This analysis builds a Support Vector Machine (SVM) to classify bacterium cell DNA into two groups;Flagged, and Not Flagged for further study. The dataset consists of 14 unidentified columns and 1,217 observations. The target label is scaled 0 to 10, where 0 is not flagged for further study.

According to François Chollet, modern SVM models were developed in the 1990s at Bell Labs, and first published in 1995, but their oldest form was published in 1963. They can be used for both regression and classification, though they’re more popularly applied to the latter. Of note, as opposed to a previous K-means analysis, which was predicted quickly on very tall datasets, SVMs run relatively faster on short, wide datasets.

Support Vector Machines can be thought of as a step up from Logistic Regression, which seeks to divide a group in half (similar to the perpendicual or Linear Regression best fit line). Logitistic Regression, however, is vulnerable to outliers, which can cause large swings in the dividing line. SVMs overcome this shortcoming with a novel adjustment. The models find what are called decision boundaries between groups. Using the kernel method, the data is mapped to a high-dimensional space where a straight line can be found to divide the data. This video provides an excellent visualization of the process. Once the data and lines are mapped back to the original space, the dataset’s grouping is complete.

This is just one of the five machine learning modeling guides you can find here.

Overview

Perform an analysis on the cellDNA dataset using the Support Vector Machine method to predict which observations are worthy of further study, given 13 features.

Pre-Modeling

Support Vector Machines can require heavy computation, making them sometimes unfeasible for dealing with larger datasets. We’ll measure how long this calculation takes, using a stopwatch method. This computer is running an i7-65000 with 16GB DDR4-2400 RAM. You can use CPU-Z to determine your RAM speed.

Start the stopwatch!

start_time <- Sys.time()

Load Required Packages

There are two ways to load the required packages.

Install pacman using the following code.

#After experiencing my repository referencing the wrong mirror several times now, I keep this code available to avoid issues, especially when using knitr.
local({r <- getOption("repos")
       r["CRAN"] <- "http://cran.r-project.org" 
       options(repos=r)
})

# #install.packages("pacman")
# library("pacman")

Or use this function and see if it works for you. If not, again, try the code above.

#Check for and install required packages, using pacman
#if (!require("pacman")) install.packages("pacman")
#pacman::p_load() #No packages required :)

Load Data

The dataset we will be loading appears as:

Document Preview

cellDNA <- read.csv("C:/Users/G/Google Drive/aStThomas/6MachineLearning/Assignments/R/8 SVM/CellDNA.csv", header = TRUE)

Preview Data

Examine the data structure.

#Preview structure
str(cellDNA)

## 'data.frame':    1216 obs. of  14 variables:
##  $ X222         : int  73 256 126 225 233 288 260 231 100 74 ...
##  $ X31.18918919 : num  29.5 58.8 71 90.8 91.4 ...
##  $ X40.34234234 : num  271 290 477 542 280 ...
##  $ X35.57908668 : num  15.5 37.2 13.1 44.5 40 ...
##  $ X8.883916969 : num  6.41 9.86 12.79 7.86 9.26 ...
##  $ X0.968324558 : num  0.911 0.964 0.22 0.984 0.973 ...
##  $ X.80.11367302: num  76 85.3 63.5 -52.9 80.3 ...
##  $ X222.1       : int  73 256 126 225 233 288 263 232 100 74 ...
##  $ X1           : int  1 1 1 1 1 1 -1 0 1 1 ...
##  $ X16.81247093 : num  9.64 18.05 12.67 16.93 17.22 ...
##  $ X0.816176471 : num  0.859 0.753 0.881 0.728 0.733 ...
##  $ X0.578125    : num  0.608 0.563 0.646 0.253 0.525 ...
##  $ X78.591      : num  39.2 89.1 43.8 90.1 88.6 ...
##  $ X0           : int  0 0 0 7 0 0 0 0 0 0 ...

Examine the top 5 rows.

