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# # Distance/Similarity

# PyCM's `distance` method provides users with a wide range of string distance/similarity metrics to evaluate a confusion matrix by measuring its distance to a perfect confusion matrix. Distance/Similarity metrics measure the distance between two vectors of numbers. Small distances between two objects indicate similarity. In the PyCM's `distance` method, a distance measure can be chosen from `DistanceType`. The measures' names are chosen based on the namig style suggested in [[1]](#ref1).

# In[1]:


from pycm import ConfusionMatrix, DistanceType


# In[2]:


cm = ConfusionMatrix(matrix={0: {0: 3, 1: 0, 2: 0}, 1: {0: 0, 1: 1, 2: 2}, 2: {0: 2, 1: 1, 2: 3}})


# $$TP \rightarrow True Positive$$
# $$TN \rightarrow True Negative$$
# $$FP \rightarrow False Positive$$
# $$FN \rightarrow False Negative$$
# $$POP \rightarrow Population$$

# ## AMPLE

# AMPLE similarity [[2]](#ref2) [[3]](#ref3).

# $$sim_{AMPLE}=|\frac{TP}{TP+FP}-\frac{FN}{FN+TN}|$$

# In[3]:


cm.distance(metric=DistanceType.AMPLE)


# <ul>
#     <li><span style="color:red;">Notice </span> :  new in <span style="color:red;">version 3.8</span> </li>
# </ul>

# ## Anderberg's D

# Anderberg's D [[4]](#ref4).

# $$sim_{Anderberg} =
# \frac{(max(TP,FP)+max(FN,TN)+max(TP,FN)+max(FP,TN))-
# (max(TP+FP,FP+TN)+max(TP+FP,FN+TN))}{2\times POP}$$

# In[4]:


cm.distance(metric=DistanceType.Anderberg)


# <ul>
#     <li><span style="color:red;">Notice </span> :  new in <span style="color:red;">version 3.8</span> </li>
# </ul>

# ## Andres & Marzo's Delta

# Andres & Marzo's Delta correlation [[5]](#ref5).

# $$corr_{AndresMarzo_\Delta} = \Delta =
# \frac{TP+TN-2 \times \sqrt{FP \times FN}}{POP}$$

# In[5]:


cm.distance(metric=DistanceType.AndresMarzoDelta)


# <ul>
#     <li><span style="color:red;">Notice </span> :  new in <span style="color:red;">version 3.8</span> </li>
# </ul>

# ## Baroni-Urbani & Buser I

# Baroni-Urbani & Buser I similarity [[6]](#ref6).

# $$sim_{BaroniUrbaniBuserI} =
# \frac{\sqrt{TP\times TN}+TP}{\sqrt{TP\times TN}+TP+FP+FN}$$

# In[6]:


cm.distance(metric=DistanceType.BaroniUrbaniBuserI)


# <ul>
#     <li><span style="color:red;">Notice </span> :  new in <span style="color:red;">version 3.8</span> </li>
# </ul>

# ## Baroni-Urbani & Buser II

# Baroni-Urbani & Buser II correlation [[6]](#ref6).

# $$corr_{BaroniUrbaniBuserII} =
# \frac{\sqrt{TP \times TN}+TP-FP-FN}{\sqrt{TP \times TN}+TP+FP+FN}$$

# In[7]:


cm.distance(metric=DistanceType.BaroniUrbaniBuserII)


# <ul>
#     <li><span style="color:red;">Notice </span> :  new in <span style="color:red;">version 3.8</span> </li>
# </ul>

# ## Batagelj & Bren

# Batagelj & Bren distance [[7]](#ref7).

# $$dist_{BatageljBren} =
# \frac{FP \times FN}{TP \times TN}$$

# In[8]:


cm.distance(metric=DistanceType.BatageljBren)


# <ul>
#     <li><span style="color:red;">Notice </span> :  new in <span style="color:red;">version 3.8</span> </li>
# </ul>

# ## Baulieu I

# Baulieu I distance [[8]](#ref8).

# $$sim_{BaulieuI} =
# \frac{(TP+FP) \times (TP+FN)-TP^2}{(TP+FP) \times (TP+FN)}$$

# In[9]:


cm.distance(metric=DistanceType.BaulieuI)


# <ul>
#     <li><span style="color:red;">Notice </span> :  new in <span style="color:red;">version 3.8</span> </li>
# </ul>

