"->0.8951`,"length of kernel"->5.386`," width of kernel"->3.312`,"asymmetry coefficient"->2.462`,"length of kernel groove"->4.956`\[RightAssociation],\[LeftAssociation]"area"->14.69`,"perimeter"->14.49`,"compactness"->0.8799`,"length of kernel"->5.563`," width of kernel"->3.259`,"asymmetry coefficient"->3.586`,"length of kernel groove"->5.219`\[RightAssociation],\[LeftAssociation]"area"->14.11`,"perimeter"->14.1`,"compactness"->0.8911`,"length of kernel"->5.42`," width of kernel"->3.302`,"asymmetry coefficient"->2.7`,"length of kernel groove"->5\[RightAssociation],\[LeftAssociation]"area"->16.63`,"perimeter"->15.46`,"compactness"->0.8747`,"length of kernel"->6.053`," width of kernel"->3.465`,"asymmetry coefficient"->2.04`,"length of kernel 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width of kernel"->3.156`,"asymmetry coefficient"->3.136`,"length of kernel groove"->4.872`\[RightAssociation],\[LeftAssociation]"area"->13.74`,"perimeter"->14.05`,"compactness"->0.8744`,"length of kernel"->5.482`," width of kernel"->3.114`,"asymmetry coefficient"->2.932`,"length of kernel groove"->4.825`\[RightAssociation],\[LeftAssociation]"area"->14.59`,"perimeter"->14.28`,"compactness"->0.8993`,"length of kernel"->5.351`," width of kernel"->3.333`,"asymmetry coefficient"->4.185`,"length of kernel groove"->4.781`\[RightAssociation],\[LeftAssociation]"area"->13.99`,"perimeter"->13.83`,"compactness"->0.9183`,"length of kernel"->5.119`," width of kernel"->3.383`,"asymmetry coefficient"->5.234`,"length of kernel groove"->4.781`\[RightAssociation],\[LeftAssociation]"area"->15.69`,"perimeter"->14.75`,"compactness"->0.9058`,"length of kernel"->5.527`," width of kernel"->3.514`,"asymmetry coefficient"->1.599`,"length of kernel groove"->5.046`\[RightAssociation],\[LeftAssociation]"area"->14.7`,"perimeter"->14.21`,"compactness"->0.9153`,"length of kernel"->5.205`," width of kernel"->3.466`,"asymmetry coefficient"->1.767`,"length of kernel groove"->4.649`\[RightAssociation],\[LeftAssociation]"area"->12.72`,"perimeter"->13.57`,"compactness"->0.8686`,"length of kernel"->5.226`," width of kernel"->3.049`,"asymmetry coefficient"->4.102`,"length of kernel groove"->4.914`\[RightAssociation],\[LeftAssociation]"area"->14.16`,"perimeter"->14.4`,"compactness"->0.8584`,"length of kernel"->5.658`," width of kernel"->3.129`,"asymmetry coefficient"->3.072`,"length of kernel groove"->5.176`\[RightAssociation],\[LeftAssociation]"area"->14.11`,"perimeter"->14.26`,"compactness"->0.8722`,"length of kernel"->5.52`," width of kernel"->3.168`,"asymmetry coefficient"->2.688`,"length of kernel groove"->5.219`\[RightAssociation],\[LeftAssociation]"area"->15.88`,"perimeter"->14.9`,"compactness"->0.8988`,"length of kernel"->5.618`," width of kernel"->3.507`,"asymmetry coefficient"->0.7651`,"length of kernel groove"->5.091`\[RightAssociation],\[LeftAssociation]"area"->12.08`,"perimeter"->13.23`,"compactness"->0.8664`,"length of kernel"->5.099`," width of kernel"->2.936`,"asymmetry coefficient"->1.415`,"length of kernel groove"->4.961`\[RightAssociation],\[LeftAssociation]"area"->15.01`,"perimeter"->14.76`,"compactness"->0.8657`,"length of kernel"->5.789`," width of kernel"->3.245`,"asymmetry coefficient"->1.791`,"length of kernel