#Preview top 5 rows
head(cellDNA, n=5)

##   X222 X31.18918919 X40.34234234 X35.57908668 X8.883916969 X0.968324558
## 1   73     29.49315     271.3973     15.51720     6.407490    0.9107636
## 2  256     58.81641     289.9414     37.22601     9.863895    0.9642558
## 3  126     71.02381     477.4127     13.11298    12.790672    0.2203507
## 4  225     90.80889     541.9467     44.46311     7.858879    0.9842557
## 5  233     91.40773     279.6223     40.03947     9.256891    0.9729076
##   X.80.11367302 X222.1 X1 X16.81247093 X0.816176471 X0.578125 X78.591 X0
## 1      76.04295     73  1     9.640876    0.8588235 0.6083333  39.217  0
## 2      85.32474    256  1    18.054067    0.7529412 0.5626374  89.111  0
## 3      63.52348    126  1    12.666025    0.8811189 0.6461538  43.832  0
## 4     -52.87498    225  1    16.925688    0.7281553 0.2525253  90.072  7
## 5      80.28062    233  1    17.223960    0.7327044 0.5247748  88.623  0

Preprocessing

The dataset is raw and requires some tidying up. We’ll give the dataset header names and drop the ID column, which carries no useful information.

#give col names
colnames(cellDNA) <- c("X1","X2", "X3", "X4","X5", "X6", "X7","X8", "X9", "X10","X11", "X12", "X13","Y")

We are going to give a binary classification to the Y target variable now, where anything other than 0 will equal to 1. The value 0 indicates a bacterium worthy of further study.

#ifelse(test, true, false)
cellDNA$Y <- ifelse(cellDNA$Y>0, 1, 0)

Because all measurements in our dataframe are in different units, we need to standardize.

#standardize all X variables
tempdf <- scale(cellDNA[,1:13])

#Bring Y back in
cellDNA = cbind(tempdf, cellDNA[,14])

#cellDNA$Y <- as.factor(cellDNA$Y))

#And reappoint names using code from above.
colnames(cellDNA) <- c("X1","X2", "X3", "X4","X5", "X6", "X7","X8", "X9", "X10","X11", "X12", "X13","Y")

Y <- as.factor(cellDNA[,14])

Modeling

We’ll now use the e1071 alogorithm to train a SVM. Because the dataframe is now atomic, we no longer use notation cellDNA$Y, but rather need to use cellDNA[,14], as explained here.

#e1071 will be used to fit a SVM model.
if (!require("pacman")) install.packages("pacman")

## Loading required package: pacman

pacman::p_load(e1071)

#fit <- svm(vs ~ hp+mpg+gear #That is, vs = hp + mpg + gear
fit <- svm(Y~., data = cellDNA[,1:13], type = 'C', kernel='linear', probability = TRUE, scale = FALSE) #scaling has already been applied.

A total of 228 Support Vectors were created. A list of the resulting support vectors can be obtained using the value ‘index’ from the fit object. Let’s call up a summary of the fit.

summary(fit)

## 
## Call:
## svm(formula = Y ~ ., data = cellDNA[, 1:13], type = "C", kernel = "linear", 
##     probability = TRUE, scale = FALSE)
## 
## 
## Parameters:
##    SVM-Type:  C-classification 
##  SVM-Kernel:  linear 
##        cost:  1 
##       gamma:  0.07692308 
## 
## Number of Support Vectors:  228
## 
##  ( 115 113 )
## 
## 
## Number of Classes:  2 
## 
## Levels: 
##  0 1

We did not split the dataset earlier, but you can use the following code to run a prediction using the above SVM model.

pred <- predict(fit, data = cellDNA[,1:13], probability = TRUE)

Finally, we’ll print out the first 20 predictions of wether observations belong to class 0 (Flagged) or 1 (Not Flagged).

head(pred, 20)

##  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 
##  0  0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  0  0  0  0 
## Levels: 0 1

Finally, we will count how many of the bacterium were flagged for further study.

table(pred)

## pred
##    0    1 
## 1032  184

From the results, we see that 1,032 bacterium were Flagged, and 184 were Not Flagged for further study. This is slightly moved from our original dataset where 1,017 were Flagged, and 200 were Not Flagged for further study.

