Hierarchical clustering on Variables Part 2

Short Introduction

After this study we can extract five interesting groups.
On this groups we discover some interesting values.
Immigrant are not the cause of the violent crimes and are really interested to work on the country.
The unemployement , the poverty and the graduations of people are really the most direct impact on the violent crimes. An other fact is that black people are really unemployed. A more interesting thing to do if we imagine one day to decrease the violent criminality is to offer more jobs for black race as in south affrica.

First Group

PctHousNoPhone,PctIlleg,PctLess9thGrade,PctNotHSGrad,PctOccupManu,PctPopUnderPov,PctUnemployed,PctVacantBoarded,PctWOFullPlumb,pctWPubAsst,racepctblack,ViolentCrimesPerPop
We can note that this group is corresponding on poor people living without phone , not graduate, under poverty, unemployed or manual employment, with public assistance and in a city where a great part of house area vacant and boarded. A hard life environment.

Second Group

agePct12t21,agePct12t29,agePct16t24,agePct65up,FemalePctDiv,householdsize,MalePctDivorce,MalePctNevMarr,MedOwnCostPctInc,MedOwnCostPctIncNoMtg,MedRentPctHousInc,MedYrHousBuilt,PctEmplManu,PctEmplProfServ,PctHousLess3BR,PctImmigRec10,PctImmigRec5,PctImmigRec8,,,PctImmigRecent,PctSameHouse85,PctVacMore6Mos,PctWorkMom,PctWorkMomYoungKids,pctWRetire,pctWSocSec,PersPerFam,PersPerOccupHous,PersPerOwnOccHous,PersPerRentOccHous,TotalPctDiv
Correponding to big family and immigrants whose living in renting their house  , with unstability on mariage . Where the mom works.

Third Group

AsianPerCap,blackPerCap,HispPerCap,indianPerCap,medFamInc,medIncome,MedNumBR,MedRent,OwnOccHiQuart,OwnOccLowQuart,OwnOccMedVal,PctBSorMore,PctOccupMgmtProf,pctWFarmSelf,perCapInc,RentHighQ,RentLowQ,RentMedian,whitePerCap
Corresponding to a group of different ethny, renting , owner of their house . A stable situation.

Fourth Group

PctBornSameState,PctEmploy,PctFam2Par,PctHousOccup,PctHousOwnOcc,PctKids2Par,PctPersOwnOccup,PctSameCity85,PctSameState85,PctSpeakEnglOnly,PctTeen2Par,pctUrban,pctWInvInc,pctWWage,PctYoungKids2Par,racePctWhite
This group correspond to the perfect idea of a family: two childs, living on the same city/state, speaking in english, white race, owner of their house.

Fifth Group

HousVacant,LandArea,LemasPctOfficDrugUn,numbUrban,NumIlleg,NumImmig,NumInShelters,NumStreet,NumUnderPov,PctForeignBorn,PctLargHouseFam,PctLargHouseOccup,PctNotSpeakEnglWell,PctPersDenseHous,PctRecentImmig,PctRecImmig10,PctRecImmig5,PctRecImmig8,PctUsePubTrans,PopDens,population,racePctAsian,racePctHisp
Corresponding to a group with immigrant(Asian Hisp ...) living on density environment using public transport and not speaking english.

Hierarchical clustering on Variablles

The study of variables follow our last study on the variables of our Principal Component Analysis. It was the first real interesting result in searching the understanding of our data. 

The actual case of the hierarchical agglomeration clustering offers, for the variables point of view, this dendrogram :

This dendogram gives an interesting that the best interesting point or number of classes is 5. Because this is the bigger jump on the dendograme that indicate the better force on the grouping possibility.

For the knowledge of this dendrogram and to understand this information , I give all the graphical result from 2 classes to 10 classes.

We can see that the better graphical choice is Five. With a good balance between classes, this is the appropriated choice.

Two classes

Three classes

Four classes

Five classes

Six classes

Seven classes

Height Classes

Nine Classes

Ten classes

Hierarchical clustering on Individuals

The data classification is an important thing to extract some interesting information. The internal structure of ur data set is really complex. If we arrive to extract some templates or some forms in our information, we can create some usable groups and study independently each group.
In this study there are a lot of classical methods as k-means, Hierarchical clustering and Self Organized Map.

We start with the Hierarchical clustering analysis on individuals
In this analysis we group data or data group by distance one by one. After a certain time, a result can be extracted easily  And two notices are usable: searching the best jump or by selecting manually a number of classes.
The result of this classification is this screen.

In this result we can see a Hierarchical clustering structure that permir to estimate a minimum four classes.

The results colored in a two first axes Principal Component Analysis is: