Crater_ID @shananigains-blog - Tumblr Blog

Running K-means Cluster Analysis

A k-means cluster analysis was conducted to identify whether education impacted a persons success in life based off 14 variables that represent characteristics that would impact personal income. Clustering variables included binary responses to gender, race(Hispanic/Latino, Black/African American, Asian and White), born in the United States, lived with at least one parent growing up, working full-time, working part-time and quantitate responses to age, highest form of education, total family income, in the last 4 weeks how often a person felt down hearted/depressed, and in the last four weeks how often physical/emotional problems kept someone from social events. All clustering variables were standardized to have a mean of 0 and a standard deviation of 1.

Data were randomly split into a training set that included 70% of the observations (N=29807) and a test set that included 30% of the observations (N=12775). A series of k-means cluster analyses were conducted on the training data specifying k=1-9 clusters, using Euclidean distance. The variance in the clustering variables that was accounted for by the clusters (r-square) was plotted for each of the nine cluster solutions in an elbow curve to provide guidance for choosing the number of clusters to interpret.

The Elbow Curve was inconclusive, suggesting 2,3 and 5-cluster solutions might be interpreted. The results below are for the 5-cluster solution.

Canonical discriminant analyses was used to reduce the 14 clustering variable down a few variables that accounted for most of the variance in the clustering variables. A scatterplot of the first two canonical variables by cluster indicated that the observations in all clusters were densely packed with relatively low within cluster variance, and did overlap with the other clusters. The results of this plot suggest that the best cluster solution may have more than 5 clusters, so it will be especially important to also evaluate the cluster solutions with more than 5 clusters. The data overlaps probably based off so many data points being tested.

In order to externally validate the clusters, an Analysis of Variance (ANOVA) was conducting to test for significant differences between the clusters on personal income. A tukey test was used for post hoc comparisons between the clusters. Results indicated significant differences between the clusters on personal income (p-value = 1853, p<.0001). The tukey post hoc comparisons showed significant differences between clusters on personal income. People in cluster 2 had the highest personal income (mean=9.48, sd=4.17), and cluster 1 had the lowest personal income (mean=4.86, sd=3.57).

Running a Lasso Regression Analysis

A lasso regression analysis was conducted to identify a subset of variables from a pool of 14 categorical and quantitative predictor variables that best predicted a quantitative response variable measuring highest grade of education a person had. These variables were age, gender, race(Hispanic/Latino, Black/African American, Asian and White), born in the United States, Lived with at least on parent growing up, working full-time, working part-time, total personal income, total family income, in the last 4 weeks how often a person felt down hearted/depressed, and in the last four weeks how often physical/emotional problems kept someone from social events.

Data were randomly split into a training set that included 70% of the observations (N=29807) and a test set that included 30% of the observations (N=12775). The least angle regression algorithm with k=10 fold cross validation was used to estimate the lasso regression model in the training set, and the model was validated using the test set. The change in the cross validation average (mean) squared error at each step was used to identify the best subset of predictor variables.

All variables were retained in the model with age (-0.40) being the largest negative correlation to highest grade of education and personal income being the highest (0.89).

These 14 variables accounted for 28.3% of variance in the highest grade of education response variable.

Running a Random Forest

Model on prediction of a person getting Breast Cancer.

From running this important feature code, it shows that although most of these feature have roughly the same amount of pull, life expectancy has the largest value at 0.1798.

From this we see that at 9 trees we get about 3% accuracy. This is a poor level of accuracy and its probably because this data does not have enough variables to chose from in order to predict if a person is going to get breast cancer.

Running a Classification Tree

I chose to run a model to see if there was a correlation between breast cancer and other outside factors like income, urban rate, co2 emissions as well as others. The decision tree is very extensive but it don’t seem to find a correlation between breast cancer and these other factors.

Testing a Logistic Regression Model

I tested my logistic regression model on where the most craters on Mars were located to see if there was a correlation as to direction of the mass comet and astroid collisions. Location and number of layers are used as binary categories by breaking Mars up in four quadrants and the number of layers were split up into a category of 3 or less layers and 4 or more layers. This break up of layers divides the smaller craters from the higher impact craters. The odds of being in quadrant 1 of Mars were more than 3 times as likely with values (OR = 3.19, 95% CI =1.85-5.51 , p < 0.001). This proves that the mass comet and astroid collisions came from impacts largely from one direction.

Test a Multiple Regression Model

For this assignment I chose to test the relationship between the diameter, depth, and layers around a crater on Mars. From looking at the following code, you can see that diameter, depth and number of layers are all confounding variables that work together to make a better model. Adding each one of these variables gave a slightly larger r-squared value, with the highest value being 56% which isn’t great but still and increase from the first model. All of the p-values were less than 0.05 and because the t values and coefficients were all positive we can conclude that they are positively correlated.

Looking further down to the plots, you can see from the figure 2 that the model is pretty well fitted. The leverage plot shows that although at first glance there looks like outliers, I chose not to get rid of them because they either where close to the zero value of H-leverage or they seemed to be influential to the dataset.

Testing a Basic Linear Regression Model

For this assignment I have categorized my explanatory variable, location, into 2 categories, upper and lower part of Mars. I then ran an ols code against the number of layers the crater had to test the linear regression model. The results on the linear regression model indicate that Location (beta = 0.0225, p < 0.0001) is insignificantly associated with the number of layers a crater has.