Click the stopwatch off.

#stop watch
end_time <- Sys.time()
total_time <- end_time - start_time
total_time

## Time difference of 0.8475249 secs

The total time required to process all rows into two classes was 0.8475249 minutes.

Results

A Support Vector Machine was used to classify 1,216 bacterium into Flagged or Not Flagged for further study, given 13 features. The data was never split into training-testing, or cross-validated, but we do for the sake of coding run a prediction. The prediction resulted in 16 fewer bacterium being classified as Not Flagged for further study.

Thank you for reading, and happy regressing or classifying with SVMs!

R

#The above includes the code in the output, but it won't be evaluated

start_time <- Sys.time()

#After experiencing my repository referencing the wrong mirror several times now, I keep this code available to avoid issues, especially when using knitr.
local({r <- getOption("repos")
       r["CRAN"] <- "http://cran.r-project.org" 
       options(repos=r)
})

# #install.packages("pacman")
# library("pacman")

#Check for and install required packages, using pacman
#if (!require("pacman")) install.packages("pacman")
#pacman::p_load() #No packages required :)

cellDNA <- read.csv("C:/Users/G/Google Drive/aStThomas/6MachineLearning/Assignments/R/8 SVM/CellDNA.csv", header = TRUE)

#Preview structure
str(cellDNA)

#Preview top 5 rows
head(cellDNA, n=5)

#give col names
colnames(cellDNA) <- c("X1","X2", "X3", "X4","X5", "X6", "X7","X8", "X9", "X10","X11", "X12", "X13","Y")

#ifelse(test, true, false)
cellDNA$Y <- ifelse(cellDNA$Y>0, 1, 0)

#standardize all X variables
tempdf <- scale(cellDNA[,1:13])

#Bring Y back in
cellDNA = cbind(tempdf, cellDNA[,14])

#cellDNA$Y <- as.factor(cellDNA$Y))

#And reappoint names using code from above.
colnames(cellDNA) <- c("X1","X2", "X3", "X4","X5", "X6", "X7","X8", "X9", "X10","X11", "X12", "X13","Y")

Y <- as.factor(cellDNA[,14])

#e1071 will be used to fit a SVM model.
if (!require("pacman")) install.packages("pacman")
pacman::p_load(e1071)

#fit <- svm(vs ~ hp+mpg+gear #That is, vs = hp + mpg + gear
fit <- svm(Y~., data = cellDNA[,1:13], type = 'C', kernel='linear', probability = TRUE, scale = FALSE) #scaling has already been applied.

summary(fit)

pred <- predict(fit, data = cellDNA[,1:13], probability = TRUE)

head(pred, 20)

table(pred)

#stop watch
end_time <- Sys.time()
total_time <- end_time - start_time
total_time

Markdown

To view this entire document’s markdown code, click here.

MATLAB

%% Target———————————————————-

Y = VarName14;

% clear VarName14;

%Convert this dependent variable to binary values.

%Y = 0 means bacterium is not interesting to study

%We need binary vector

%If Y > 0, set equal to 1

Y(Y ~= 0) = 1;

%for mnrfit(), we need categorical response variable, not numeric

Y_cat = categorical(Y);

%% Matrix———————————————————-

XAll = [VarName1 VarName2 VarName3 VarName4 VarName5 VarName6 VarName7, > VarName8 VarName9 VarName10 VarName11 VarName12 VarName13];

% Standardize numerics——————————————–

% Standardize predictors first using Z score

% various numeric measurements (i.e. size, center, etc) from thousands

% of bacterium under microscope. All the measurements are

% in different units.