groove"->5.001`\[RightAssociation],\[LeftAssociation]"area"->16.19`,"perimeter"->15.16`,"compactness"->0.8849`,"length of kernel"->5.833`," width of kernel"->3.421`,"asymmetry coefficient"->0.903`,"length of kernel groove"->5.307`\[RightAssociation],\[LeftAssociation]"area"->13.02`,"perimeter"->13.76`,"compactness"->0.8641`,"length of kernel"->5.395`," width of kernel"->3.026`,"asymmetry coefficient"->3.373`,"length of kernel groove"->4.825`\[RightAssociation],\[LeftAssociation]"area"->12.74`,"perimeter"->13.67`,"compactness"->0.8564`,"length of kernel"->5.395`," width of kernel"->2.956`,"asymmetry coefficient"->2.504`,"length of kernel groove"->4.869`\[RightAssociation],\[LeftAssociation]"area"->14.11`,"perimeter"->14.18`,"compactness"->0.882`,"length of kernel"->5.541`," width of kernel"->3.221`,"asymmetry coefficient"->2.754`,"length of kernel groove"->5.038`\[RightAssociation],\[LeftAssociation]"area"->13.45`,"perimeter"->14.02`,"compactness"->0.8604`,"length of kernel"->5.516`," width of kernel"->3.065`,"asymmetry coefficient"->3.531`,"length of kernel groove"->5.097`\[RightAssociation],\[LeftAssociation]"area"->13.16`,"perimeter"->13.82`,"compactness"->0.8662`,"length of kernel"->5.454`," width of kernel"->2.975`,"asymmetry coefficient"->0.8551`,"length of kernel groove"->5.056`\[RightAssociation],\[LeftAssociation]"area"->15.49`,"perimeter"->14.94`,"compactness"->0.8724`,"length of kernel"->5.757`," width of kernel"->3.371`,"asymmetry coefficient"->3.412`,"length of kernel groove"->5.228`\[RightAssociation],\[LeftAssociation]"area"->14.09`,"perimeter"->14.41`,"compactness"->0.8529`,"length of kernel"->5.717`," width of kernel"->3.186`,"asymmetry coefficient"->3.92`,"length of kernel groove"->5.299`\[RightAssociation],\[LeftAssociation]"area"->13.94`,"perimeter"->14.17`,"compactness"->0.8728`,"length of kernel"->5.585`," width of kernel"->3.15`,"asymmetry coefficient"->2.124`,"length of kernel groove"->5.012`\[RightAssociation],\[LeftAssociation]"area"->15.05`,"perimeter"->14.68`,"compactness"->0.8779`,"length of kernel"->5.712`," width of kernel"->3.328`,"asymmetry coefficient"->2.129`,"length of kernel groove"->5.36`\[RightAssociation],\[LeftAssociation]"area"->16.12`,"perimeter"->15,"compactness"->0.9`,"length of kernel"->5.709`," width of kernel"->3.485`,"asymmetry coefficient"->2.27`,"length of kernel groove"->5.443`\[RightAssociation],\[LeftAssociation]"area"->16.2`,"perimeter"->15.27`,"compactness"->0.8734`,"length of kernel"->5.826`," width of kernel"->3.464`,"asymmetry coefficient"->2.823`,"length of kernel groove"->5.527`\[RightAssociation],\[LeftAssociation]"area"->17.08`,"perimeter"->15.38`,"compactness"->0.9079`,"length of kernel"->5.832`," width of kernel"->3.683`,"asymmetry coefficient"->2.956`,"length of kernel groove"->5.484`\[RightAssociation],\[LeftAssociation]"area"->14.8`,"perimeter"->14.52`,"compactness"->0.8823`,"length of kernel"->5.656`," width of kernel"->3.288`,"asymmetry coefficient"->3.112`,"length of kernel groove"->5.309`\[RightAssociation],\[LeftAssociation]"area"->14.28`,"perimeter"->14.17`,"compactness"->0.8944`,"length of kernel"->5.397`," width of kernel"->3.298`,"asymmetry coefficient"->6.685`,"length of kernel