From 293e7b05ab49dab37522d7d6c9545774e8729f54 Mon Sep 17 00:00:00 2001 From: Carlos Camara Date: Fri, 3 Nov 2023 13:08:39 +0000 Subject: [PATCH] Built site for gh-pages --- .nojekyll | 2 +- content/labs/Lab_5/IM939_Lab_5_1.html | 182 +++++++++++------- .../figure-html/cell-10-output-1.png | Bin 168884 -> 171341 bytes .../figure-html/cell-11-output-1.png | Bin 176407 -> 175941 bytes .../figure-html/cell-14-output-1.png | Bin 178606 -> 178929 bytes .../figure-html/cell-15-output-1.png | Bin 176918 -> 177329 bytes content/references.html | 5 + search.json | 25 +-- sitemap.xml | 92 ++++----- 9 files changed, 173 insertions(+), 133 deletions(-) diff --git a/.nojekyll b/.nojekyll index 272c6f7..3f7b689 100644 --- a/.nojekyll +++ b/.nojekyll @@ -1 +1 @@ -0f89abff \ No newline at end of file +d47f63f6 \ No newline at end of file diff --git a/content/labs/Lab_5/IM939_Lab_5_1.html b/content/labs/Lab_5/IM939_Lab_5_1.html index 03c10f7..050fe4d 100644 --- a/content/labs/Lab_5/IM939_Lab_5_1.html +++ b/content/labs/Lab_5/IM939_Lab_5_1.html @@ -54,7 +54,26 @@ @media screen { pre > code.sourceCode > span > a:first-child::before { text-decoration: underline; } } - +/* CSS for citations */ +div.csl-bib-body { } +div.csl-entry { + clear: both; +} +.hanging-indent div.csl-entry { + margin-left:2em; + text-indent:-2em; +} +div.csl-left-margin { + min-width:2em; + float:left; +} +div.csl-right-inline { + margin-left:2em; + padding-left:1em; +} +div.csl-indent { + margin-left: 2em; +} @@ -545,16 +564,13 @@

Table of contents

-
+
@@ -574,14 +590,21 @@

21  https://data.london.gov.uk/london-area-profiles/

However, unlike the data that we explored during the session, this data set has several features (i.e., columns or variables), 76 of them to be precise.

-

What we would like to do in this notebook is to make use of a dimension reduction algorithm – Multidimensial Scaling – to help us create various different “spaces”. Each of these space will be a different way of “seeing this data” and if we adopt the language from Scott Page, they will have different “attentions”.

+

What we would like to do in this notebook is to make use of a dimension reduction algorithm – Multidimensional Scaling – to help us create various different “spaces”. Each of these space will be a different way of “seeing this data” and if we adopt the language from Scott Page (2018), they will have different “attentions”.

What the following exercise will do is to walk you through the variables of this data set through a few visualisations. It will then create a few different projections and will give them some names. What we expect you to do is to create your own projections and try to interpret them.

If you want to be reminded of what MDS is, you can have a look at the slides from last week. In a super tiny nutshell, MDS tries to create a space where “real” distances in the data are preserved as much as possible while “projecting” the data elements on a lower dimensional space. For instance, the following is from the slide deck:

-

An MDS plot of cities.

+
+
+

+
An MDS plot of cities.
+
+

What we see here are a few cities that would normally “exist” in our 3-dimensional world and the distances between them would normally be on this spherical coordinate system. But we create here is a 2D map and the distances between cities are preserved as much as possible. Near cities in the world are closer, and the further ones are further but not as accurate as it is in the world. The dimensions here carry no real meaning it is the distances that will “tell a story” (if there is one).

OK, let’s get on with the data now.

+
+

21.1 Data exploration and wrangling

import warnings
 warnings.filterwarnings('ignore')
@@ -590,7 +613,7 @@ 

21  df = pd.read_excel('data/london-borough-profilesV3.xlsx', engine = 'openpyxl') df.columns

-
+
Index(['Code', 'Area/INDICATOR', 'Inner/ Outer London',
        'GLA Population Estimate 2013', 'GLA Household Estimate 2013',
        'Inland Area (Hectares)', 'Population density (per hectare) 2013',
@@ -658,7 +681,7 @@ 

21 
df.head()
-
+
@@ -817,7 +840,7 @@

21 
def isnumber(x):
     try:
@@ -832,7 +855,7 @@ 

21  # apply isnumber function to every element df = df[df.applymap(isnumber)] df.head()

-
+
@@ -992,7 +1015,7 @@

21 
# get only numeric columns
 numericColumns = df._get_numeric_data()
@@ -1018,7 +1041,7 @@

21 
numericColumns.head()
-
+
@@ -1184,7 +1207,12 @@

21  #sns_plot.savefig("figs/output.png")

Given that this takes quite a while (around 10 minutes), this is the image that would result from uncommenting and running the code above.

+

+
+
+
+

21.2 Dimension reduction

Dimension reduction will help us here!

We could apply various different types of dimension reduction here. We are specifically going to capture the dissimilarity in the data using multidimensional scaling. Our distance matrix will come in useful here.