XAll_scaled = zscore(XAll);

X_mean = mean(XAll_scaled); %check mean ~= 0

%% Support Vector Machine——————————————

SVMModel = fitcsvm(XAll_scaled, Y_cat)

%% diagnosis

% 1. How many support vectors did you find?

countSupportVectors = sum(SVMModel.IsSupportVector == 1);

beta0 = SVMModel.Bias;

betas = SVMModel.Beta;

%ImportantRecords = [SVMModel.IsSupportVector SVMModel.alpha]

% score = wtX + b. shows criticalness of point. if 0, right on decision

% boundary. If -1, right on bottom right.

% label = predicted label e.g. (-1, 1)

%SVM, slide 30

[label, score] = predict(SVMModel, XAll_scaled);

absolute = abs(score); %this returns 2 identical columns

%I want top 3, not top 1

%[M,I] = min(absolute)

%Minimums = topkrows(absolute, 3, ‘ascend’) %introduced in 2016b, i have 2016a.

%here is a workaround

%https://www.mathworks.com/matlabcentral/answers/371490-what-am-i-doing-wrong-w> ith-the-function-topkrows

S = sortrows(absolute);

S(1:3,1:1)

%% The “wT . X + b” values for the following records:

% 131, 165, 892, 1057 are:

score(131, 1)

score(165, 1)

score(892, 1)

score(1057, 1)

%These are all support vectors

%%

%Try a graph

sv = SVMModel.SupportVectors;

figure

gscatter(XAll_scaled(:,1),XAll_scaled(:,2),Y_cat)

hold on

plot(sv(:,1),sv(:,2),‘ko’,‘MarkerSize’,10)

legend(‘not interesting’,‘interesting’,‘Support Vector’)

hold off

Data

If you don’t have the dataset, copy the table below, and after pasting it into Excel, save it as a comma seperated file named patients.csv in your preferred directory.

X1	X2	X3	X4	X5	X6	X7	X8	X9	X10	X11	X12	X13	Y
-0.9383189	-1.8122911	0.4232759	-0.9326550	-0.8166931	0.0196865	1.4996027	-0.9087279	0.2332976	-1.2207648	0.7070236	0.8437406	-0.8134493	0
0.4100449	-1.6761346	0.5542688	0.2003774	0.1337987	0.5017105	1.6831906	0.3741902	0.2332976	0.5980575	-0.1914661	0.5552170	0.2085787	0
-0.5478092	-1.6194521	1.8785362	-1.0581369	0.9386461	-6.2016990	1.2519758	-0.5371724	0.2332976	-0.5667670	0.8962161	1.0825387	-0.7189157	0
0.1816336	-1.5275842	2.3343939	0.5780980	-0.4175694	0.6819318	-1.0503097	0.1568653	0.2332976	0.3541167	-0.4017921	-1.4028257	0.2282638	1
0.2405784	-1.5248037	0.4813764	0.3472180	-0.0331239	0.5796733	1.5834212	0.2129491	0.2332976	0.4185994	-0.3631900	0.3161532	0.1985825	0
0.6458244	-1.4398125	-0.1673253	0.4600407	-0.0531007	0.6078208	-0.0170739	0.5985256	0.2332976	0.8348175	0.5651568	1.6653679	0.1692699	0
0.4395174	-1.4738526	0.2467807	0.0877932	0.9468208	0.2000653	1.5374045	0.4232636	-0.7316341	0.6284320	-1.1598628	-0.0552665	0.4272862	0
0.2258422	-1.4567862	2.3009193	0.3253292	-0.3650905	0.6358602	-0.9568389	0.2059387	-0.2491682	0.4025838	0.7884656	-0.9965387	0.0415728	0
-0.7393800	-1.4805425	-0.3138166	-0.7016624	-0.2162329	-0.0551610	-1.7637336	-0.7194449	0.2332976	-0.8655878	-0.1521383	0.6951220	-0.6306502	0
-0.9309508	-1.4847817	2.0797087	-1.0036634	-0.6885351	-0.3096234	-1.6270720	-0.9017174	0.2332976	-1.2065378	1.1716746	2.1371820	-0.9708277	0
-0.7246438	-1.4698393	-0.0424889	-1.0433570	0.4575751	-3.0844902	-1.7584122	-0.6984134	-0.2491682	-0.8413145	0.5725389	1.5064145	-0.7270478	0
1.6478871	-1.4007585	0.1377994	1.7022205	0.9025681	0.6564937	1.7564367	1.5589616	-0.2491682	1.7180536	-1.9738733	-0.3281444	2.4837145	0
-0.0467778	-1.3155468	2.5073250	0.2542072	-0.6064144	0.6640396	-0.7477376	-0.0604596	0.2332976	0.0927067	0.1112770	-1.2220300	0.0393605	0
0.0563757	-1.3157843	-0.3247995	-0.0541565	0.1364666	0.3938136	1.3345285	0.0376871	0.2332976	0.2131689	0.3139344	0.0428001	-0.1646190	0
-0.0394097	-1.3309404	0.0129766	0.5763496	-0.8024637	0.7280688	1.7481897	-0.0534492	0.2332976	0.1014525	-0.7129300	0.3393919	0.3713854	1
0.3658363	-1.2739718	-0.0752142	0.9957272	0.9533686	0.5495946	-1.3338509	0.4162531	-1.6965657	0.5520474	-2.8126373	-1.5622697	1.2497592	0
0.4468855	-1.2680602	0.2850659	0.8546056	-0.1252231	0.6777809	1.6695217	0.4092426	0.2332976	0.6359890	-0.9878547	-0.0492344	0.4901311	1
1.1984325	-1.0521218	-1.1222304	1.0956221	0.4710489	0.6344134	-0.6765332	1.1663746	-0.2491682	1.3427015	-1.4037141	-1.3820609	1.2770439	0
-0.0983546	-1.1281435	1.7542891	0.0944876	0.0589363	0.4827558	-1.6865143	-0.1095330	0.2332976	0.0308448	-1.3263134	0.1766988	0.0728723	0
-0.5478092	-1.0957552	-1.0581717	-0.8133287	-0.0460087	-0.4756487	-0.7142974	-0.5371724	0.2332976	-0.5667670	1.4583922	1.0825387	-0.7653324	0
0.2405784	-1.0511082	-0.0685725	-0.5619931	1.1938912	-1.0228404	-0.0921597	0.2269701	-0.2491682	0.4185994	1.2342007	2.0066732	-0.4434675	0
0.0490076	-1.0609770	1.7072832	0.1155262	-0.3572238	0.5887418	-1.7268420	0.0306766	0.2332976	0.2047015	0.9905986	2.2728734	-0.1961439	0
-0.4814962	-1.0477156	1.3378272	-0.5403670	-0.2998794	0.2204126	-1.7503403	-0.4740780	0.2332976	-0.4706597	-0.0717809	0.8772238	-0.4261791	0