groove"->5.001`\[RightAssociation],\[LeftAssociation]"area"->13.54`,"perimeter"->13.85`,"compactness"->0.8871`,"length of kernel"->5.348`," width of kernel"->3.156`,"asymmetry coefficient"->2.587`,"length of kernel groove"->5.178`\[RightAssociation],\[LeftAssociation]"area"->13.5`,"perimeter"->13.85`,"compactness"->0.8852`,"length of kernel"->5.351`," width of kernel"->3.158`,"asymmetry coefficient"->2.249`,"length of kernel groove"->5.176`\[RightAssociation],\[LeftAssociation]"area"->13.16`,"perimeter"->13.55`,"compactness"->0.9009`,"length of kernel"->5.138`," width of kernel"->3.201`,"asymmetry coefficient"->2.461`,"length of kernel groove"->4.783`\[RightAssociation],\[LeftAssociation]"area"->15.5`,"perimeter"->14.86`,"compactness"->0.882`,"length of kernel"->5.877`," width of kernel"->3.396`,"asymmetry coefficient"->4.711`,"length of kernel groove"->5.528`\[RightAssociation],\[LeftAssociation]"area"->15.11`,"perimeter"->14.54`,"compactness"->0.8986`,"length of kernel"->5.579`," width of kernel"->3.462`,"asymmetry coefficient"->3.128`,"length of kernel groove"->5.18`\[RightAssociation],\[LeftAssociation]"area"->13.8`,"perimeter"->14.04`,"compactness"->0.8794`,"length of kernel"->5.376`," width of kernel"->3.155`,"asymmetry coefficient"->1.56`,"length of kernel groove"->4.961`\[RightAssociation],\[LeftAssociation]"area"->15.36`,"perimeter"->14.76`,"compactness"->0.8861`,"length of kernel"->5.701`," width of kernel"->3.393`,"asymmetry coefficient"->1.367`,"length of kernel groove"->5.132`\[RightAssociation],\[LeftAssociation]"area"->14.99`,"perimeter"->14.56`,"compactness"->0.8883`,"length of kernel"->5.57`," width of kernel"->3.377`,"asymmetry coefficient"->2.958`,"length of kernel groove"->5.175`\[RightAssociation],\[LeftAssociation]"area"->14.79`,"perimeter"->14.52`,"compactness"->0.8819`,"length of kernel"->5.545`," width of kernel"->3.291`,"asymmetry coefficient"->2.704`,"length of kernel groove"->5.111`\[RightAssociation],\[LeftAssociation]"area"->14.86`,"perimeter"->14.67`,"compactness"->0.8676`,"length of kernel"->5.678`," width of kernel"->3.258`,"asymmetry coefficient"->2.129`,"length of kernel groove"->5.351`\[RightAssociation],\[LeftAssociation]"area"->14.43`,"perimeter"->14.4`,"compactness"->0.8751`,"length of kernel"->5.585`," width of kernel"->3.272`,"asymmetry coefficient"->3.975`,"length of kernel groove"->5.144`\[RightAssociation],\[LeftAssociation]"area"->15.78`,"perimeter"->14.91`,"compactness"->0.8923`,"length of kernel"->5.674`," width of kernel"->3.434`,"asymmetry coefficient"->5.593`,"length of kernel groove"->5.136`\[RightAssociation],\[LeftAssociation]"area"->14.49`,"perimeter"->14.61`,"compactness"->0.8538`,"length of kernel"->5.715`," width of kernel"->3.113`,"asymmetry coefficient"->4.116`,"length of kernel groove"->5.396`\[RightAssociation],\[LeftAssociation]"area"->14.33`,"perimeter"->14.28`,"compactness"->0.8831`,"length of kernel"->5.504`," width of kernel"->3.199`,"asymmetry coefficient"->3.328`,"length of kernel groove"->5.224`\[RightAssociation],\[LeftAssociation]"area"->14.52`,"perimeter"->14.6`,"compactness"->0.8557`,"length of kernel"->5.741`," width of kernel"->3.113`,"asymmetry coefficient"->1.481`,"length of kernel