Writing about your Data

Sample:

The sample of Mars Crater Dataset is from a study by Stuart Robbins to present a global database for Mars. This dataset contains data for 378,540 craters with diameters greater than 1 km. This dataset is curtail to understanding the heavily cratered terrain that was created during the “heavy bombardment” between 4.2 and 3.8 billion years ago.

Procedure:

The data was collected through Archetypal imaging of all Crater Ejecta Morphologies. This describes the depth, diameter, and layers produced around the crater from impact of asteroids, proto-planets, and comets.

Measures:

Each Crater was given an ID based on the region of the planet it was in. The location and diameter were then derived using the center of a non-linear least-squares circle fit. The depth floor was determined manually by points selected as the lowest elevation. The number of layers produced by the craters was the maximum number of cohesive layers in any azimuthal direction that could be reliably identified.

Testing potential Moderator

I chose to do the Pearson Correlation with my explanatory variable being Crater diameter and my response variable being depth. I then chose to see if there was a correlation between diameter, depth, and location on Mars. All of the p-values for the four different locations on the craters on Mars are very small. With that being said, the correlation coefficients and their fraction of variability are rather high. There seems to be a significant relationship between crater diameter and depth in the locations 3 and 4 on Mars in the 60th percent tile. This the the bottom half of Mars in my code.

Generating a Correlation Coefficient

Using Pearson correlation, Is there a positive correlation between a craters depth and diameter?

I chose to do the pearson correlation twice. I used a sub dataset of values of diameters between 25 and 50 and then corresponding depth values as shown in the plot. This gave me a correlation of .0881 and a p-value of .0314. I also did the pearson correlation test on the whole dataset of diameter and depth. This gave me a correlation of.576 and a p-value of zero. Upon calculating the fraction of variability I got that my subdata set is .8% predictable, which is insignificant. The whole dataset gives us roughly 33% predictability.

Running a Chi-Square Test for comparison on location of Mars Craters

comp12 = chi: 15.390556045895853, p-value: 0.0015115567574012986, expected counts: 3

comp13 = chi: 3.463180648481729, p-value: 0.17700269434414428, expected counts: 2

comp14 = chi: 10.953861852433281, p-value: 0.011977996111128056, expected counts: 3

comp23 = chi: 14.019917577667067, p-value: 0.002878166517605965, expected counts: 3

comp24 = chi: 8.780550092377377, p-value: 0.03235546289797779, expected counts: 3

comp34 = chi: 5.808564663789922, p-value: 0.12130464830193209, expected counts: 3

After running a Chi-Square Test of Independence to check for a Type 1 error and adjusting the p-value for the number of comparisons I took. The new acceptable p-value is .0083. This means that I'm going to accept the null hypothesis for all comparisons except for quadrants 1:2 and 2:3. Those are the only ones with p-values less than .0083.

Running an Analysis of Variance

For easy understanding I have put my comments in Bold.

The original hypothesis was to see if there was a correlation between a craters size/abundance and the craters location on Mars.

import numpy as np import pandas as pd import statsmodels.formula.api as smf import statsmodels.stats.multicomp as multi

data = pd.read_csv('MarsCraterData.csv',low_memory = False)

# upper case all DataFrame column names, meant for less confusion data.columns = map(str.upper, data.columns)

# bug fix for display runtime errors pd.set_option('display.float_format', lambda x: '%f'%x)

sub1 = data[(data['NUMBER_LAYERS'] >= 1) & (data['DEPTH_RIMFLOOR_TOPOG'] >= 0.5)] # Making a copy sub2 = sub1.copy()

# dividing Mars into 2 quadrants (upper and lower)

def LOCATION(row):

if row['LATITUDE_CIRCLE_IMAGE'] >= 0 and row['LONGITUDE_CIRCLE_IMAGE'] >= 0 :

return 1

else :

return 2

data['LOCATION'] = data.apply(lambda row: LOCATION(row), axis=1)

sub2['LOCATION'] = sub2.apply(lambda row: LOCATION(row), axis=1)

# this uses all data sets

sub3 = data[['CRATER_ID','LATITUDE_CIRCLE_IMAGE',

'LONGITUDE_CIRCLE_IMAGE','DEPTH_RIMFLOOR_TOPOG',

'NUMBER_LAYERS','LOCATION']]

# This is the data with 1 or more layers to the craters edge.

sub4 = sub2[['CRATER_ID','LATITUDE_CIRCLE_IMAGE',

'LONGITUDE_CIRCLE_IMAGE','DEPTH_RIMFLOOR_TOPOG',

'NUMBER_LAYERS','LOCATION']]

sub2['LOCATION'] = sub2['LOCATION'].astype('category')

data['LOCATION'] = data['LOCATION'].astype('category')

pt5 = sub2.groupby('LOCATION').size()*100/len(sub2)

print('% groupby',pt5)

pt6 = data.groupby('LOCATION').size()*100/len(data)

print('% groupby all data',pt6)

% groupby LOCATION 1 26.506024 2 73.493976 dtype: float64 % groupby all data LOCATION 1 52.362631 2 47.637369 dtype: float64