# ## Baulieu II

# Baulieu II similarity [[8]](#ref8).

# $$sim_{BaulieuII} =
# \frac{TP^2 \times TN^2}{(TP+FP) \times (TP+FN) \times (FP+TN) \times (FN+TN)}$$

# In[10]:


cm.distance(metric=DistanceType.BaulieuII)


# <ul>
#     <li><span style="color:red;">Notice </span> :  new in <span style="color:red;">version 3.8</span> </li>
# </ul>

# ## Baulieu III

# Baulieu III distance [[8]](#ref8).

# $$sim_{BaulieuIII} =
# \frac{POP^2 - 4 \times (TP \times TN-FP \times FN)}{2 \times POP^2}$$

# In[11]:


cm.distance(metric=DistanceType.BaulieuIII)


# <ul>
#     <li><span style="color:red;">Notice </span> :  new in <span style="color:red;">version 3.8</span> </li>
# </ul>

# ## Baulieu IV

# Baulieu IV distance [[9]](#ref9).

# $$dist_{BaulieuIV} = \frac{FP+FN-(TP+\frac{1}{2})\times(TN+\frac{1}{2})\times TN  \times k}{POP}$$

# In[12]:


cm.distance(metric=DistanceType.BaulieuIV)


# * The default value of k is Euler's number $e$

# <ul>
#     <li><span style="color:red;">Notice </span> :  new in <span style="color:red;">version 3.8</span> </li>
# </ul>

# ## Baulieu V

# Baulieu V distance [[9]](#ref9).

# $$dist_{BaulieuV} = \frac{FP+FN+1}{TP+FP+FN+1}$$

# In[13]:


cm.distance(metric=DistanceType.BaulieuV)


# <ul>
#     <li><span style="color:red;">Notice </span> :  new in <span style="color:red;">version 3.8</span> </li>
# </ul>

# ## Baulieu VI

# Baulieu VI distance [[9]](#ref9).

# $$dist_{BaulieuVI} = \frac{FP+FN}{TP+FP+FN+1}$$

# In[14]:


cm.distance(metric=DistanceType.BaulieuVI)


# <ul>
#     <li><span style="color:red;">Notice </span> :  new in <span style="color:red;">version 3.8</span> </li>
# </ul>

# ## Baulieu VII

# Baulieu VII distance [[9]](#ref9).

# $$dist_{BaulieuVII} = \frac{FP+FN}{POP + TP \times (TP-4)^2}$$

# In[15]:


cm.distance(metric=DistanceType.BaulieuVII)


# <ul>
#     <li><span style="color:red;">Notice </span> :  new in <span style="color:red;">version 3.8</span> </li>
# </ul>

# ## Baulieu VIII

# Baulieu VIII distance [[9]](#ref9).

# $$dist_{BaulieuVIII} = \frac{(FP-FN)^2}{POP^2}$$

# In[16]:


cm.distance(metric=DistanceType.BaulieuVIII)


# <ul>
#     <li><span style="color:red;">Notice </span> :  new in <span style="color:red;">version 3.8</span> </li>
# </ul>

# ## Baulieu IX

# Baulieu IX distance [[9]](#ref9).

# $$dist_{BaulieuIX} = \frac{FP+2 \times FN}{TP+FP+2 \times FN+TN}$$

# In[17]:


cm.distance(metric=DistanceType.BaulieuIX)


# <ul>
#     <li><span style="color:red;">Notice </span> :  new in <span style="color:red;">version 3.8</span> </li>
# </ul>

# ## Baulieu X

# Baulieu X distance [[9]](#ref9).

# $$dist_{BaulieuX} = \frac{FP+FN+max(FP,FN)}{POP+max(FP,FN)}$$

# In[18]:


cm.distance(metric=DistanceType.BaulieuX)


# <ul>
#     <li><span style="color:red;">Notice </span> :  new in <span style="color:red;">version 3.8</span> </li>
# </ul>

# ## Baulieu XI

# Baulieu XI distance [[9]](#ref9).

# $$dist_{BaulieuXI} = \frac{FP+FN}{FP+FN+TN}$$

# In[19]:


cm.distance(metric=DistanceType.BaulieuXI)


# <ul>
#     <li><span style="color:red;">Notice </span> :  new in <span style="color:red;">version 3.8</span> </li>
# </ul>