groove"->5.487`\[RightAssociation],\[LeftAssociation]"area"->15.03`,"perimeter"->14.77`,"compactness"->0.8658`,"length of kernel"->5.702`," width of kernel"->3.212`,"asymmetry coefficient"->1.933`,"length of kernel groove"->5.439`\[RightAssociation],\[LeftAssociation]"area"->14.46`,"perimeter"->14.35`,"compactness"->0.8818`,"length of kernel"->5.388`," width of kernel"->3.377`,"asymmetry coefficient"->2.802`,"length of kernel groove"->5.044`\[RightAssociation],\[LeftAssociation]"area"->14.92`,"perimeter"->14.43`,"compactness"->0.9006`,"length of kernel"->5.384`," width of kernel"->3.412`,"asymmetry coefficient"->1.142`,"length of kernel groove"->5.088`\[RightAssociation],\[LeftAssociation]"area"->15.38`,"perimeter"->14.77`,"compactness"->0.8857`,"length of kernel"->5.662`," width of kernel"->3.419`,"asymmetry coefficient"->1.999`,"length of kernel groove"->5.222`\[RightAssociation],\[LeftAssociation]"area"->12.11`,"perimeter"->13.47`,"compactness"->0.8392`,"length of kernel"->5.159`," width of kernel"->3.032`,"asymmetry coefficient"->1.502`,"length of kernel groove"->4.519`\[RightAssociation],\[LeftAssociation]"area"->11.42`,"perimeter"->12.86`,"compactness"->0.8683`,"length of kernel"->5.008`," width of kernel"->2.85`,"asymmetry coefficient"->2.7`,"length of kernel groove"->4.607`\[RightAssociation],\[LeftAssociation]"area"->11.23`,"perimeter"->12.63`,"compactness"->0.884`,"length of kernel"->4.902`," width of kernel"->2.879`,"asymmetry coefficient"->2.269`,"length of kernel groove"->4.703`\[RightAssociation],\[LeftAssociation]"area"->12.36`,"perimeter"->13.19`,"compactness"->0.8923`,"length of kernel"->5.076`," width of kernel"->3.042`,"asymmetry coefficient"->3.22`,"length of kernel groove"->4.605`\[RightAssociation],\[LeftAssociation]"area"->13.22`,"perimeter"->13.84`,"compactness"->0.868`,"length of kernel"->5.395`," width of kernel"->3.07`,"asymmetry coefficient"->4.157`,"length of kernel groove"->5.088`\[RightAssociation],\[LeftAssociation]"area"->12.78`,"perimeter"->13.57`,"compactness"->0.8716`,"length of kernel"->5.262`," width of kernel"->3.026`,"asymmetry coefficient"->1.176`,"length of kernel groove"->4.782`\[RightAssociation],\[LeftAssociation]"area"->12.88`,"perimeter"->13.5`,"compactness"->0.8879`,"length of kernel"->5.139`," width of kernel"->3.119`,"asymmetry coefficient"->2.352`,"length of kernel groove"->4.607`\[RightAssociation],\[LeftAssociation]"area"->14.34`,"perimeter"->14.37`,"compactness"->0.8726`,"length of kernel"->5.63`," width of kernel"->3.19`,"asymmetry coefficient"->1.313`,"length of kernel groove"->5.15`\[RightAssociation],\[LeftAssociation]"area"->14.01`,"perimeter"->14.29`,"compactness"->0.8625`,"length of kernel"->5.609`," width of kernel"->3.158`,"asymmetry coefficient"->2.217`,"length of kernel groove"->5.132`\[RightAssociation],\[LeftAssociation]"area"->14.37`,"perimeter"->14.39`,"compactness"->0.8726`,"length of kernel"->5.569`," width of kernel"->3.153`,"asymmetry coefficient"->1.464`,"length of kernel groove"->5.3`\[RightAssociation],\[LeftAssociation]"area"->12.73`,"perimeter"->13.75`,"compactness"->0.8458`,"length of kernel"->5.412`," width of kernel"->2.882`,"asymmetry coefficient"->3.533`,"length of kernel groove"->5.067`\[RightAssociation],\[LeftAssociation]"area"->17.63`,"perimeter"->15.98`,"compactness"->0.8673`,"length