-0.4372875	-0.9901497	-1.2557147	-0.6628374	0.0383505	-0.1863579	1.2398942	-0.4320151	0.2332976	-0.4083591	0.3353940	0.3496200	-0.4622718	0
-0.8572697	-0.9361697	-0.2125850	-0.7276007	-0.9736472	0.4083197	0.4540711	-0.8316126	0.2332976	-1.0692415	0.6927619	-0.0507404	-0.7434760	0
-0.1425632	-0.9248134	-0.1278171	-0.0883300	-0.3643578	0.5281297	0.5741035	-0.1515959	0.2332976	-0.0231077	0.3691300	-0.3082519	-0.3050572	0
-0.3562383	-0.9115218	-0.7644897	-0.4517772	0.0460734	0.1256159	-1.4313457	-0.3548999	0.2332976	-0.2974914	-0.3194064	0.2125182	-0.1425988	0
2.7531034	-0.8803976	-0.4183799	2.1046063	1.5983810	0.6303984	-1.6163058	3.0802360	-0.7316341	2.5394116	-1.5280161	-0.6453993	2.9026529	0
-0.3636064	-0.8993605	-1.0983030	-0.1877301	-0.5349820	0.5388793	-1.5183580	-0.3619103	0.2332976	-0.3074008	-0.2374284	-0.0085152	-0.1825835	0
-0.7614843	-0.8657698	-0.8753447	-0.9394010	-0.2403869	-0.6769517	0.8686377	-0.7404763	0.2332976	-0.9024575	0.9708004	0.6267363	-0.8034531	0
1.9868201	-0.8190593	1.6139733	2.2587457	-0.3057680	0.7712810	1.4692321	1.8744332	0.2332976	1.9835158	0.2485477	-1.2052538	1.4491298	1
1.7510406	-0.8204713	-0.6964397	0.9958787	1.9132598	0.3759698	-1.7420169	1.9936114	-3.1439633	1.8003079	-1.5850912	-0.0267775	2.0834164	0
-0.2604529	-0.8064520	1.3088869	-0.2330013	-0.2888772	0.4422731	0.7617376	-0.2637636	0.2332976	-0.1715192	-0.3020425	-0.7422719	-0.1795109	0
-0.4225513	-0.8025382	-0.0261824	-0.2301262	-0.5133851	0.5158842	0.8666206	-0.4179942	0.2332976	-0.3878879	0.3533324	-0.8475049	-0.3541778	0
0.8373952	-0.7357551	-0.5454094	0.8922979	-0.1232775	0.6817353	-1.6528527	0.7807981	0.2332976	1.0176469	-0.2816219	0.1497035	0.7884598	1
-0.3267659	-0.7319499	1.5402696	-0.5377211	-0.0045314	0.0496613	1.4945736	-0.3268579	0.2332976	-0.2581759	0.7735784	1.0729051	-0.4775119	0
-0.8646378	-0.7278270	1.3724712	-0.9706208	-0.5383129	-0.3922373	-1.3306227	-0.8386231	0.2332976	-1.0825894	1.3329378	1.4818846	-0.9150908	0
-0.2972935	-0.5914219	-0.7997206	-0.4306184	-0.1307038	0.2397739	1.6478704	-0.2988160	0.2332976	-0.2193614	0.8384966	1.3950703	-0.4416035	0
-0.4446556	-0.5103799	-1.0236822	-0.1917168	-0.3679923	0.4877301	1.4648759	-0.4390256	0.2332976	-0.4186491	-0.4569991	-0.2690015	-0.2987891	0
-0.4741281	-0.5012806	-0.1528441	-0.9791569	0.7496348	-3.1280008	1.7389460	-0.4670676	0.2332976	-0.4601815	1.3783090	1.4063327	-0.7516081	0
-0.3488702	-0.4756439	-0.4687894	-0.7354584	0.8764210	-1.3483892	1.3321255	-0.2847950	-1.2140999	-0.2876145	-0.5420396	0.5806579	-0.3433418	0
-0.2162443	-0.4403568	-0.9847390	-0.5553848	0.6299259	-0.4521520	1.4366109	-0.2217007	0.2332976	-0.1150556	-0.4581065	0.0270790	0.1919867	0
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0.9921255	1.2171418	-1.0300216	0.9413818	-0.0882044	0.6829543	-1.7310642	0.9420392	-0.2491682	1.1598547	0.5260778	1.2758339	0.4489583	0
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0.6384563	1.3760882	-1.0246150	1.1840453	-0.3228036	0.7268483	-0.4078184	0.6055361	-0.2491682	0.8276241	-0.9562314	-1.2464319	0.6717421	0
0.9626530	1.3967811	-0.8878988	1.0708855	-0.0177719	0.6883108	-0.1860523	0.8999763	0.2332976	1.1331188	-0.6299240	-0.3815857	0.7293226	0
1.2868498	1.4949838	-0.6365258	2.2627789	0.1958960	0.7455825	-0.2562244	1.2154480	-0.2491682	1.4188983	-1.9689131	-1.4833633	1.4809824	0