@@ -1197,7 +1225,7 @@

21  Y = mds.fit_transform(distMatrix)

To interpret what is happening, let us plot the boroughs on the projected two dimensional space.

-
+
from matplotlib import pyplot as plt
 
 fig, ax = plt.subplots()
@@ -1207,12 +1235,12 @@ 

21  for i, txt in enumerate(placeNames): ax.annotate(txt, (Y[:, 0][i],Y[:, 1][i]))

-
-

+
+

Our data also include happiness metrics. Pulling these out of our data and carrying out more multidimensional scaling can help us see how the boroughs differ in happiness.

-
+
# get the data columns relating to emotions and feelings
 dataOnEmotions = numericColumns[["Life satisfaction score 2012-13 (out of 10)", "Worthwhileness score 2012-13 (out of 10)","Happiness score 2012-13 (out of 10)"]]
 
@@ -1230,8 +1258,8 @@ 

21  for i, txt in enumerate(placeNames): ax.annotate(txt, (Y2[:, 0][i],Y2[:, 1][i]))

-
-

+
+

The location of the different boroughs on the 2 dimensional multidimensional scaling space from the happiness metrics is

@@ -1239,39 +1267,39 @@

21 
results_fixed = Y2.copy()
 print(results_fixed)

-
[[ 0.69748015 -0.81185707]
- [ 0.10899922  0.30108097]
- [ 0.136424   -0.16806795]
- [ 0.14093651 -0.21554052]
- [-0.1955195   0.22624968]
- [ 0.11407816 -0.43327937]
- [-0.15588862  0.17993318]
- [-0.002926    0.30743178]
- [-0.24032095 -0.1095705 ]
- [-0.19206059 -0.11253457]
- [-0.00332174  0.21289684]
- [-0.05208774  0.31915627]
- [ 0.17067002  0.20747103]
- [-0.08759646  0.15876571]
- [-0.11614813 -0.12219902]
- [ 0.04170797 -0.13784647]
- [-0.0391623  -0.15857883]
- [-0.03689777 -0.07960966]
- [-0.17214418  0.5249188 ]
- [ 0.27412767 -0.53867284]
- [-0.11080249  0.07685239]
- [-0.05270751  0.3549546 ]
- [ 0.1381328   0.02876136]
- [-0.00367913  0.12615481]
- [-0.13965941 -0.0227915 ]
- [-0.19901919 -0.03232374]
- [ 0.01668134 -0.22351004]
- [ 0.07414358 -0.02966198]
- [ 0.02302576  0.07491519]
- [-0.08739731 -0.07324658]
- [ 0.09066387 -0.06756996]
- [-0.07999907 -0.01517745]
- [-0.05973298  0.25249544]]
+
[[ 0.26955023 -1.03193546]
+ [-0.30697124  0.04988649]
+ [ 0.11267823 -0.18603719]
+ [ 0.09951239 -0.23709264]
+ [-0.11233607  0.27677033]
+ [ 0.31687906 -0.31587447]
+ [-0.08799261  0.21880538]
+ [-0.20905701  0.24461554]
+ [ 0.21012164  0.17125381]
+ [ 0.19306487  0.13163987]
+ [-0.18659     0.0989468 ]
+ [-0.2618981   0.18342251]
+ [-0.2551384  -0.05507685]
+ [-0.10018359  0.14805073]
+ [ 0.16711463  0.05098098]
+ [ 0.10854867 -0.09812561]
+ [ 0.16605853 -0.03341054]
+ [ 0.09654886  0.00279667]
+ [-0.49153577  0.23630239]
+ [ 0.4181435  -0.44518512]
+ [-0.01774271  0.12920108]
+ [-0.29575096  0.19446001]
+ [-0.07852039 -0.10487395]
+ [-0.10459205  0.06451135]
+ [ 0.09001571  0.12021746]
+ [ 0.12164733  0.16641986]
+ [ 0.19424041 -0.11717992]
+ [ 0.00238345 -0.07364946]
+ [-0.07160448  0.01590297]
+ [ 0.11278589  0.05034198]
+ [ 0.03510502 -0.10010882]
+ [ 0.05868884  0.07204286]
+ [-0.19317386  0.17198096]]

We may want to look at if the general happiness rating captures the position of the boroughs. To do this we need to assign colours based on the binned happiness score.

