## Kaggle Digit Recognizer: Finding pixels with no variance using R

I’ve written previously about our attempts at the Kaggle Digit Recogniser problem and our approach so far has been to use the data provided and plug it into different algorithms and see what we end up with.

From browsing through the forums we saw others mentioning feature extraction – an approach where we transform the data into another format , the thinking being that we can train a better classifier with better data.

There was quite a nice quote from a post written by Rachel Schutt about the Columbia Data Science course which summed up the mistake we’d made:

The Space between the Data Set and the Algorithm

Many people go straight from a data set to applying an algorithm. But there’s a huge space in between of important stuff. It’s easy to run a piece of code that predicts or classifies. That’s not the hard part. The hard part is doing it well.

One thing we’d noticed while visually scanning the data set was that a lot of the features seemed to consistently have a value of 0. We thought we’d try and find out which pixels those were by finding the features which had zero variance in their values.

I started out by loading a subset of the data set and then taking a sample of that to play around with:

initial <- read.csv("train.csv", nrows=10000, header = TRUE) # take a sample of 1000 rows of the input sampleSet <- initial[sample(1:nrow(initial), 1000), ] |

Just for fun I thought it’d be interesting to see how well the labels were distributed in my sample which we can do with the following code:

# get all the labels sampleSet.labels <- as.factor(sampleSet$label) > table(sampleSet.labels) sampleSet.labels 0 1 2 3 4 5 6 7 8 9 102 116 100 97 95 91 79 122 102 96 |

There are a few more 1’s and 7s than the other labels but they’re roughly in the same ballpark so it’s ok.

I wanted to exclude the ‘label’ field from the data set because the variance of labels isn’t interesting to us on this occasion. We can do that with the following code:

# get data set excluding label excludingLabel <- subset( sampleSet, select = -label) |

To find all the features with no variance we then do this:

# show all the features which don't have any variance - all have the same value variances <- apply(excludingLabel, 2, var) # get the names of the labels which have no variance > pointlessFeatures <- names(excludingLabel[variances == 0][1,]) [1] "pixel0" "pixel1" "pixel2" "pixel3" "pixel4" "pixel5" "pixel6" "pixel7" [9] "pixel8" "pixel9" "pixel10" "pixel11" "pixel12" "pixel13" "pixel14" "pixel15" [17] "pixel16" "pixel17" "pixel18" "pixel19" "pixel20" "pixel21" "pixel22" "pixel23" [25] "pixel24" "pixel25" "pixel26" "pixel27" "pixel28" "pixel29" "pixel30" "pixel31" [33] "pixel32" "pixel33" "pixel51" "pixel52" "pixel53" "pixel54" "pixel55" "pixel56" [41] "pixel57" "pixel58" "pixel59" "pixel60" "pixel82" "pixel83" "pixel84" "pixel85" [49] "pixel86" "pixel88" "pixel110" "pixel111" "pixel112" "pixel113" "pixel114" "pixel139" [57] "pixel140" "pixel141" "pixel142" "pixel168" "pixel169" "pixel196" "pixel252" "pixel280" [65] "pixel308" "pixel335" "pixel336" "pixel364" "pixel365" "pixel392" "pixel393" "pixel420" [73] "pixel421" "pixel448" "pixel476" "pixel504" "pixel532" "pixel559" "pixel560" "pixel587" [81] "pixel615" "pixel643" "pixel644" "pixel645" "pixel671" "pixel672" "pixel673" "pixel699" [89] "pixel700" "pixel701" "pixel727" "pixel728" "pixel729" "pixel730" "pixel731" "pixel752" [97] "pixel753" "pixel754" "pixel755" "pixel756" "pixel757" "pixel758" "pixel759" "pixel760" [105] "pixel779" "pixel780" "pixel781" "pixel782" "pixel783" |

We can count how many labels there are by using the length function:

# count how many labels have no variance > length(names(excludingLabel[apply(excludingLabel, 2, var) == 0][1,])) [1] 109 |

I then wrote those out to a file so that we could use them as the input to the code which builds up our classifier.

write(file="pointless-features.txt", pointlessFeatures) |

Of course we should run the variance test against the full data set rather than just a sample and on the whole data set there are only 76 features with zero variance:

> sampleSet <- read.csv("train.csv", header = TRUE) > sampleSet.labels <- as.factor(sampleSet$label) > table(sampleSet.labels) sampleSet.labels 0 1 2 3 4 5 6 7 8 9 4132 4684 4177 4351 4072 3795 4137 4401 4063 4188 > excludingLabel <- subset( sampleSet, select = -label) > variances <- apply(excludingLabel, 2, var) > pointlessFeatures <- names(excludingLabel[variances == 0][1,]) > length(names(excludingLabel[apply(excludingLabel, 2, var) == 0][1,])) [1] 76 |

We’ve built decision trees using this reduced data set but haven’t yet submitted the forest to Kaggle to see if it’s any more accurate!

I picked up the little R I know from the Computing for Data Analysis course which started last week and from the book ‘R in a Nutshell‘ which my colleague Paul Lam recommended.

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