# ols function for calculating the F-Statistic and # associated p value

model1 = smf.ols(formula = 'NUMBER_LAYERS ~ C(LOCATION)',data = data) results1 = model1.fit() print(results1.summary())

model2 = smf.ols(formula = 'NUMBER_LAYERS ~ C(LOCATION)',data = sub2) results2 = model2.fit() print(results2.summary())

OLS Regression Results

============================================================================== Dep. Variable: NUMBER_LAYERS R-squared: 0.001 Model: OLS Adj. R-squared: 0.001 Method: Least Squares F-statistic: 48.00 Date: Mon, 22 Apr 2019 Prob (F-statistic): 4.30e-12 Time: 13:17:22 Log-Likelihood: -35314. No. Observations: 65499 AIC: 7.063e+04 Df Residuals: 65497 BIC: 7.065e+04 Df Model: 1 Covariance Type: nonrobust ==================================================================================== coef std err t P>|t| [0.025 0.975] ------------------------------------------------------------------------------------ Intercept 0.1062 0.002 47.401 0.000 0.102 0.111 C(LOCATION)[T.2] 0.0225 0.003 6.928 0.000 0.016 0.029 ============================================================================== Omnibus: 53764.522 Durbin-Watson: 1.368 Prob(Omnibus): 0.000 Jarque-Bera (JB): 1060497.174 Skew: 4.036 Prob(JB): 0.00 Kurtosis: 20.984 Cond. No. 2.57 ============================================================================== Warnings: [1] Standard Errors assume that the covariance matrix of the errors is correctly specified. OLS Regression Results ============================================================================== Dep. Variable: NUMBER_LAYERS R-squared: 0.008 Model: OLS Adj. R-squared: 0.007 Method: Least Squares F-statistic: 8.880 Date: Mon, 22 Apr 2019 Prob (F-statistic): 0.00295 Time: 13:17:22 Log-Likelihood: -1244.8 No. Observations: 1079 AIC: 2494. Df Residuals: 1077 BIC: 2504. Df Model: 1 Covariance Type: nonrobust ==================================================================================== coef std err t P>|t| [0.025 0.975] ------------------------------------------------------------------------------------ Intercept 1.6748 0.045 36.893 0.000 1.586 1.764 C(LOCATION)[T.2] -0.1578 0.053 -2.980 0.003 -0.262 -0.054 ============================================================================== Omnibus: 226.834 Durbin-Watson: 1.614 Prob(Omnibus): 0.000 Jarque-Bera (JB): 394.326 Skew: 1.321 Prob(JB): 2.36e-86 Kurtosis: 4.339 Cond. No. 3.66 ==============================================================================

Model one, using all data for Mars craters has a p-value of less than .05. Model two, using only data with more than 1 layer and more than .5 km deep craters also has a very low p-value, 0.00295. This means that there is an association between the location and the number of layers in a crater on Mars.

mc1 = multi.MultiComparison(sub2['NUMBER_LAYERS'], sub2['LOCATION']) res1 = mc1.tukeyhsd() print(res1.summary())

Multiple Comparison of Means - Tukey HSD,FWER=0.05 ============================================= group1 group2 meandiff lower upper reject --------------------------------------------- 1 2 -0.1578 -0.2617 -0.0539 True ---------------------------------------------

This multiple comparison table shows that because the reject table is true, we can reject the null hypothesis.

Creating Graphs for the Data

Here is my code along with my outputs. I have my comments in bold and the outputs are highlighted for less confusion hopefully.

import numpy as np import pandas as pd

import matplotlib.pyplot as plt

data = pd.read_csv(‘MarsCraterData.csv’,low_memory = False)

# upper case all DataFrame column names, meant for less confusion data.columns = map(str.upper, data.columns)

# bug fix for display runtime errors pd.set_option('display.float_format’, lambda x: ’%f’%x)

print(len(data)) print(len(data.columns))

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# C = counts P = percentage c1 = data['LATITUDE_CIRCLE_IMAGE’].value_counts(sort=False) # print('count latitude’,c1)

p1 = data['LATITUDE_CIRCLE_IMAGE’].value_counts(sort=False,normalize = True) # print(’% latitude’,p1)

c2 = data['LONGITUDE_CIRCLE_IMAGE’].value_counts(sort=False) # print('count longitude’,c2)

p2 = data['LONGITUDE_CIRCLE_IMAGE’].value_counts(sort=False,normalize = True) # print(’% longitude’,p2)

c3 = data['DEPTH_RIMFLOOR_TOPOG’].value_counts(sort=False) # print('count depth’,c3)

p3 = data['DEPTH_RIMFLOOR_TOPOG’].value_counts(sort=False,normalize = True) # print(’% depth’,p3)

c4 = data['NUMBER_LAYERS’].value_counts(sort=False) # print('count layers’,c4)

p4 = data['NUMBER_LAYERS’].value_counts(sort=False,normalize = True) # print(’% layers’,p4)

ct4 = data.groupby('NUMBER_LAYERS’).size() print('groupby data’,ct4) pt4 = data.groupby('NUMBER_LAYERS’).size()*100/len(data) print(’% groupby data’,pt4)

groupby data NUMBER_LAYERS 0 59840 1 3895 2 1556 3 184 4 22 5 2 dtype: int64 % groupby data NUMBER_LAYERS 0 91.360173 1 5.946656 2 2.375609 3 0.280920 4 0.033588 5 0.003053 dtype: float64