@@ -1287,7 +1315,7 @@

21 
(33, 2)

-
+
array([ 0.81636364, -0.22363636,  0.06636364,  0.18636364, -0.05363636,
         0.34636364, -0.06363636, -0.28363636, -0.04363636, -0.10363636,
        -0.12363636, -0.21363636, -0.05363636, -0.08363636,  0.05636364,
@@ -1298,7 +1326,7 @@ 

21  +
# let's look at the results
 fig, ax = plt.subplots()
 fig.set_size_inches(15, 15)
@@ -1308,11 +1336,11 @@ 

21  for i, txt in enumerate(placeNames): ax.annotate(txt, (results_fixed[:, 0][i],results_fixed[:, 1][i]))

-
-

+
+

-
+
# get the data columns relating to emotions and feelings
 dataOnDiversity = numericColumns[["Proportion of population aged 0-15, 2013", "Proportion of population of working-age, 2013", "Proportion of population aged 65 and over, 2013", "% of population from BAME groups (2013)", "% people aged 3+ whose main language is not English (2011 census)"]]
 
@@ -1330,24 +1358,38 @@ 

21  for i, txt in enumerate(placeNames): ax.annotate(txt, (Y[:, 0][i],Y[:, 1][i]))

-
-

+
+

+
+
+
+
+
-

::: callout-note

-
-

22 It is now your turn!

-
-

22.1 First task:

+
+It is now your turn! +
+
+
+
+

21.2.1 First task:

This looks very different to the one above on “emotion” related variables. Our job now is to relate these two projections to one another. Do you see similarities? Do you see clusters of boroughs? Can you reflect on how you can relate and combine these two maps conceptually?

-
-

22.2 Second task:

+
+

21.2.2 Second task:

Can you think of and then generate other maps that you can produce with this data? Have a look at the variables once again and try to produce new “perspectives” to the data and see what they have to say.

Also think of visualisations to help you here, can you colour them with a different variable? What would that change?

+
+
+
- +

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      References

      Knuth, Donald E. 1984. “Literate Programming.” Comput. J. 27 (2): 97–111. https://doi.org/10.1093/comjnl/27.2.97. +
      +Page, Scott E. 2018. “Why Many-Model +Thinkers Make Better Decisions.” +Harvard Business Review, November. https://hbr.org/2018/11/why-many-model-thinkers-make-better-decisions. +
      Redmond, Michael. 2009. Communities and Crime.” UCI Machine Learning Repository. https://doi.org/10.24432/C53W3X. diff --git a/search.json b/search.json index 64ac01f..63758c0 100644 --- a/search.json +++ b/search.json @@ -714,25 +714,18 @@ "text": "20.3 This week\nTrying to understand patterns in data often requires us to fit multiple models. We need to consider how well a given model (a kmeans cluster, a linear regression, dimension reduction, etc.) performs.\nSpecifically, we will look at:\n\nComparing clusters to the ‘ground truth’ - the wine dataset\nCross validation of linear regression - the crime dataset\nInvestigating multidimensional scaling - the london borough dataset\nVisualising the overlap in clustering results" }, { - "objectID": "content/labs/Lab_5/IM939_Lab_5_1.html", - "href": "content/labs/Lab_5/IM939_Lab_5_1.html", + "objectID": "content/labs/Lab_5/IM939_Lab_5_1.html#data-exploration-and-wrangling", + "href": "content/labs/Lab_5/IM939_Lab_5_1.html#data-exploration-and-wrangling", "title": "21  Lab: Working with multiple models", - "section": "", - "text": "22 It is now your turn!" - }, - { - "objectID": "content/labs/Lab_5/IM939_Lab_5_1.html#first-task", - "href": "content/labs/Lab_5/IM939_Lab_5_1.html#first-task", - "title": "21  Lab: Working with multiple models", - "section": "22.1 First task:", - "text": "22.1 First task:\nThis looks very different to the one above on “emotion” related variables. Our job now is to relate these two projections to one another. Do you see similarities? Do you see clusters of boroughs? Can you reflect on how you can relate and combine these two maps conceptually?" + "section": "21.1 Data exploration and wrangling", + "text": "21.1 Data exploration and wrangling\n\nimport warnings\nwarnings.filterwarnings('ignore')\n\nimport pandas as pd\n\ndf = pd.read_excel('data/london-borough-profilesV3.xlsx', engine = 'openpyxl')\ndf.columns\n\nIndex(['Code', 'Area/INDICATOR', 'Inner/ Outer London',\n 'GLA Population Estimate 2013', 'GLA Household Estimate 2013',\n 'Inland Area (Hectares)', 'Population density (per hectare) 2013',\n 'Average Age, 2013', 'Proportion of population aged 0-15, 2013',\n 'Proportion of population of working-age, 2013',\n 'Proportion of population aged 65 and over, 2013',\n '% of resident population born abroad (2013)',\n 'Largest migrant population by country of birth (2013)',\n '% of largest migrant population (2013)',\n 'Second largest migrant population by country of birth (2013)',\n '% of second largest migrant population (2013)',\n 'Third largest migrant population by country of birth (2013)',\n '% of third largest migrant population (2013)',\n '% of population from BAME groups (2013)',\n '% people aged 3+ whose main language is not English (2011 census)',\n 'Overseas nationals entering the UK (NINo), (2013/14)',\n 'New migrant (NINo) rates, (2013/14)', 'Employment rate (%) (2013/14)',\n 'Male employment rate (2013/14)', 'Female employment rate (2013/14)',\n 'Unemployment rate (2013/14)', 'Youth Unemployment rate (2013/14)',\n 'Proportion of 16-18 year olds who are NEET (%) (2013)',\n 'Proportion of the working-age population who claim benefits (%) (Feb-2014)',\n '% working-age with a disability (2012)',\n 'Proportion of working age people with no qualifications (%) 2013',\n 'Proportion of working age people in London with degree or equivalent and above (%) 2013',\n 'Gross Annual Pay, (2013)', 'Gross Annual Pay - Male (2013)',\n 'Gross Annual Pay - Female (2013)',\n '% adults that volunteered in past 12 months (2010/11 to 2012/13)',\n 'Number of jobs by workplace (2012)',\n '% of employment that is in public sector (2012)', 'Jobs Density, 2012',\n 'Number of active businesses, 2012',\n 'Two-year business survival rates 2012',\n 'Crime rates per thousand population 2013/14',\n 'Fires per thousand population (2013)',\n 'Ambulance incidents per hundred population (2013)',\n 'Median House Price, 2013',\n 'Average Band D Council Tax charge (£), 2014/15',\n 'New Homes (net) 2012/13', 'Homes Owned outright, (2013) %',\n 'Being bought with mortgage or loan, (2013) %',\n 'Rented from Local Authority or Housing Association, (2013) %',\n 'Rented from Private landlord, (2013) %',\n '% of area that is Greenspace, 2005', 'Total carbon emissions (2012)',\n 'Household Waste Recycling Rate, 2012/13',\n 'Number of cars, (2011 Census)',\n 'Number of cars per household, (2011 Census)',\n '% of adults who cycle at least once per month, 2011/12',\n 'Average Public Transport Accessibility score, 2012',\n 'Indices of Multiple Deprivation 2010 Rank of Average Score',\n 'Income Support claimant rate (Feb-14)',\n '% children living in out-of-work families (2013)',\n 'Achievement of 5 or more A*- C grades at GCSE or equivalent including English and Maths, 2012/13',\n 'Rates of Children Looked After (2013)',\n '% of pupils whose first language is not English (2014)',\n 'Male life expectancy, (2010-12)', 'Female life expectancy, (2010-12)',\n 'Teenage conception rate (2012)',\n 'Life satisfaction score 2012-13 (out of 10)',\n 'Worthwhileness score 2012-13 (out of 10)',\n 'Happiness score 2012-13 (out of 10)',\n 'Anxiety score 2012-13 (out of 10)', 'Political control in council',\n 'Proportion of seats won by Conservatives in 2014 election',\n 'Proportion of seats won by Labour in 2014 election',\n 'Proportion of seats won by Lib Dems in 2014 election',\n 'Turnout at 2014 local elections'],\n dtype='object')\n\n\n\ndf.head()\n\n\n\n\n\n\n\n\nCode\nArea/INDICATOR\nInner/ Outer London\nGLA Population Estimate 2013\nGLA Household Estimate 2013\nInland Area (Hectares)\nPopulation density (per hectare) 2013\nAverage Age, 2013\nProportion of population aged 0-15, 2013\nProportion of population of working-age, 2013\n...\nTeenage conception rate (2012)\nLife satisfaction score 2012-13 (out of 10)\nWorthwhileness score 2012-13 (out of 10)\nHappiness score 2012-13 (out of 10)\nAnxiety score 2012-13 (out of 10)\nPolitical control in council\nProportion of seats won by Conservatives in 2014 election\nProportion of seats won by Labour in 2014 election\nProportion of seats won by Lib Dems in 2014 election\nTurnout at 2014 local elections\n\n\n\n\n0\nE09000001\nCity of London\nInner London\n8000\n4514.371383\n290.4\n27.525868\n41.303887\n7.948036\n77.541617\n...\n.\n8.10\n8.23\n7.44\nx\nNaN\nNaN\nNaN\nNaN\nNaN\n\n\n1\nE09000002\nBarking and Dagenham\nOuter London\n195600\n73261.408580\n3610.8\n54.160527\n33.228935\n26.072939\n63.835021\n...\n35.4\n7.06\n7.57\n6.97\n3.3\nLab\n0.000000\n100.000000\n0.000000\n38.16\n\n\n2\nE09000003\nBarnet\nOuter London\n370000\n141385.794900\n8674.8\n42.651374\n36.896246\n20.886408\n65.505593\n...\n14.7\n7.35\n7.79\n7.27\n2.63\nCons\n50.793651\n42.857143\n1.587302\n41.1\n\n\n3\nE09000004\nBexley\nOuter London\n236500\n94701.226400\n6058.1\n39.044243\n38.883039\n20.282830\n63.146450\n...\n25.8\n7.47\n7.75\n7.21\n3.22\nCons\n71.428571\n23.809524\n0.000000\nnot avail\n\n\n4\nE09000005\nBrent\nOuter London\n320200\n114318.553900\n4323.3\n74.063670\n35.262694\n20.462585\n68.714872\n...\n19.6\n7.23\n7.32\n7.09\n3.33\nLab\n9.523810\n88.888889\n1.587302\n33\n\n\n\n\n5 rows × 76 columns\n\n\n\nLots of different features. We also have really odd NaN values such as x and not available. We can try and get rid of this.\n\ndef isnumber(x):\n try:\n float(x)\n return True\n except:\n if (len(x) > 1) & (\"not avail\" not in x):\n return True\n else:\n return False\n\n# apply isnumber function to every element\ndf = df[df.applymap(isnumber)]\ndf.head()\n\n\n\n\n\n\n\n\nCode\nArea/INDICATOR\nInner/ Outer London\nGLA Population Estimate 2013\nGLA Household Estimate 2013\nInland Area (Hectares)\nPopulation density (per hectare) 2013\nAverage Age, 2013\nProportion of population aged 0-15, 2013\nProportion of population of working-age, 2013\n...\nTeenage conception rate (2012)\nLife satisfaction score 2012-13 (out of 10)\nWorthwhileness score 2012-13 (out of 10)\nHappiness score 2012-13 (out of 10)\nAnxiety score 2012-13 (out of 10)\nPolitical control in council\nProportion of seats won by Conservatives in 2014 election\nProportion of seats won by Labour in 2014 election\nProportion of seats won by Lib Dems in 2014 election\nTurnout at 2014 local elections\n\n\n\n\n0\nE09000001\nCity of London\nInner London\n8000\n4514.371383\n290.4\n27.525868\n41.303887\n7.948036\n77.541617\n...\nNaN\n8.10\n8.23\n7.44\nNaN\nNaN\nNaN\nNaN\nNaN\nNaN\n\n\n1\nE09000002\nBarking and Dagenham\nOuter London\n195600\n73261.408580\n3610.8\n54.160527\n33.228935\n26.072939\n63.835021\n...\n35.4\n7.06\n7.57\n6.97\n3.3\nLab\n0.000000\n100.000000\n0.000000\n38.16\n\n\n2\nE09000003\nBarnet\nOuter London\n370000\n141385.794900\n8674.8\n42.651374\n36.896246\n20.886408\n65.505593\n...\n14.7\n7.35\n7.79\n7.27\n2.63\nCons\n50.793651\n42.857143\n1.587302\n41.1\n\n\n3\nE09000004\nBexley\nOuter London\n236500\n94701.226400\n6058.1\n39.044243\n38.883039\n20.282830\n63.146450\n...\n25.8\n7.47\n7.75\n7.21\n3.22\nCons\n71.428571\n23.809524\n0.000000\nNaN\n\n\n4\nE09000005\nBrent\nOuter London\n320200\n114318.553900\n4323.3\n74.063670\n35.262694\n20.462585\n68.714872\n...\n19.6\n7.23\n7.32\n7.09\n3.33\nLab\n9.523810\n88.888889\n1.587302\n33\n\n\n\n\n5 rows × 76 columns\n\n\n\nThat looks much cleaner.\nReplace the NaN values in numeric columns with the mean.\n\n# get only numeric columns\nnumericColumns = df._get_numeric_data()\n\n\nfrom sklearn.metrics import euclidean_distances\n\n# keep place names and store them in a variable\nplaceNames = df[\"Area/INDICATOR\"]\n\n# let's fill the missing values with mean()\nnumericColumns = numericColumns.fillna(numericColumns.mean())\n\n# let's centralize the data\nnumericColumns -= numericColumns.mean()\n\n# now we compute the euclidean distances between the columns by passing the same data twice\n# the resulting data matrix now has the pairwise distances between the boroughs.\n# CAUTION: note that we are now building a distance matrix in a high-dimensional data space\n# remember the Curse of Dimensionality -- we need to be cautious with the distance values\ndistMatrix = euclidean_distances(numericColumns, numericColumns)\n\nCheck to make sure everything looks ok.\n\nnumericColumns.head()\n\n\n\n\n\n\n\n\nGLA Population Estimate 2013\nGLA Household Estimate 2013\nInland Area (Hectares)\nPopulation density (per hectare) 2013\nAverage Age, 2013\nProportion of population aged 0-15, 2013\nProportion of population of working-age, 2013\nProportion of population aged 65 and over, 2013\n% of population from BAME groups (2013)\n% people aged 3+ whose main language is not English (2011 census)\n...\nAverage Public Transport Accessibility score, 2012\nIndices of Multiple Deprivation 2010 Rank of Average Score\nIncome Support claimant rate (Feb-14)\nRates of Children Looked After (2013)\nLife satisfaction score 2012-13 (out of 10)\nWorthwhileness score 2012-13 (out of 10)\nHappiness score 2012-13 (out of 10)\nProportion of seats won by Conservatives in 2014 election\nProportion of seats won by Labour in 2014 election\nProportion of seats won by Lib Dems in 2014 election\n\n\n\n\n0\n-247760.606061\n-97761.616805\n-4473.681818\n-43.279630\n5.426932\n-11.500067\n8.480871\n3.019196\n-17.390874\n-4.491385\n...\n3.753658\n157.424242\n-1.726749\n42.212121\n0.816364\n0.651212\n0.23303\n0.000000\n0.000000\n-8.881784e-16\n\n\n1\n-60160.606061\n-29014.579608\n-1153.281818\n-16.644971\n-2.648021\n6.624837\n-5.225725\n-1.399112\n5.764246\n-2.905288\n...\n-0.882730\n-82.575758\n1.787041\n20.212121\n-0.223636\n-0.008788\n-0.23697\n-32.854444\n43.384181\n-6.598065e+00\n\n\n2\n114239.393939\n39109.806712\n3910.718182\n-28.154125\n1.019290\n1.438305\n-3.555153\n2.116847\n-2.799300\n1.775548\n...\n-0.883020\n71.424242\n-0.517827\n-18.787879\n0.066364\n0.211212\n0.06303\n17.939207\n-13.758676\n-5.010764e+00\n\n\n3\n-19260.606061\n-7574.761788\n1294.018182\n-31.761255\n3.006083\n0.834727\n-5.914296\n5.079569\n-20.328016\n-15.598200\n...\n-1.364540\n69.424242\n-0.018377\n-8.787879\n0.186364\n0.171212\n0.00303\n38.574127\n-32.806295\n-6.598065e+00\n\n\n4\n64439.393939\n12042.565712\n-440.781818\n3.258171\n-0.614262\n1.014482\n-0.345874\n-0.668608\n25.000030\n15.521631\n...\n-0.174795\n-69.575758\n0.001370\n-6.787879\n-0.053636\n-0.258788\n-0.11697\n-23.330634\n32.273070\n-5.010764e+00\n\n\n\n\n5 rows × 41 columns\n\n\n\nWe can plot out our many dimension space by uncommenting the code below (also note down how long does this take).\n\n#import seaborn as sns\n#sns_plot = sns.pairplot(numericColumns)\n#sns_plot.savefig(\"figs/output.png\")\n\nGiven that this takes quite a while (around 10 minutes), this is the image that would result from uncommenting and running the code above." }, { - "objectID": "content/labs/Lab_5/IM939_Lab_5_1.html#second-task", - "href": "content/labs/Lab_5/IM939_Lab_5_1.html#second-task", + "objectID": "content/labs/Lab_5/IM939_Lab_5_1.html#dimension-reduction", + "href": "content/labs/Lab_5/IM939_Lab_5_1.html#dimension-reduction", "title": "21  Lab: Working with multiple models", - "section": "22.2 Second task:", - "text": "22.2 Second task:\nCan you think of and then generate other maps that you can produce with this data? Have a look at the variables once again and try to produce new “perspectives” to the data and see what they have to say.\nAlso think of visualisations to help you here, can you colour them with a different variable? What would that change?" + "section": "21.2 Dimension reduction", + "text": "21.2 Dimension reduction\nDimension reduction will help us here!\nWe could apply various different types of dimension reduction here. We are specifically going to capture the dissimilarity in the data using multidimensional scaling. Our distance matrix will come in useful here.\n\nfrom sklearn import manifold\n# for instance, typing distMatrix.shape on the console gives:\n# Out[115]: (38, 38) # i.e., the number of rows\n\n# first we generate an MDS object and extract the projections\nmds = manifold.MDS(n_components = 2, max_iter=3000, n_init=1, dissimilarity=\"precomputed\", normalized_stress=False)\nY = mds.fit_transform(distMatrix)\n\nTo interpret what is happening, let us plot the boroughs on the projected two dimensional space.\n\nfrom matplotlib import pyplot as plt\n\nfig, ax = plt.subplots()\nfig.set_size_inches(15, 15)\nplt.suptitle('MDS on only London boroughs')\nax.scatter(Y[:, 0], Y[:, 1], c=\"#D06B36\", s = 100, alpha = 0.8, linewidth=0)\n\nfor i, txt in enumerate(placeNames):\n ax.annotate(txt, (Y[:, 0][i],Y[:, 1][i]))\n\n\n\n\nOur data also include happiness metrics. Pulling these out of our data and carrying out more multidimensional scaling can help us see how the boroughs differ in happiness.\n\n# get the data columns relating to emotions and feelings\ndataOnEmotions = numericColumns[[\"Life satisfaction score 2012-13 (out of 10)\", \"Worthwhileness score 2012-13 (out of 10)\",\"Happiness score 2012-13 (out of 10)\"]]\n\n# a new distance matrix to represent \"emotional distance\"s\ndistMatrix2 = euclidean_distances(dataOnEmotions, dataOnEmotions)\n\n# compute a new \"embedding\" (machine learners' word for projection)\nY2 = mds.fit_transform(distMatrix2)\n\n# let's look at the results\nfig, ax = plt.subplots()\nfig.set_size_inches(15, 15)\nplt.suptitle('An \\\"emotional\\\" look at London boroughs')\nax.scatter(Y2[:, 0], Y2[:, 1], c=\"#D06B36\", s = 100, alpha = 0.8, linewidth=0)\n\nfor i, txt in enumerate(placeNames):\n ax.annotate(txt, (Y2[:, 0][i],Y2[:, 1][i]))\n\n\n\n\nThe location of the different boroughs on the 2 dimensional multidimensional scaling space from the happiness metrics is\n\nresults_fixed = Y2.copy()\nprint(results_fixed)\n\n[[ 0.26955023 -1.03193546]\n [-0.30697124 0.04988649]\n [ 0.11267823 -0.18603719]\n [ 0.09951239 -0.23709264]\n [-0.11233607 0.27677033]\n [ 0.31687906 -0.31587447]\n [-0.08799261 0.21880538]\n [-0.20905701 0.24461554]\n [ 0.21012164 0.17125381]\n [ 0.19306487 0.13163987]\n [-0.18659 0.0989468 ]\n [-0.2618981 0.18342251]\n [-0.2551384 -0.05507685]\n [-0.10018359 0.14805073]\n [ 0.16711463 0.05098098]\n [ 0.10854867 -0.09812561]\n [ 0.16605853 -0.03341054]\n [ 0.09654886 0.00279667]\n [-0.49153577 0.23630239]\n [ 0.4181435 -0.44518512]\n [-0.01774271 0.12920108]\n [-0.29575096 0.19446001]\n [-0.07852039 -0.10487395]\n [-0.10459205 0.06451135]\n [ 0.09001571 0.12021746]\n [ 0.12164733 0.16641986]\n [ 0.19424041 -0.11717992]\n [ 0.00238345 -0.07364946]\n [-0.07160448 0.01590297]\n [ 0.11278589 0.05034198]\n [ 0.03510502 -0.10010882]\n [ 0.05868884 0.07204286]\n [-0.19317386 0.17198096]]\n\n\nWe may want to look at if the general happiness rating captures the position of the boroughs. To do this we need to assign colours based on the binned happiness score.\n\nimport numpy as np\n\ncolorMappingValuesHappiness = np.asarray(dataOnEmotions[[\"Life satisfaction score 2012-13 (out of 10)\"]]).flatten()\nprint(results_fixed.shape)\ncolorMappingValuesHappiness.shape\n\ncolorMappingValuesHappiness\n#c = colorMappingValuesCrime, cmap = plt.cm.Greens\n\n(33, 2)\n\n\narray([ 0.81636364, -0.22363636, 0.06636364, 0.18636364, -0.05363636,\n 0.34636364, -0.06363636, -0.28363636, -0.04363636, -0.10363636,\n -0.12363636, -0.21363636, -0.05363636, -0.08363636, 0.05636364,\n 0.11636364, 0.06636364, 0.01636364, -0.20363636, 0.39636364,\n 0.00636364, -0.19363636, -0.05363636, -0.10363636, -0.06363636,\n -0.00363636, 0.13636364, -0.01363636, -0.03363636, -0.00363636,\n -0.04363636, -0.05363636, -0.19363636])\n\n\nFinally, we can plot this. What can you see?\n\n# let's look at the results\nfig, ax = plt.subplots()\nfig.set_size_inches(15, 15)\nplt.suptitle('An \\\"emotional\\\" look at London boroughs')\n#ax.scatter(results_fixed[:, 0], results_fixed[:, 1], c = colorMappingValuesHappiness, cmap='viridis')\nplt.scatter(results_fixed[:, 0], results_fixed[:, 1], c = colorMappingValuesHappiness, s = 100, cmap=plt.cm.Greens)\n\nfor i, txt in enumerate(placeNames):\n ax.annotate(txt, (results_fixed[:, 0][i],results_fixed[:, 1][i]))\n\n\n\n\n\n# get the data columns relating to emotions and feelings\ndataOnDiversity = numericColumns[[\"Proportion of population aged 0-15, 2013\", \"Proportion of population of working-age, 2013\", \"Proportion of population aged 65 and over, 2013\", \"% of population from BAME groups (2013)\", \"% people aged 3+ whose main language is not English (2011 census)\"]]\n\n# a new distance matrix to represent \"emotional distance\"s\ndistMatrix3 = euclidean_distances(dataOnDiversity, dataOnDiversity)\n\nmds = manifold.MDS(n_components = 2, max_iter=3000, n_init=1, dissimilarity=\"precomputed\", normalized_stress = False)\nY = mds.fit_transform(distMatrix3)\n\n# Visualising the data.\nfig, ax = plt.subplots()\nfig.set_size_inches(15, 15)\nplt.suptitle('An \\\"diversity\\\" look at London boroughs')\nax.scatter(Y[:, 0], Y[:, 1], s = 100, c = colorMappingValuesHappiness, cmap=plt.cm.Greens)\n\nfor i, txt in enumerate(placeNames):\n ax.annotate(txt, (Y[:, 0][i],Y[:, 1][i]))\n\n\n\n\n\n\n\n\n\n\nIt is now your turn!