of kernel"->6.191`," width of kernel"->3.561`,"asymmetry coefficient"->4.076`,"length of kernel groove"->6.06`\[RightAssociation],\[LeftAssociation]"area"->16.84`,"perimeter"->15.67`,"compactness"->0.8623`,"length of kernel"->5.998`," width of kernel"->3.484`,"asymmetry coefficient"->4.675`,"length of kernel groove"->5.877`\[RightAssociation],\[LeftAssociation]"area"->17.26`,"perimeter"->15.73`,"compactness"->0.8763`,"length of kernel"->5.978`," width of kernel"->3.594`,"asymmetry coefficient"->4.539`,"length of kernel groove"->5.791`\[RightAssociation],\[LeftAssociation]"area"->19.11`,"perimeter"->16.26`,"compactness"->0.9081`,"length of kernel"->6.154`," width of kernel"->3.93`,"asymmetry coefficient"->2.936`,"length of kernel groove"->6.079`\[RightAssociation],\[LeftAssociation]"area"->16.82`,"perimeter"->15.51`,"compactness"->0.8786`,"length of kernel"->6.017`," width of kernel"->3.486`,"asymmetry coefficient"->4.004`,"length of kernel groove"->5.841`\[RightAssociation],\[LeftAssociation]"area"->16.77`,"perimeter"->15.62`,"compactness"->0.8638`,"length of kernel"->5.927`," width of kernel"->3.438`,"asymmetry coefficient"->4.92`,"length of kernel groove"->5.795`\[RightAssociation],\[LeftAssociation]"area"->17.32`,"perimeter"->15.91`,"compactness"->0.8599`,"length of kernel"->6.064`," width of kernel"->3.403`,"asymmetry coefficient"->3.824`,"length of kernel groove"->5.922`\[RightAssociation],\[LeftAssociation]"area"->20.71`,"perimeter"->17.23`,"compactness"->0.8763`,"length of kernel"->6.579`," width of kernel"->3.814`,"asymmetry coefficient"->4.451`,"length of kernel groove"->6.451`\[RightAssociation],\[LeftAssociation]"area"->18.94`,"perimeter"->16.49`,"compactness"->0.875`,"length of kernel"->6.445`," width of kernel"->3.639`,"asymmetry coefficient"->5.064`,"length of kernel groove"->6.362`\[RightAssociation],\[LeftAssociation]"area"->17.12`,"perimeter"->15.55`,"compactness"->0.8892`,"length of kernel"->5.85`," width of kernel"->3.566`,"asymmetry coefficient"->2.858`,"length of kernel groove"->5.746`\[RightAssociation],\[LeftAssociation]"area"->16.53`,"perimeter"->15.34`,"compactness"->0.8823`,"length of kernel"->5.875`," width of kernel"->3.467`,"asymmetry coefficient"->5.532`,"length of kernel groove"->5.88`\[RightAssociation],\[LeftAssociation]"area"->18.72`,"perimeter"->16.19`,"compactness"->0.8977`,"length of kernel"->6.006`," width of kernel"->3.857`,"asymmetry coefficient"->5.324`,"length of kernel groove"->5.879`\[RightAssociation],\[LeftAssociation]"area"->20.2`,"perimeter"->16.89`,"compactness"->0.8894`,"length of kernel"->6.285`," width of kernel"->3.864`,"asymmetry coefficient"->5.173`,"length of kernel groove"->6.187`\[RightAssociation],\[LeftAssociation]"area"->19.57`,"perimeter"->16.74`,"compactness"->0.8779`,"length of kernel"->6.384`," width of kernel"->3.772`,"asymmetry coefficient"->1.472`,"length of kernel groove"->6.273`\[RightAssociation],\[LeftAssociation]"area"->19.51`,"perimeter"->16.71`,"compactness"->0.878`,"length of kernel"->6.366`," width of kernel"->3.801`,"asymmetry coefficient"->2.962`,"length of kernel groove"->6.185`\[RightAssociation],\[LeftAssociation]"area"->18.27`,"perimeter"->16.09`,"compactness"->0.887`,"length