# ## Baulieu XII

# Baulieu XII distance [[9]](#ref9).

# $$dist_{BaulieuXII} = \frac{FP+FN}{TP+FP+FN-1}$$

# In[20]:


cm.distance(metric=DistanceType.BaulieuXII)


# <ul>
#     <li><span style="color:red;">Notice </span> :  new in <span style="color:red;">version 3.8</span> </li>
# </ul>

# ## Baulieu XIII

# Baulieu XIII distance [[9]](#ref9).

# $$dist_{BaulieuXIII} = \frac{FP+FN}{TP+FP+FN+TP \times (TP-4)^2}$$

# In[21]:


cm.distance(metric=DistanceType.BaulieuXIII)


# <ul>
#     <li><span style="color:red;">Notice </span> :  new in <span style="color:red;">version 3.8</span> </li>
# </ul>

# ## Baulieu XIV

# Baulieu XIV distance [[9]](#ref9).

# $$dist_{BaulieuXIV} = \frac{FP+2 \times FN}{TP+FP+2 \times FN}$$

# In[22]:


cm.distance(metric=DistanceType.BaulieuXIV)


# <ul>
#     <li><span style="color:red;">Notice </span> :  new in <span style="color:red;">version 3.8</span> </li>
# </ul>

# ## Baulieu XV

# Baulieu XV distance [[9]](#ref9).

# $$dist_{BaulieuXV} = \frac{FP+FN+max(FP, FN)}{TP+FP+FN+max(FP, FN)}$$

# In[23]:


cm.distance(metric=DistanceType.BaulieuXV)


# <ul>
#     <li><span style="color:red;">Notice </span> :  new in <span style="color:red;">version 3.8</span> </li>
# </ul>

# ## Benini I

# Benini I correlation [[10]](#ref10).

# $$corr_{BeniniI} = \frac{TP \times TN-FP \times FN}{(TP+FN)\times(FN+TN)}$$

# In[24]:


cm.distance(metric=DistanceType.BeniniI)


# <ul>
#     <li><span style="color:red;">Notice </span> :  new in <span style="color:red;">version 3.8</span> </li>
# </ul>

# ## Benini II

# Benini II correlation [[10]](#ref10).

# $$corr_{BeniniII} = \frac{TP \times TN-FP \times FN}{min((TP+FN)\times(FN+TN), (TP+FP)\times(FP+TN))}$$

# In[25]:


cm.distance(metric=DistanceType.BeniniII)


# <ul>
#     <li><span style="color:red;">Notice </span> :  new in <span style="color:red;">version 3.8</span> </li>
# </ul>

# ## Canberra

# Canberra distance [[11]](#ref11) [[12]](#ref12).

# $$sim_{Canberra} =
# \frac{FP+FN}{(TP+FP)+(TP+FN)}$$

# In[26]:


cm.distance(metric=DistanceType.Canberra)


# <ul>
#     <li><span style="color:red;">Notice </span> :  new in <span style="color:red;">version 3.8</span> </li>
# </ul>

# ## Clement

# Clement similarity [[13]](#ref13).

# $$sim_{Clement} =
# \frac{TP}{TP+FP}\times\Big(1 - \frac{TP+FP}{POP}\Big) +
# \frac{TN}{FN+TN}\times\Big(1 - \frac{FN+TN}{POP}\Big)$$

# In[27]:


cm.distance(metric=DistanceType.Clement)


# <ul>
#     <li><span style="color:red;">Notice </span> :  new in <span style="color:red;">version 3.8</span> </li>
# </ul>

# ## Consonni & Todeschini I

# Consonni & Todeschini I similarity [[14]](#ref14).

# $$sim_{ConsonniTodeschiniI} =
# \frac{log(1+TP+TN)}{log(1+POP)}$$

# In[28]:


cm.distance(metric=DistanceType.ConsonniTodeschiniI)


# <ul>
#     <li><span style="color:red;">Notice </span> :  new in <span style="color:red;">version 3.8</span> </li>
# </ul>

# ## Consonni & Todeschini II

# Consonni & Todeschini II similarity [[14]](#ref14).

# $$sim_{ConsonniTodeschiniII} =
# \frac{log(1+POP)-log(1+FP+FN)}{log(1+POP)}$$

# In[29]:


cm.distance(metric=DistanceType.ConsonniTodeschiniII)


# <ul>
#     <li><span style="color:red;">Notice </span> :  new in <span style="color:red;">version 3.8</span> </li>
# </ul>