Making a subset of data. Craters that have 1 or more layers and that are at least 0.5 meters in depth. This is to be used for comparison later on.

sub1 = data[(data['NUMBER_LAYERS’] >= 1) & (data['DEPTH_RIMFLOOR_TOPOG’] >= 0.5)] # Making a copy sub2 = sub1.copy()

print(sub1.head(10))

CRATER_ID CRATER_NAME LATITUDE_CIRCLE_IMAGE LONGITUDE_CIRCLE_IMAGE \ 1 01-000001 Korolev 72.760000 164.464000 20 01-000020 65.135000 177.982000 25 01-000025 70.051000 -7.939000 26 01-000026 70.884000 -166.427000 27 01-000027 66.330000 39.798000 28 01-000028 Louth 70.173000 103.226000 37 01-000037 77.116000 89.130000 39 01-000039 66.394000 144.036000 40 01-000040 73.909000 -173.606000 47 01-000047 67.909000 92.848000 DIAM_CIRCLE_IMAGE DEPTH_RIMFLOOR_TOPOG MORPHOLOGY_EJECTA_1 \ 1 82.020000 1.970000 Rd/MLERS 20 45.710000 1.860000 Rd/DLEPC/DLERS 25 39.510000 2.080000 SLERS 26 36.850000 1.980000 MLERS 27 36.410000 1.900000 MLERS 28 36.280000 1.410000 SLERS 37 30.880000 0.710000 SLERS 39 29.460000 1.770000 Rd/DLERS 40 28.450000 1.410000 MLERS 47 27.230000 1.850000 Rd/DLERC/DLERS MORPHOLOGY_EJECTA_2 MORPHOLOGY_EJECTA_3 NUMBER_LAYERS 1 HuBL 3 20 HuBL 2 25 HuSL 1 26 HuBL Inner is Small-Crown 4 27 HuBL 3 28 HuBL 1 37 HuSL 1 39 HuBL 2 40 HuBL 3 47 HuBL 2

# dividing Mars into 2 quadrants (upper and lower) def LOCATION(row): if row['LATITUDE_CIRCLE_IMAGE’] >= 0 and row['LONGITUDE_CIRCLE_IMAGE’] >= 0 : return 1 else : return 2

data['LOCATION’] = data.apply(lambda row: LOCATION(row), axis=1) sub2['LOCATION’] = sub2.apply(lambda row: LOCATION(row), axis=1)

# this uses all data sets

sub3 = data[['CRATER_ID’,'LATITUDE_CIRCLE_IMAGE’, 'LONGITUDE_CIRCLE_IMAGE’,'DEPTH_RIMFLOOR_TOPOG’, 'NUMBER_LAYERS’,'LOCATION’]]

print(sub3.head(10))

CRATER_ID LATITUDE_CIRCLE_IMAGE LONGITUDE_CIRCLE_IMAGE \ 0 01-000000 84.367000 108.746000 1 01-000001 72.760000 164.464000 2 01-000002 69.244000 -27.240000 3 01-000003 70.107000 160.575000 4 01-000004 77.996000 95.617000 5 01-000005 68.547000 137.849000 6 01-000006 69.492000 169.751000 7 01-000007 78.716000 -87.249000 8 01-000008 75.539000 13.829000 9 01-000009 69.371000 75.147000 DEPTH_RIMFLOOR_TOPOG NUMBER_LAYERS LOCATION 0 0.220000 0 1 1 1.970000 3 1 2 0.090000 0 2 3 0.130000 0 1 4 0.110000 0 1 5 0.190000 0 1 6 0.100000 0 1 7 0.050000 0 2 8 0.110000 0 1 9 0.000000 0 1

# This is the data with 1 or more layers to the craters edge.

sub4 = sub2[['CRATER_ID’,'LATITUDE_CIRCLE_IMAGE’, 'LONGITUDE_CIRCLE_IMAGE’,'DEPTH_RIMFLOOR_TOPOG’, 'NUMBER_LAYERS’,'LOCATION’]]

print(sub4.head(10))

CRATER_ID LATITUDE_CIRCLE_IMAGE LONGITUDE_CIRCLE_IMAGE \ 1 01-000001 72.760000 164.464000 20 01-000020 65.135000 177.982000 25 01-000025 70.051000 -7.939000 26 01-000026 70.884000 -166.427000 27 01-000027 66.330000 39.798000 28 01-000028 70.173000 103.226000 37 01-000037 77.116000 89.130000 39 01-000039 66.394000 144.036000 40 01-000040 73.909000 -173.606000 47 01-000047 67.909000 92.848000 DEPTH_RIMFLOOR_TOPOG NUMBER_LAYERS LOCATION 1 1.970000 3 1 20 1.860000 2 1 25 2.080000 1 2 26 1.980000 4 2 27 1.900000 3 1 28 1.410000 1 1 37 0.710000 1 1 39 1.770000 2 1 40 1.410000 3 2 47 1.850000 2 1

print('Quadrant of craters with 1 or more layers’) p5 = sub2['LOCATION’].value_counts(sort = False) print(p5)

print('Quadrant of craters’) p6 = data['LOCATION’].value_counts(sort = False) print(p6)

Quadrant of craters with 1 or more layers 1 286 2 793 Name: LOCATION, dtype: int64 Quadrant of craters 1 34297 2 31202 Name: LOCATION, dtype: int64

pt5 = sub2.groupby('LOCATION’).size()*100/len(sub2) print(’% groupby’,pt5)

pt6 = data.groupby('LOCATION’).size()*100/len(data) print(’% groupby all data’,pt6)

% groupby LOCATION 1 26.506024 2 73.493976 dtype: float64 % groupby all data LOCATION 1 52.362631 2 47.637369 dtype: float64

From this data we can see that over 73% of the larger impact craters (ie. 1 or more layers) landed on the lower half of Mars where as an almost even distribution of craters 52% and 47% are recorded using all of the data.