of kernel"->6.173`," width of kernel"->3.651`,"asymmetry coefficient"->2.443`,"length of kernel groove"->6.197`\[RightAssociation],\[LeftAssociation]"area"->18.88`,"perimeter"->16.26`,"compactness"->0.8969`,"length of kernel"->6.084`," width of kernel"->3.764`,"asymmetry coefficient"->1.649`,"length of kernel groove"->6.109`\[RightAssociation],\[LeftAssociation]"area"->18.98`,"perimeter"->16.66`,"compactness"->0.859`,"length of kernel"->6.549`," width of kernel"->3.67`,"asymmetry coefficient"->3.691`,"length of kernel groove"->6.498`\[RightAssociation],\[LeftAssociation]"area"->21.18`,"perimeter"->17.21`,"compactness"->0.8989`,"length of kernel"->6.573`," width of kernel"->4.033`,"asymmetry coefficient"->5.78`,"length of kernel groove"->6.231`\[RightAssociation],\[LeftAssociation]"area"->20.88`,"perimeter"->17.05`,"compactness"->0.9031`,"length of kernel"->6.45`," width of kernel"->4.032`,"asymmetry coefficient"->5.016`,"length of kernel groove"->6.321`\[RightAssociation],\[LeftAssociation]"area"->20.1`,"perimeter"->16.99`,"compactness"->0.8746`,"length of kernel"->6.581`," width of kernel"->3.785`,"asymmetry coefficient"->1.955`,"length of kernel groove"->6.449`\[RightAssociation],\[LeftAssociation]"area"->18.76`,"perimeter"->16.2`,"compactness"->0.8984`,"length of kernel"->6.172`," width of kernel"->3.796`,"asymmetry coefficient"->3.12`,"length of kernel groove"->6.053`\[RightAssociation],\[LeftAssociation]"area"->18.81`,"perimeter"->16.29`,"compactness"->0.8906`,"length of kernel"->6.272`," width of kernel"->3.693`,"asymmetry coefficient"->3.237`,"length of kernel groove"->6.053`\[RightAssociation],\[LeftAssociation]"area"->18.59`,"perimeter"->16.05`,"compactness"->0.9066`,"length of kernel"->6.037`," width of kernel"->3.86`,"asymmetry coefficient"->6.001`,"length of kernel groove"->5.877`\[RightAssociation],\[LeftAssociation]"area"->18.36`,"perimeter"->16.52`,"compactness"->0.8452`,"length of kernel"->6.666`," width of kernel"->3.485`,"asymmetry coefficient"->4.933`,"length of kernel groove"->6.448`\[RightAssociation],\[LeftAssociation]"area"->16.87`,"perimeter"->15.65`,"compactness"->0.8648`,"length of kernel"->6.139`," width of kernel"->3.463`,"asymmetry coefficient"->3.696`,"length of kernel groove"->5.967`\[RightAssociation],\[LeftAssociation]"area"->19.31`,"perimeter"->16.59`,"compactness"->0.8815`,"length of kernel"->6.341`," width of kernel"->3.81`,"asymmetry coefficient"->3.477`,"length of kernel groove"->6.238`\[RightAssociation],\[LeftAssociation]"area"->18.98`,"perimeter"->16.57`,"compactness"->0.8687`,"length of kernel"->6.449`," width of kernel"->3.552`,"asymmetry coefficient"->2.144`,"length of kernel groove"->6.453`\[RightAssociation],\[LeftAssociation]"area"->18.17`,"perimeter"->16.26`,"compactness"->0.8637`,"length of kernel"->6.271`," width of kernel"->3.512`,"asymmetry coefficient"->2.853`,"length of kernel 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width of kernel"->2.63`,"asymmetry coefficient"->4.853`,"length of kernel groove"->5.089`\[RightAssociation],\[LeftAssociation]"area"->12.11`,"perimeter"->13.27`,"compactness"->0.8639`,"length of kernel"->5.236`," width of kernel"->2.975`,"asymmetry coefficient"->4.132`,"length of kernel