# ## Consonni & Todeschini III

# Consonni & Todeschini III similarity [[14]](#ref14).

# $$sim_{ConsonniTodeschiniIII} =
# \frac{log(1+TP)}{log(1+POP)}$$

# In[30]:


cm.distance(metric=DistanceType.ConsonniTodeschiniIII)


# <ul>
#     <li><span style="color:red;">Notice </span> :  new in <span style="color:red;">version 3.8</span> </li>
# </ul>

# ## Consonni & Todeschini IV

# Consonni & Todeschini IV similarity [[14]](#ref14).

# $$sim_{ConsonniTodeschiniIV} =
# \frac{log(1+TP)}{log(1+TP+FP+FN)}$$

# In[31]:


cm.distance(metric=DistanceType.ConsonniTodeschiniIV)


# <ul>
#     <li><span style="color:red;">Notice </span> :  new in <span style="color:red;">version 3.8</span> </li>
# </ul>

# ## Consonni & Todeschini V

# Consonni & Todeschini V correlation [[14]](#ref14).

# $$corr_{ConsonniTodeschiniV} =
# \frac{log(1+TP \times TN)-log(1+FP \times FN)}{log(1+\frac{POP^2}{4})}$$

# In[32]:


cm.distance(metric=DistanceType.ConsonniTodeschiniV)


# <ul>
#     <li><span style="color:red;">Notice </span> :  new in <span style="color:red;">version 3.8</span> </li>
# </ul>

# ## Dennis

# Dennis similarity [[15]](#ref15).

# $$sim_{Dennis} =
# \frac{TP-\frac{(TP+FP)\times(TP+FN)}{POP}}{\sqrt{\frac{(TP+FP)\times(TP+FN)}{POP}}}$$

# In[33]:


cm.distance(metric=DistanceType.Dennis)


# <ul>
#     <li><span style="color:red;">Notice </span> :  new in <span style="color:red;">version 3.9</span> </li>
# </ul>

# ## Digby

# Digby correlation [[16]](#ref16).

# $$corr_{Digby} =
# \frac{(TP \times TN) ^\frac{3}{4}-(FP \times FN)^\frac{3}{4}}{(TP \times TN)^\frac{3}{4}+(FP \times FN)^\frac{3}{4}}$$

# In[34]:


cm.distance(metric=DistanceType.Digby)


# <ul>
#     <li><span style="color:red;">Notice </span> :  new in <span style="color:red;">version 3.9</span> </li>
# </ul>

# ## Dispersion

# Dispersion correlation [[17]](#ref17).

# $$corr_{dispersion} =
# \frac{TP \times TN -FP \times FN}{POP^2}
# $$

# In[35]:


cm.distance(metric=DistanceType.Dispersion)


# <ul>
#     <li><span style="color:red;">Notice </span> :  new in <span style="color:red;">version 3.9</span> </li>
# </ul>

# ## Doolittle

# Doolittle similarity [[18]](#ref18).

# $$sim_{Doolittle} =
# \frac{(TP\times POP - (TP+FP)\times(TP+FN))^2}{(TP+FP)\times(TP+FN)\times(FP+TN)\times(FN+TN)}$$

# In[36]:


cm.distance(metric=DistanceType.Doolittle)


# <ul>
#     <li><span style="color:red;">Notice </span> :  new in <span style="color:red;">version 3.9</span> </li>
# </ul>

# ## Eyraud

# Eyraud similarity [[19]](#ref19).

# $$sim_{Eyraud} =
# \frac{TP-(TP+FP)\times(TP+FN)}{(TP+FP)\times(TP+FN)\times(FP+TN)\times(FN+TN)}$$

# In[37]:


cm.distance(metric=DistanceType.Eyraud)


# <ul>
#     <li><span style="color:red;">Notice </span> :  new in <span style="color:red;">version 3.9</span> </li>
# </ul>

# ## Fager & McGowan

# Fager & McGowan similarity [[20]](#ref20) [[21]](#ref21).

# $$sim_{FagerMcGowan} =
# \frac{TP}{\sqrt{(TP+FP)\times(TP+FN)}} - \frac{1}{2\sqrt{max(TP+FP, TP+FN)}}$$

# In[38]:


cm.distance(metric=DistanceType.FagerMcGowan)


# <ul>
#     <li><span style="color:red;">Notice </span> :  new in <span style="color:red;">version 3.9</span> </li>
# </ul>