# Categorial seaborn.countplot(x = 'LOCATION', data = sub2) plt.xlabel('Location') plt.ylabel('Number of Craters with more than 1 layer') plt.title('Mars Craters Location')

# Categorial seaborn.countplot(x = 'LOCATION', data = data) plt.xlabel('Location') plt.ylabel('Number of Craters ') plt.title('Mars Craters Location')

# Distributions of depth of craters formed on Mars mean = data['DEPTH_RIMFLOOR_TOPOG'].mean() print(mean) mode = data['DEPTH_RIMFLOOR_TOPOG'].mode() print(mode) data['DEPTH_RIMFLOOR_TOPOG'].describe()

0.04500709934502822 0 0.000000 dtype: float64

count 65499.000000 mean 0.045007 std 0.164268 min -0.030000 25% 0.000000 50% 0.000000 75% 0.000000 max 3.140000 Name: DEPTH_RIMFLOOR_TOPOG, dtype: float64

sub2['DEPTH_RIMFLOOR_TOPOG'].describe()

count 1079.000000 mean 0.841409 std 0.309688 min 0.500000 25% 0.620000 50% 0.760000 75% 0.970000 max 2.260000 Name: DEPTH_RIMFLOOR_TOPOG, dtype: float64

This gives us more information because there is such a large number of zero layered craters that gave us very low values of distributions.

scat1 = seaborn.regplot(x = 'LONGITUDE_CIRCLE_IMAGE', y = 'LATITUDE_CIRCLE_IMAGE', fit_reg = False, data = data) plt.xlabel('Longitude decimal degrees East') plt.ylabel('Latitude decimal degrees North') plt.title('Scatter plot of location of Craters on Mars all data')

This graph is useless because there are so many data points clustered that you cannot decipher anything.

scat2 = seaborn.regplot(x = 'LONGITUDE_CIRCLE_IMAGE', y = 'LATITUDE_CIRCLE_IMAGE', fit_reg = False, data = sub2) plt.xlabel('Longitude decimal degrees East') plt.ylabel('Latitude decimal degrees North') plt.title('Scatter plot of location of Craters on Mars all data')

This is a very interesting plot because there is a large amount of empty space in the graph roughly between longitude -80-180 with latitude 0-30. This could possibly be from lack of data on that part of Mars.

data['NUMBER_LAYERS'] = data['NUMBER_LAYERS'].convert_objects(convert_numeric=True)

scat3 = seaborn.factorplot(x = 'NUMBER_LAYERS', y ='DEPTH_RIMFLOOR_TOPOG', data = data, ci = None) plt.xlabel('Number of Layers') plt.ylabel('Depth of crater rim in $km$') plt.title('Association between crater depth and layers of all data')

scat4 = seaborn.factorplot(x = 'NUMBER_LAYERS', y ='DEPTH_RIMFLOOR_TOPOG', data = sub2, ci = None) plt.xlabel('Number of Layers') plt.ylabel('Depth of crater rim in $km$') plt.title('Association between crater depth and layers excluding \n zero layers data and depth less than 0.5 $km$')

These last two graphs show the association between crater depth and the layers around the crater rim. As you can see there is a large correlation between a deeper crater and the number of layers around it.

Making Data Management Decisions

Here is my code along with my outputs. I have my comments in bold and the outputs are highlighted for less confusion hopefully.

import numpy as np import pandas as pd

data = pd.read_csv('MarsCraterData.csv',low_memory = False)

# upper case all DataFrame column names, meant for less confusion data.columns = map(str.upper, data.columns)

# bug fix for display runtime errors pd.set_option('display.float_format', lambda x: '%f'%x)

print(len(data)) print(len(data.columns))

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# C = counts P = percentage c1 = data['LATITUDE_CIRCLE_IMAGE'].value_counts(sort=False) # print('count latitude',c1)

p1 = data['LATITUDE_CIRCLE_IMAGE'].value_counts(sort=False,normalize = True) # print('% latitude',p1)

c2 = data['LONGITUDE_CIRCLE_IMAGE'].value_counts(sort=False) # print('count longitude',c2)

p2 = data['LONGITUDE_CIRCLE_IMAGE'].value_counts(sort=False,normalize = True) # print('% longitude',p2)

c3 = data['DEPTH_RIMFLOOR_TOPOG'].value_counts(sort=False) # print('count depth',c3)

p3 = data['DEPTH_RIMFLOOR_TOPOG'].value_counts(sort=False,normalize = True) # print('% depth',p3)

c4 = data['NUMBER_LAYERS'].value_counts(sort=False) # print('count layers',c4)

p4 = data['NUMBER_LAYERS'].value_counts(sort=False,normalize = True) # print('% layers',p4)

ct4 = data.groupby('NUMBER_LAYERS').size() print('groupby data',ct4) pt4 = data.groupby('NUMBER_LAYERS').size()*100/len(data) print('% groupby data',pt4)

groupby data NUMBER_LAYERS 0 59840 1 3895 2 1556 3 184 4 22 5 2 dtype: int64 % groupby data NUMBER_LAYERS 0 91.360173 1 5.946656 2 2.375609 3 0.280920 4 0.033588 5 0.003053 dtype: float64

Making a subset of data. Craters that have 1 or more layers and that are at least 0.5 meters in depth. This is to be used for comparison later on.

sub1 = data[(data['NUMBER_LAYERS'] >= 1) & (data['DEPTH_RIMFLOOR_TOPOG'] >= 0.5)] # Making a copy sub2 = sub1.copy()

print(sub1.head(10))

# dividing Mars into 2 quadrants (upper and lower) def LOCATION(row): if row['LATITUDE_CIRCLE_IMAGE'] >= 0 and row['LONGITUDE_CIRCLE_IMAGE'] >= 0 : return 1 else : return 2

data['LOCATION'] = data.apply(lambda row: LOCATION(row), axis=1) sub2['LOCATION'] = sub2.apply(lambda row: LOCATION(row), axis=1)

# this uses all data sets

sub3 = data[['CRATER_ID','LATITUDE_CIRCLE_IMAGE', 'LONGITUDE_CIRCLE_IMAGE','DEPTH_RIMFLOOR_TOPOG', 'NUMBER_LAYERS','LOCATION']]

print(sub3.head(10))

# This is the data with 1 or more layers to the craters edge.

sub4 = sub2[['CRATER_ID','LATITUDE_CIRCLE_IMAGE', 'LONGITUDE_CIRCLE_IMAGE','DEPTH_RIMFLOOR_TOPOG', 'NUMBER_LAYERS','LOCATION']]

print(sub4.head(10))

print('Quadrant of craters with 1 or more layers') p5 = sub2['LOCATION'].value_counts(sort = False) print(p5)

print('Quadrant of craters') p6 = data['LOCATION'].value_counts(sort = False) print(p6)

Quadrant of craters with 1 or more layers 1 286 2 793 Name: LOCATION, dtype: int64 Quadrant of craters 1 34297 2 31202 Name: LOCATION, dtype: int64

pt5 = sub2.groupby('LOCATION').size()*100/len(sub2) print('% groupby',pt5)

pt6 = data.groupby('LOCATION').size()*100/len(data) print('% groupby all data',pt6)

% groupby LOCATION 1 26.506024 2 73.493976 dtype: float64 % groupby all data LOCATION 1 52.362631 2 47.637369 dtype: float64

Running Your First Program

Code for my first program:

import numpy as np import pandas as pd

data = pd.read_csv('MarsCraterData.csv',low_memory = False)

# upper case all DataFrame column names, meant for less confusion data.columns = map(str.upper, data.columns)

# bug fix for display runtime errors pd.set_option('display.float_format', lambda x: '%f'%x)

print(len(data)) print(len(data.columns))

# C = counts P = percentage c1 = data['LATITUDE_CIRCLE_IMAGE'].value_counts(sort=False) print('count latitude',c1)

p1 = data['LATITUDE_CIRCLE_IMAGE'].value_counts(sort=False,normalize = True) print('% latitude',p1)

c2 = data['LONGITUDE_CIRCLE_IMAGE'].value_counts(sort=False) print('count longitude',c2)

p2 = data['LONGITUDE_CIRCLE_IMAGE'].value_counts(sort=False,normalize = True) print('% longitude',p2)

c3 = data['DEPTH_RIMFLOOR_TOPOG'].value_counts(sort=False) print('count depth',c3)

p3 = data['DEPTH_RIMFLOOR_TOPOG'].value_counts(sort=False,normalize = True) print('% depth',p3)

c4 = data['NUMBER_LAYERS'].value_counts(sort=False) print('count layers',c4)

p4 = data['NUMBER_LAYERS'].value_counts(sort=False,normalize = True) print('% layers',p4)

ct4 = data.groupby('NUMBER_LAYERS').size() print(ct4) pt4 = data.groupby('NUMBER_LAYERS').size()*100/len(data) print('%',pt4)

Output for my codes:

65499 10

count latitude 72.000000 1 32.000000 2 64.000000 2 2.000000 1 51.038000 1 8.000000 1 42.011000 2 55.815000 1 22.543000 1 51.212000 3 36.631000 1 31.996000 5 62.795000 2 61.626000 1 38.451000 1 41.262000 3 30.687000 1 6.944000 1 38.299000 1 36.369000 2 52.144000 2 30.795000 1 49.563000 2 72.217000 1 64.445000 3 73.555000 1 63.718000 1 31.992000 1 42.278000 2 58.502000 2 .. 46.987000 2 20.538000 2 53.890000 1 60.713000 1 39.721000 1 53.610000 1 56.830000 1 69.328000 2 62.961000 2 69.672000 1 46.590000 1 56.238000 1 68.871000 1 68.129000 1 51.836000 2 46.156000 3 63.100000 1 42.908000 1 74.664000 1 66.836000 1 26.707000 1 9.826000 1 49.430000 1 37.454000 2 65.457000 1 66.543000 1 24.460000 1 60.335000 2 52.971000 3 59.614000 1 Name: LATITUDE_CIRCLE_IMAGE, Length: 36562, dtype: int64 % latitude 72.000000 0.000015 32.000000 0.000031 64.000000 0.000031 2.000000 0.000015 51.038000 0.000015 8.000000 0.000015 42.011000 0.000031 55.815000 0.000015 22.543000 0.000015 51.212000 0.000046 36.631000 0.000015 31.996000 0.000076 62.795000 0.000031 61.626000 0.000015 38.451000 0.000015 41.262000 0.000046 30.687000 0.000015 6.944000 0.000015 38.299000 0.000015 36.369000 0.000031 52.144000 0.000031 30.795000 0.000015 49.563000 0.000031 72.217000 0.000015 64.445000 0.000046 73.555000 0.000015 63.718000 0.000015 31.992000 0.000015 42.278000 0.000031 58.502000 0.000031 ... 46.987000 0.000031 20.538000 0.000031 53.890000 0.000015 60.713000 0.000015 39.721000 0.000015 53.610000 0.000015 56.830000 0.000015 69.328000 0.000031 62.961000 0.000031 69.672000 0.000015 46.590000 0.000015 56.238000 0.000015 68.871000 0.000015 68.129000 0.000015 51.836000 0.000031 46.156000 0.000046 63.100000 0.000015 42.908000 0.000015 74.664000 0.000015 66.836000 0.000015 26.707000 0.000015 9.826000 0.000015 49.430000 0.000015 37.454000 0.000031 65.457000 0.000015 66.543000 0.000015 24.460000 0.000015 60.335000 0.000031 52.971000 0.000046 59.614000 0.000015 Name: LATITUDE_CIRCLE_IMAGE, Length: 36562, dtype: float64 count longitude 64.000000 1 -8.000000 1 -0.250000 1 2.000000 1 0.500000 1 0.125000 1 10.942000 1 -175.595000 1 -47.992000 1 73.912000 1 108.157000 1 55.552000 1 -0.368000 2 -151.891000 1 -72.283000 1 88.967000 1 152.401000 1 -121.555000 1 153.599000 1 -87.317000 1 -38.154000 1 -63.190000 2 -74.543000 1 -176.478000 1 176.522000 1 -150.504000 1 53.280000 1 -149.614000 1 137.265000 1 -64.434000 1 .. -52.004000 1 52.246000 1 -137.473000 1 -137.527000 1 -10.648000 1 -39.721000 1 -107.220000 1 21.211000 1 -4.333000 1 -50.961000 1 -50.789000 1 53.816000 1 -137.742000 1 71.654000 2 -99.577000 1 46.156000 1 126.893000 1 16.920000 1 10.333000 1 -28.709000 1 94.810000 1 -148.871000 1 161.489000 1 6.042000 1 89.207000 1 -178.586000 1 74.543000 1 137.457000 1 -138.543000 1 67.652000 1 Name: LONGITUDE_CIRCLE_IMAGE, Length: 59191, dtype: int64 % longitude 64.000000 0.000015 -8.000000 0.000015 -0.250000 0.000015 2.000000 0.000015 0.500000 0.000015 0.125000 0.000015 10.942000 0.000015 -175.595000 0.000015 -47.992000 0.000015 73.912000 0.000015 108.157000 0.000015 55.552000 0.000015 -0.368000 0.000031 -151.891000 0.000015 -72.283000 0.000015 88.967000 0.000015 152.401000 0.000015 -121.555000 0.000015 153.599000 0.000015 -87.317000 0.000015 -38.154000 0.000015 -63.190000 0.000031 -74.543000 0.000015 -176.478000 0.000015 176.522000 0.000015 -150.504000 0.000015 53.280000 0.000015 -149.614000 0.000015 137.265000 0.000015 -64.434000 0.000015 ... -52.004000 0.000015 52.246000 0.000015 -137.473000 0.000015 -137.527000 0.000015 -10.648000 0.000015 -39.721000 0.000015 -107.220000 0.000015 21.211000 0.000015 -4.333000 0.000015 -50.961000 0.000015 -50.789000 0.000015 53.816000 0.000015 -137.742000 0.000015 71.654000 0.000031 -99.577000 0.000015 46.156000 0.000015 126.893000 0.000015 16.920000 0.000015 10.333000 0.000015 -28.709000 0.000015 94.810000 0.000015 -148.871000 0.000015 161.489000 0.000015 6.042000 0.000015 89.207000 0.000015 -178.586000 0.000015 74.543000 0.000015 137.457000 0.000015 -138.543000 0.000015 67.652000 0.000015 Name: LONGITUDE_CIRCLE_IMAGE, Length: 59191, dtype: float64 count depth 0.000000 54380 0.250000 122 0.500000 49 1.000000 17 2.000000 1 0.220000 122 0.190000 172 1.970000 2 0.130000 248 0.090000 370 0.420000 65 0.790000 26 0.110000 333 0.940000 15 0.880000 15 2.150000 1 0.380000 78 2.310000 1 1.600000 3 0.440000 56 0.430000 74 1.760000 1 1.020000 15 1.150000 9 2.080000 2 0.600000 34 1.860000 2 0.920000 14 1.310000 1 2.100000 1 ... 0.370000 76 0.900000 18 0.080000 441 1.870000 1 2.140000 1 1.850000 1 -0.030000 1 1.980000 2 1.160000 4 1.060000 12 1.450000 4 1.130000 4 0.710000 33 0.890000 22 0.310000 90 1.300000 1 0.580000 45 0.870000 19 0.800000 13 1.740000 3 0.160000 218 0.340000 75 1.320000 8 1.210000 8 0.290000 97 1.180000 9 0.240000 102 0.410000 84 1.410000 6 2.400000 1 Name: DEPTH_RIMFLOOR_TOPOG, Length: 218, dtype: int64 % depth 0.000000 0.830242 0.250000 0.001863 0.500000 0.000748 1.000000 0.000260 2.000000 0.000015 0.220000 0.001863 0.190000 0.002626 1.970000 0.000031 0.130000 0.003786 0.090000 0.005649 0.420000 0.000992 0.790000 0.000397 0.110000 0.005084 0.940000 0.000229 0.880000 0.000229 2.150000 0.000015 0.380000 0.001191 2.310000 0.000015 1.600000 0.000046 0.440000 0.000855 0.430000 0.001130 1.760000 0.000015 1.020000 0.000229 1.150000 0.000137 2.080000 0.000031 0.600000 0.000519 1.860000 0.000031 0.920000 0.000214 1.310000 0.000015 2.100000 0.000015 ... 0.370000 0.001160 0.900000 0.000275 0.080000 0.006733 1.870000 0.000015 2.140000 0.000015 1.850000 0.000015 -0.030000 0.000015 1.980000 0.000031 1.160000 0.000061 1.060000 0.000183 1.450000 0.000061 1.130000 0.000061 0.710000 0.000504 0.890000 0.000336 0.310000 0.001374 1.300000 0.000015 0.580000 0.000687 0.870000 0.000290 0.800000 0.000198 1.740000 0.000046 0.160000 0.003328 0.340000 0.001145 1.320000 0.000122 1.210000 0.000122 0.290000 0.001481 1.180000 0.000137 0.240000 0.001557 0.410000 0.001282 1.410000 0.000092 2.400000 0.000015 Name: DEPTH_RIMFLOOR_TOPOG, Length: 218, dtype: float64 count layers 0 59840 1 3895 2 1556 3 184 4 22 5 2 Name: NUMBER_LAYERS, dtype: int64 % layers 0 0.913602 1 0.059467 2 0.023756 3 0.002809 4 0.000336 5 0.000031 Name: NUMBER_LAYERS, dtype: float64

groupby data NUMBER_LAYERS 0 59840 1 3895 2 1556 3 184 4 22 5 2 dtype: int64 % groupby data NUMBER_LAYERS 0 91.360173 1 5.946656 2 2.375609 3 0.280920 4 0.033588 5 0.003053 dtype: float64

Its easiest to see the data in the group by section of the code mostly because there is such a large number of data for the Mars Crater Codebook. It shows you how many craters have 0-5 layers around them. 59840 craters have zero layers around them and that makes up over 91% of the craters in the dataset!

Getting My research project started. Mars craters

After looking through the codebook options, I have chosen to do my project on the Mars Craters data. What interests me is the possible correlation between the Rim depth floor and the number of layers in the crater so I’ve added those variables into my codebook.

The next thing I thought about is was there a side of Mars that got hit with more craters during the Heavy Bombardment? I could use the Longitude and latitude data to see if there are clusters of craters on Mars or if they are relatively evenly distributed. From this, we could possibly infer the directional flow of the heavy bombardment.

Upon doing a little research on this topic, the first article, Martian Planetwide Crater Distributions: Implications for geologic history and surface processes categorizes craters in three different size brackets according to data from Mariner 9 imagery (Soderblom). They then classify Mars into two classes of terrain, densely cratered and very lightly cratered. This is basically what I would like to do also but I would like to see if there is a relationship or directional pattern of flow.

The next article I found, Cratering Chronology and the Evolution of Mars, was along a similar line but it uses data in order to show when these craters on Mars were formed. It again shows that there are higher crater densities in some areas but it has data to be able to predict dates from which these craters were formed (Hartmann). The codebook I’m using does not have all of this information but again it shows a pattern in distribution of caters on Mars.

From all of this I’m going to use the relationship between the crater depth and the crater layers to predict a relationship of a high force impact and then use this information along with the longitudinal and latitudinal coordinates to see if there was a directional force of the Heavy Bombardment or if it just came at Mars from all directions.

Hartmann W.K., Neukum G. (2001) Cratering Chronology and the Evolution of Mars. In: Kallenbach R., Geiss J., Hartmann W.K. (eds) Chronology and Evolution of Mars. Space Sciences Series of ISSI, vol 12. Springer, Dordrecht

Soderblom, L.a., et al. “Martian Planetwide Crater Distributions: Implications for Geologic History and Surface Processes.” Icarus, vol. 22, no. 3, 1974, pp. 239–263., doi:10.1016/0019-1035(74)90175-4.

#mars #research #coursea #datascience

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