groove"->5.012`\[RightAssociation],\[LeftAssociation]"area"->12.8`,"perimeter"->13.47`,"compactness"->0.886`,"length of kernel"->5.16`," width of kernel"->3.126`,"asymmetry coefficient"->4.873`,"length of kernel groove"->4.914`\[RightAssociation],\[LeftAssociation]"area"->12.79`,"perimeter"->13.53`,"compactness"->0.8786`,"length of kernel"->5.224`," width of kernel"->3.054`,"asymmetry coefficient"->5.483`,"length of kernel groove"->4.958`\[RightAssociation],\[LeftAssociation]"area"->13.37`,"perimeter"->13.78`,"compactness"->0.8849`,"length of kernel"->5.32`," width of kernel"->3.128`,"asymmetry coefficient"->4.67`,"length of kernel groove"->5.091`\[RightAssociation],\[LeftAssociation]"area"->12.62`,"perimeter"->13.67`,"compactness"->0.8481`,"length of kernel"->5.41`," width of kernel"->2.911`,"asymmetry coefficient"->3.306`,"length of kernel groove"->5.231`\[RightAssociation],\[LeftAssociation]"area"->12.76`,"perimeter"->13.38`,"compactness"->0.8964`,"length of kernel"->5.073`," width of kernel"->3.155`,"asymmetry coefficient"->2.828`,"length of kernel groove"->4.83`\[RightAssociation],\[LeftAssociation]"area"->12.38`,"perimeter"->13.44`,"compactness"->0.8609`,"length of kernel"->5.219`," width of kernel"->2.989`,"asymmetry coefficient"->5.472`,"length of kernel groove"->5.045`\[RightAssociation],\[LeftAssociation]"area"->12.67`,"perimeter"->13.32`,"compactness"->0.8977`,"length of kernel"->4.984`," width of kernel"->3.135`,"asymmetry coefficient"->2.3`,"length of kernel groove"->4.745`\[RightAssociation],\[LeftAssociation]"area"->11.18`,"perimeter"->12.72`,"compactness"->0.868`,"length of kernel"->5.009`," width of kernel"->2.81`,"asymmetry coefficient"->4.051`,"length of kernel groove"->4.828`\[RightAssociation],\[LeftAssociation]"area"->12.7`,"perimeter"->13.41`,"compactness"->0.8874`,"length of kernel"->5.183`," width of kernel"->3.091`,"asymmetry coefficient"->8.456`,"length of kernel groove"->5\[RightAssociation],\[LeftAssociation]"area"->12.37`,"perimeter"->13.47`,"compactness"->0.8567`,"length of kernel"->5.204`," width of kernel"->2.96`,"asymmetry coefficient"->3.919`,"length of kernel groove"->5.001`\[RightAssociation],\[LeftAssociation]"area"->12.19`,"perimeter"->13.2`,"compactness"->0.8783`,"length of kernel"->5.137`," width of kernel"->2.981`,"asymmetry coefficient"->3.631`,"length of kernel groove"->4.87`\[RightAssociation],\[LeftAssociation]"area"->11.23`,"perimeter"->12.88`,"compactness"->0.8511`,"length of kernel"->5.14`," width of kernel"->2.795`,"asymmetry coefficient"->4.325`,"length of kernel groove"->5.003`\[RightAssociation],\[LeftAssociation]"area"->13.2`,"perimeter"->13.66`,"compactness"->0.8883`,"length of kernel"->5.236`," width of kernel"->3.232`,"asymmetry coefficient"->8.315`,"length of kernel groove"->5.056`\[RightAssociation],\[LeftAssociation]"area"->11.84`,"perimeter"->13.21`,"compactness"->0.8521`,"length of kernel"->5.175`," width of kernel"->2.836`,"asymmetry coefficient"->3.598`,"length of kernel groove"->5.044`\[RightAssociation],\[LeftAssociation]"area"->12.3`,"perimeter"->13.34`,"compactness"->0.8684`,"length of kernel"->5.243`," width of kernel"->2.974`,"asymmetry coefficient"->5.637`,"length of kernel groove"->5.063`\[RightAssociation]};