# ## Faith

# Faith similarity [[22]](#ref22).

# $$sim_{Faith} =
# \frac{TP+\frac{TN}{2}}{POP}$$

# In[39]:


cm.distance(metric=DistanceType.Faith)


# <ul>
#     <li><span style="color:red;">Notice </span> :  new in <span style="color:red;">version 3.9</span> </li>
# </ul>

# ## Fleiss-Levin-Paik

# Fleiss-Levin-Paik similarity [[23]](#ref23).

# $$sim_{FleissLevinPaik} =
# \frac{2 \times TN}{2 \times TN + FP + FN}$$

# In[40]:


cm.distance(metric=DistanceType.FleissLevinPaik)


# <ul>
#     <li><span style="color:red;">Notice </span> :  new in <span style="color:red;">version 3.9</span> </li>
# </ul>

# ## Forbes I

# Forbes I similarity [[24]](#ref24) [[25]](#ref25).

# $$sim_{ForbesI} =
# \frac{POP \times TP}{(TP+FP)\times(TP+FN)}$$

# In[41]:


cm.distance(metric=DistanceType.ForbesI)


# <ul>
#     <li><span style="color:red;">Notice </span> :  new in <span style="color:red;">version 3.9</span> </li>
# </ul>

# ## Forbes II

# Forbes II correlation [[26]](#ref26).

# $$corr_{ForbesII} =
# \frac{FP \times FN-TP \times TN}{(TP+FP)\times(TP+FN) - POP \times min(TP+FP, TP+FN)}$$

# In[42]:


cm.distance(metric=DistanceType.ForbesII)


# <ul>
#     <li><span style="color:red;">Notice </span> :  new in <span style="color:red;">version 3.9</span> </li>
# </ul>

# ## Fossum

# Fossum similarity [[27]](#ref27).

# $$sim_{Fossum} =
# \frac{POP \times (TP-\frac{1}{2})^2}{(TP+FP)\times(TP+FN)}$$

# In[43]:


cm.distance(metric=DistanceType.Fossum)


# <ul>
#     <li><span style="color:red;">Notice </span> :  new in <span style="color:red;">version 3.9</span> </li>
# </ul>

# ## Gilbert & Wells

# Gilbert & Wells similarity [[28]](#ref28).

# $$sim_{GilbertWells} =
# ln \frac{POP^3}{2\pi (TP+FP)\times(TP+FN)\times(FP+TN)\times(FN+TN)} +
# 2ln \frac{POP! \times TP! \times FP! \times FN! \times TN!}{(TP+FP)! \times (TP+FN)! \times (FP+TN)! \times (FN+TN)!}$$

# In[44]:


cm.distance(metric=DistanceType.GilbertWells)


# <ul>
#     <li><span style="color:red;">Notice </span> :  new in <span style="color:red;">version 3.9</span> </li>
# </ul>

# ## Goodall

# Goodall similarity [[29]](#ref29) [[30]](#ref30).

# $$sim_{Goodall} =\frac{2}{\pi} \sin^{-1}\Big(
# \sqrt{\frac{TP + TN}{POP}}
# \Big)$$

# In[45]:


cm.distance(metric=DistanceType.Goodall)


# <ul>
#     <li><span style="color:red;">Notice </span> :  new in <span style="color:red;">version 3.9</span> </li>
# </ul>

# ## Goodman & Kruskal's Lambda

# Goodman & Kruskal's Lambda similarity [[31]](#ref31).

# $$sim_{GK_\lambda} =
# \frac{\frac{1}{2}((max(TP,FP)+max(FN,TN)+max(TP,FN)+max(FP,TN))-
# (max(TP+FP,FN+TN)+max(TP+FN,FP+TN)))}
# {POP-\frac{1}{2}(max(TP+FP,FN+TN)+max(TP+FN,FP+TN))}$$

# In[46]:


cm.distance(metric=DistanceType.GoodmanKruskalLambda)


# <ul>
#     <li><span style="color:red;">Notice </span> :  new in <span style="color:red;">version 3.9</span> </li>
# </ul>

# ## Goodman & Kruskal Lambda-r

# Goodman & Kruskal Lambda-r correlation [[31]](#ref31).

# $$corr_{GK_{\lambda_r}} =
# \frac{TP + TN - \frac{1}{2}(max(TP+FP,FN+TN)+max(TP+FN,FP+TN))}
# {POP - \frac{1}{2}(max(TP+FP,FN+TN)+max(TP+FN,FP+TN))}
# $$