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0.3437319	1.4080888	-0.4736925	0.5737421	-0.3372352	0.6705158	-1.3076348	0.3110959	0.2332976	0.5288353	-0.0512034	-0.8754239	0.1997706	0
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0.8373952	1.5225111	-0.7334110	1.1210762	-0.2535918	0.7161640	-0.2050968	0.7807981	0.2332976	1.0176469	-0.3112647	-0.2998635	0.6422656	0
0.9184444	1.4708691	-0.1577438	1.0660787	1.7386889	0.4317687	-1.6163323	0.8579134	0.2332976	1.0927102	-2.1539778	-0.5972138	0.9041739	0
0.1963698	1.5492484	-1.1776699	1.0176672	-0.7705099	0.7538831	0.0017392	0.1708862	0.2332976	0.3703434	-0.3062568	0.8975009	0.4191336	1
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0.2111060	1.5581112	-1.2632848	0.6472203	-0.4799770	0.6977469	-0.0083898	0.1849072	0.2332976	0.3864988	-0.1032810	1.0191290	0.3623929	0
0.4468855	1.5308838	-0.9331355	0.8954526	-0.4351894	0.7160022	-1.3897683	0.4092426	0.2332976	0.6359890	-0.4625574	-1.0810454	0.5082594	0
0.0047990	1.5888592	-0.2284548	0.5222573	-0.4767426	0.6829024	0.6983628	-0.0113863	0.2332976	0.1534623	-0.9700915	-1.5283879	0.4088301	0
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0.5205665	1.6027787	-0.9284633	1.3244534	-0.6775902	0.7612274	-1.2849896	0.4793474	0.2332976	0.7107772	-0.3486544	-1.4789966	0.6620941	1
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0.1153206	-1.7583240	-1.2716800	0.1594133	-0.2936726	0.5864144	0.1965741	0.0937710	0.2332976	0.2801876	0.0125076	0.2811485	-0.0389293	0
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1.0731747	-1.7734891	0.5969024	1.2953855	-0.1442485	0.7189714	1.4361914	1.0051335	0.2332976	1.2325661	-0.3070837	-0.8741967	0.7322108	0
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0.9700212	-1.1745480	0.4653208	1.3603851	-0.1817900	0.7264333	-1.3000998	0.9069868	0.2332976	1.1398178	-0.3340202	-1.3453806	1.0017391	1
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1.4931568	-0.7164828	-0.7650111	2.7171805	-0.1170214	0.7742189	-0.6526809	1.4327729	-0.2491682	1.5920825	-1.7573811	-2.0110119	1.8257689	1
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1.7289363	-0.4348616	-0.7418651	2.3650430	-0.2444569	0.7712390	-0.8898447	1.6290664	0.2332976	1.7827939	-0.8842830	-1.9201747	1.4293628	1
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2.2299677	-0.3177518	-0.8532546	2.6300109	-0.1945437	0.7754231	-0.4073333	2.1057791	0.2332976	2.1660270	-0.3767651	-1.5994078	1.8360723	1
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1.7068320	-0.2492651	-1.1044861	2.0774149	-0.1112150	0.7558297	0.3230449	1.6080349	0.2332976	1.7652195	-0.8528543	-1.2487782	1.7508589	1
0.7489779	-0.2679344	-0.6845771	0.8294165	-0.2012364	0.6840389	-0.5869130	0.6966723	0.2332976	0.9342440	0.2349448	-1.0904430	0.3814021	0
0.6900330	-0.2459539	-0.9724285	0.3139072	0.7703991	0.3825326	0.2403713	0.7457457	-0.2491682	0.8777183	-0.8848211	0.1759154	0.8808016	0
0.1521611	-0.2757606	-0.4929074	-0.1168800	0.1764863	0.3448871	-0.9266062	0.1288234	0.2332976	0.3214453	0.4694530	-0.3594771	-0.2006913	0
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0.4026768	-0.1317611	-0.8593875	0.2284446	1.8686162	-0.0443346	-0.3431885	0.3741902	-0.2491682	0.5904269	-2.1099354	-0.9643546	1.5652126	0