Dataset[datasetKernels]

classifierKernels = ClusterClassify[datasetKernels]

This means there are three types of wheat.

labelsKernels = classifierKernels[datasetKernels]

Dataset/@(Pick[datasetKernels, labelsKernels, #]&/@{1,2,3})

Visualization:

ListPointPlot3D[Pick[DimensionReduce[Values/@datasetKernels, 3], labelsKernels, #]&/@{1,2,3}]

LearnDistribution

({{, , , , , }, {, , , , , }, {, , , , , }, {, , , , , }, {, , , , , }, {, , , , , }})

Goal: learn “black box” distribution from a dataset

LearnDistribution will learn the joint probability of the features.

This is pretty much the best you can hope for.

You can marginalize: P(A) = (∑_B)P(A, B), ...

You can condition: P(B|A) = P(A, B)/P(A)

...

It will output a LearnedDistribution object:

LearnDistribution[{ex1,ex2, ...}] -> LearnedDistribution[...]

You will be able to perform the “classical” operations on it:

Compute the PDF

PDF[LearnedDistribution[...],example]-> 0.756

Compute samples

RandomVariate[LearnedDistribution[...]]->

You will be able to condition and marginalize

Conditioned[LearnedDistribution[...],{1, 3}]-> ConditionalLearnedDistribution[...]

ConditionalLearnedDistribution[...][<|{1,3}->{0.5,"A"}|>]-> LearnedDistribution[...]

({{, }})

MarginalDistribution[LearnedDistribution[...], {1,3}]-> LearnedDistribution[...]

Mushrooms

mushrooms = ExampleData[{"MachineLearning","Mushroom"}, "Data"];

mushrooms[[1]]

We consider the class as an extra feature and learn the whole distribution.

mushrooms = Flatten/@List@@@mushrooms;
mushrooms = DeleteMissing[mushrooms, 1, 2];

mushrooms[[1]]

model = DecisionTree[mushrooms];

Predict the label given the other features:

{"convex","smooth","brown",True,"pungent","free","close","narrow","black","enlarging","equal","smooth","smooth","white","white","partial","white","one","pendant","black","scattered","urban"}

Pdf[model, {"convex","smooth","brown",True,"pungent","free","close","narrow","black","enlarging","equal","smooth","smooth","white","white","partial","white","one","pendant","black","scattered","urban","poisonous"}]

Pdf[model, {"convex","smooth","brown",True,"pungent","free","close","narrow","black","enlarging","equal","smooth","smooth","white","white","partial","white","one","pendant","black","scattered","urban","edible"}]

SeedRandom[11]
testList = ExampleData[{"MachineLearning","Mushroom"}, "TestData"];
testList = Flatten/@List@@@testList;
testList = RandomSample[testList, 20];

testList[[1]]

trueclasses = testList[[All, -1]];

testList[[All, -1]] = Nothing;

testList[[1]]

classResultFromTree = Flatten[Ordering[#, 1, Greater]&/@(Flatten[Table[Pdf[model, Append[#, i]], {i, {"edible", "poisonous"}}]]&/@testList)];
classResultFromTree = {"edible", "poisonous"}[[classResultFromTree]];

Transpose[{classResultFromTree, trueclasses}]//MatrixForm

Note: Classify predicts the class as a function of the features. Here we can predict any feature as a function of the others.

Predict the color given the other features:

colors = DeleteDuplicates[mushrooms[[All, 3]]]

testList[[4]]

res = Ordering[#, 1, Greater]&[Flatten[Pdf[model, {"convex","scaly",#,True,"none","free","close","broad","purple","tapering","bulbous","smooth","smooth","white","pink","partial","white","one","pendant","black","several","woods", "edible"}]&/@(colors)]];
colors[[First@res]]

The MNIST dataset:

Sampling:

NADE model trained on the MNIST dataset.

Get["digitsModel.mx"]

Multicolumn[Table[Image@ArrayReshape[sampleNADE[model], {28, 28}], {36}], 6, Frame->All]

Anomaly Detection:

You need to be able to compute the probability density from your model.

NotebookOpen["/Users/giorgiaf/Dropbox/Mathematica/GraphicalModel/DynamicNumbers.nb"]

Missing values imputation:

Take the previous picture and  delete the last pixels.

Sample the missing points from the conditional distribution.

vector = Flatten@imgdata;
vector[[Range[550, 784]]] = .5;
Image[ArrayReshape[vector, {28, 28}], ImageSize -> {160, 160}]

v2 = vector/.{0.5->Missing[]};
vr =reconstructNADE[model, v2];
Image[ArrayReshape[vr, {28, 28}], ImageSize -> {160, 160}]

Thank you!