# In[47]:


cm.distance(metric=DistanceType.GoodmanKruskalLambdaR)


# <ul>
#     <li><span style="color:red;">Notice </span> :  new in <span style="color:red;">version 3.9</span> </li>
# </ul>

# ## Guttman's Lambda A

# Guttman's Lambda A similarity [[32]](#ref32).

# $$sim_{Guttman_{\lambda_a}} =
# \frac{max(TP, FN) + max(FP, TN) - max(TP+FP, FN+TN)}{POP - max(TP+FP, FN+TN)}
# $$

# In[48]:


cm.distance(metric=DistanceType.GuttmanLambdaA)


# <ul>
#     <li><span style="color:red;">Notice </span> :  new in <span style="color:red;">version 3.9</span> </li>
# </ul>

# ## Guttman's Lambda B

# Guttman's Lambda B similarity [[32]](#ref32).

# $$sim_{Guttman_{\lambda_b}} =
# \frac{max(TP, FP) + max(FN, TN) - max(TP+FN, FP+TN)}{POP - max(TP+FN, FP+TN)}
# $$

# In[49]:


cm.distance(metric=DistanceType.GuttmanLambdaB)


# <ul>
#     <li><span style="color:red;">Notice </span> :  new in <span style="color:red;">version 3.9</span> </li>
# </ul>

# ## Hamann

# Hamann correlation [[33]](#ref33).

# $$corr_{Hamann} =
# \frac{TP+TN-FP-FN}{POP}
# $$

# In[50]:


cm.distance(metric=DistanceType.Hamann)


# <ul>
#     <li><span style="color:red;">Notice </span> :  new in <span style="color:red;">version 3.9</span> </li>
# </ul>

# ## Harris & Lahey

# Harris & Lahey similarity [[34]](#ref34).

# $$sim_{HarrisLahey} =
# \frac{TP}{TP+FP+FN} \times \frac{2TN+FP+FN}{2POP}+
# \frac{TN}{TN+FP+FN} \times \frac{2TP+FP+FN}{2POP}
# $$

# In[51]:


cm.distance(metric=DistanceType.HarrisLahey)


# <ul>
#     <li><span style="color:red;">Notice </span> :  new in <span style="color:red;">version 3.9</span> </li>
# </ul>

# ## Hawkins & Dotson

# Hawkins & Dotson similarity [[35]](#ref35).

# $$sim_{HawkinsDotson} =
# \frac{1}{2} \times \Big(\frac{TP}{TP+FP+FN}+\frac{TN}{FP+FN+TN}\Big)
# $$

# In[52]:


cm.distance(metric=DistanceType.HawkinsDotson)


# <ul>
#     <li><span style="color:red;">Notice </span> :  new in <span style="color:red;">version 3.9</span> </li>
# </ul>

# ## Kendall's Tau

# Kendall's Tau correlation [[36]](#ref36).

# $$corr_{KendallTau} =
# \frac{2 \times (TP+TN-FP-FN)}{POP \times (POP-1)}
# $$

# In[53]:


cm.distance(metric=DistanceType.KendallTau)


# <ul>
#     <li><span style="color:red;">Notice </span> :  new in <span style="color:red;">version 3.9</span> </li>
# </ul>

# ## Kent & Foster I

# Kent & Foster I similarity [[37]](#ref37).

# $$sim_{KentFosterI} =
# \frac{TP-\frac{(TP+FP)\times(TP+FN)}{TP+FP+FN}}{TP-\frac{(TP+FP)\times(TP+FN)}{TP+FP+FN}+FP+FN}
# $$

# In[54]:


cm.distance(metric=DistanceType.KentFosterI)


# <ul>
#     <li><span style="color:red;">Notice </span> :  new in <span style="color:red;">version 3.9</span> </li>
# </ul>

# ## Kent & Foster II

# Kent & Foster II similarity [[37]](#ref37).

# $$sim_{KentFosterII} =
# \frac{TN-\frac{(FP+TN)\times(FN+TN)}{FP+FN+TN}}{TN-\frac{(FP+TN)\times(FP+TN)}{FP+FN+TN}+FP+FN}
# $$

# In[55]:


cm.distance(metric=DistanceType.KentFosterII)


# <ul>
#     <li><span style="color:red;">Notice </span> :  new in <span style="color:red;">version 3.9</span> </li>
# </ul>

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