0.8668676	-0.1332130	0.1304524	1.1557586	0.3781648	0.6532656	1.1151359	0.8088400	0.2332976	1.0450925	-1.3102885	-1.4586861	0.7430673	0
0.5574071	-0.1388743	-0.5860509	1.1628079	-0.5340453	0.7430604	1.5023478	0.5143998	0.2332976	0.7476537	-0.7108937	-0.8162154	0.5973647	1
1.2279049	-0.0654012	-0.9559207	0.6634222	1.8994422	0.2428161	-0.5409492	1.1663746	-0.7316341	1.3682385	-2.1882506	-0.7605556	1.7698476	0
0.8005547	-0.0768479	-0.5522830	1.1117721	-0.2806914	0.7179826	1.4951433	0.7457457	0.2332976	0.9830928	-0.1540290	-0.6063090	0.6839301	0
0.4837260	-0.0318189	-1.1804729	0.6826826	-0.2138181	0.6681354	1.1414215	0.4442950	0.2332976	0.6735588	-0.2402605	-1.1815691	0.4100182	0
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1.3236904	0.0885576	-0.5544334	1.8483472	-0.2186639	0.7534247	1.0983738	1.2434899	0.2332976	1.4502867	-0.5421874	-1.7592300	1.0744368	1
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0.1447930	0.1010511	-0.3851293	0.2072698	-0.3018650	0.5997089	1.2845210	0.1218129	0.2332976	0.3132314	0.0866379	-0.6587536	0.0700250	0
0.7563460	0.2090666	-1.2279464	1.2529254	0.8101178	0.6136302	-0.0225464	0.7036828	0.2332976	0.9412568	-1.8015848	-0.3943585	0.7537395	0
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0.9847574	0.3330108	1.6153586	1.2674200	-0.1868911	0.7207328	-1.3558371	0.9350287	-0.7316341	1.1531857	-0.3516364	-1.1260411	0.8809655	1
0.1890017	0.4558447	-1.2822286	0.4539217	-0.0484314	0.6057870	-0.1989417	0.1638758	0.2332976	0.3622390	-1.2830014	-0.4938269	0.4442265	0
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1.0879109	0.6870456	-1.2282877	1.1701777	0.5379892	0.6360213	-0.4294647	1.0191545	0.2332976	1.2456616	-1.2695101	-1.1272521	0.9148460	0
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0.8373952	0.9018776	0.8028395	0.6399844	0.2331021	0.5948408	1.7379069	0.7807981	0.2332976	1.0176469	-0.1909873	1.0323901	0.4349062	0
0.1816336	1.1028093	0.0219121	0.2595023	-0.2455814	0.6006224	-1.1926948	0.1568653	0.2332976	0.3541167	0.2872257	-0.9472713	0.1294900	0
0.1963698	1.4189294	-0.5673790	0.1557260	-0.0310748	0.5265695	0.3749510	0.1708862	0.2332976	0.3703434	0.0615569	-0.4424099	0.2280590	0
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0.9405487	1.5281075	-1.1571359	1.5528349	-0.0757251	0.7296820	1.1411327	0.8789449	0.2332976	1.1129607	-1.4264272	-1.7012794	1.0754609	1
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0.1668973	1.6291379	0.1697192	1.0493184	-0.2019260	0.7053997	1.4442555	0.1428443	0.2332976	0.3378176	-1.8499283	-1.4008733	0.6908741	0
-0.8351654	1.6026680	0.3827147	-1.0400388	-0.2352344	-1.2123855	0.3633324	-0.8105811	0.2332976	-1.0296675	1.5320105	1.6977473	-0.9552394	0

Publications

Videos

I’ve recorded a 45 minute video on how to bring machine learning to the next level in an applied Wine Quality Prediction Project.

If you’re not ready for that and want a tutorial on the basics of Machine Learning, my 1.5 hour Overview of Machine Learning might be better. It will guide you through many of the general concepts, as well as some of the various models listed below.

More RPubs:

Contact

Email: mortensengarth@hotmail.com

LinkedIn: https://www.linkedin.com/in/mortensengarth/.

Support Vector Machine: Bacteria Classification

Garth Mortensen

September 2, 2018