\n\n\n\n\n21.2.1 First task:\nThis looks very different to the one above on “emotion” related variables. Our job now is to relate these two projections to one another. Do you see similarities? Do you see clusters of boroughs? Can you reflect on how you can relate and combine these two maps conceptually?\n\n\n21.2.2 Second task:\nCan you think of and then generate other maps that you can produce with this data? Have a look at the variables once again and try to produce new “perspectives” to the data and see what they have to say.\nAlso think of visualisations to help you here, can you colour them with a different variable? What would that change?\n\n\n\n\n\n\n\nPage, Scott E. 2018. “Why ‘Many-Model Thinkers’ Make Better Decisions.” Harvard Business Review, November. https://hbr.org/2018/11/why-many-model-thinkers-make-better-decisions." }, { "objectID": "content/labs/Lab_5/IM939_Lab_5_2.html#data-wrangling", @@ -1117,7 +1110,7 @@ "href": "content/references.html", "title": "References", "section": "", - "text": "Calero Valdez, André, Martina Ziefle, and Michael Sedlmair. 2018.\n“Studying Biases in Visualization\nResearch: Framework and\nMethods.” In Cognitive Biases in\nVisualizations, edited by Geoffrey Ellis, 13–27. Cham:\nSpringer International Publishing. https://doi.org/10.1007/978-3-319-95831-6_2.\n\n\nCortez, Paulo, A Cerdeira, F Almeida, T Matos, and J. Reis. 2009.\n“Wine Quality.” UCI Machine Learning\nRepository. https://doi.org/10.24432/C56S3T.\n\n\nFisher, R. A. 1936. “Iris.” UCI Machine Learning\nRepository. https://doi.org/10.24432/C56C76.\n\n\nIgual, Laura, and Santi Seguí. 2017. “Regression\nAnalysis.” In Introduction to Data\nScience: A Python\nApproach to Concepts, Techniques\nand Applications, 97–114. Cham: Springer International\nPublishing. https://doi.org/10.1007/978-3-319-50017-1_6.\n\n\nKnuth, Donald E. 1984. “Literate Programming.” Comput.\nJ. 27 (2): 97–111. https://doi.org/10.1093/comjnl/27.2.97.\n\n\nRedmond, Michael. 2009. “Communities and\nCrime.” UCI Machine Learning Repository. https://doi.org/10.24432/C53W3X.\n\n\nRouncefield, Mary. 1995. “The Statistics of\nPoverty and Inequality.” Journal of\nStatistics Education 3 (2): 8. https://doi.org/10.1080/10691898.1995.11910491." + "text": "Calero Valdez, André, Martina Ziefle, and Michael Sedlmair. 2018.\n“Studying Biases in Visualization\nResearch: Framework and\nMethods.” In Cognitive Biases in\nVisualizations, edited by Geoffrey Ellis, 13–27. Cham:\nSpringer International Publishing. https://doi.org/10.1007/978-3-319-95831-6_2.\n\n\nCortez, Paulo, A Cerdeira, F Almeida, T Matos, and J. Reis. 2009.\n“Wine Quality.” UCI Machine Learning\nRepository. https://doi.org/10.24432/C56S3T.\n\n\nFisher, R. A. 1936. “Iris.” UCI Machine Learning\nRepository. https://doi.org/10.24432/C56C76.\n\n\nIgual, Laura, and Santi Seguí. 2017. “Regression\nAnalysis.” In Introduction to Data\nScience: A Python\nApproach to Concepts, Techniques\nand Applications, 97–114. Cham: Springer International\nPublishing. https://doi.org/10.1007/978-3-319-50017-1_6.\n\n\nKnuth, Donald E. 1984. “Literate Programming.” Comput.\nJ. 27 (2): 97–111. https://doi.org/10.1093/comjnl/27.2.97.\n\n\nPage, Scott E. 2018. “Why ‘Many-Model\nThinkers’ Make Better Decisions.”\nHarvard Business Review, November. https://hbr.org/2018/11/why-many-model-thinkers-make-better-decisions.\n\n\nRedmond, Michael. 2009. “Communities and\nCrime.” UCI Machine Learning Repository. https://doi.org/10.24432/C53W3X.\n\n\nRouncefield, Mary. 1995. “The Statistics of\nPoverty and Inequality.” Journal of\nStatistics Education 3 (2): 8. https://doi.org/10.1080/10691898.1995.11910491." }, { "objectID": "content/labs/labs_setup.html#install-anaconda", diff --git a/sitemap.xml b/sitemap.xml index 4186024..99c0a1f 100644 --- a/sitemap.xml +++ b/sitemap.xml @@ -2,186 +2,186 @@ https://warwickcim.github.io/IM939_handbook/index.html - 2023-11-03T12:32:27.120Z + 2023-11-03T13:08:35.090Z https://warwickcim.github.io/IM939_handbook/content/about/teaching_staff.html - 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2023-11-03T12:32:28.075Z + 2023-11-03T13:08:36.063Z https://warwickcim.github.io/IM939_handbook/content/sessions/session-09.html - 2023-11-03T12:32:28.082Z + 2023-11-03T13:08:36.070Z https://warwickcim.github.io/IM939_handbook/content/references.html - 2023-11-03T12:32:28.090Z + 2023-11-03T13:08:36.078Z https://warwickcim.github.io/IM939_handbook/content/labs/labs_setup.html - 2023-11-03T12:32:28.099Z + 2023-11-03T13:08:36.087Z https://warwickcim.github.io/IM939_handbook/content/files-and-folders.html - 2023-11-03T12:32:28.105Z + 2023-11-03T13:08:36.093Z

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