Clojure for Data Science

A talk given to the Bristol Clojurians on 21st April 2015.

Transcript

1. CLOJURE FOR DATA SCIENCE
2. WHY AM I GIVING THIS TALK? I am in the final stages of writing Clojure for Data Science. It will be published by later this year. http://packtpub.com
3. AM I QUALIFIED? I co-founded and was CTO of a data analytics company. I am a software engineer, not a statistician.
4. WHY IS DATA SCIENCE IMPORTANT? The robots are coming! The rise of the computational developer. These trends influence the kinds of systems we are all expected to build.
5. WHY CLOJURE? Clojure lends itself to interactive exploration and learning. It has fantastic data manipulating abstractions. The JVM hosts many of the workhorse data storage and processing frameworks.
6. WHAT I WILL COVER Distributions Statistics Visualisation with Quil Correlation Simple linear regression Multivariable linear regression with Incanter Break Categorical data Bayes classification Logistic regression with Apache Commons Math Clustering with Parkour and Apache Mahout
7. FOLLOW ALONG The book's GitHub is available at http://github.com/clojuredatascience ch1-introduction ch2-statistical-inference ch3-linear-regression ch5-classification ch6-clustering
8. PART 1: SPOTTING ELECTION FRAUD
9. LOADING UK ELECTION DATA Using incanter's excel namespace ( n s c l j d s . c h 1 . d a t a ( : r e q u i r e [ i n c a n t e r [ c o r e : a s i ] [ e x c e l : a s x l s ] ] [ c l o j u r e . j a v a . i o : a s i o ] ) ) ( d e f n u k - d a t a [ ] ( - > ( i o / r e s o u r c e " U K 2 0 1 0 . x l s " ) ( s t r ) ( x l s / r e a d - x l s ) ) ) ( i / v i e w ( u k - d a t a ) )
10. IF YOU'RE FOLLOWING ALONG g i t c l o n e g i t @ g i t h u b . c o m : c l o j u r e d a t a s c i e n c e / c h 1 - i n t r o d u c t i o n . g i t c d c h 1 - i n t r o d u c t i o n s c r i p t / d o w n l o a d - d a t a . s h l e i n r u n - e 1 . 1
11. COLUMN NAMES ( d e f n e x - 1 - 1 [ ] ( i / c o l - n a m e s ( u k - d a t a ) ) ) ; ; = > [ " P r e s s A s s o c i a t i o n R e f e r e n c e " " C o n s t i t u e n c y N a m e " " R e g i o n " " E l e c t i o n Y e a r " " E l e c t o r a t e " " V o t e s " " A C " " A D " " A G S " " A P N I " " A P P " " A W L " " A W P " " B B " " B C P " " B e a n " " B e s t " " B G P V " " B I B " " B I C " " B l u e " " B N P " " B P E l v i s " " C 2 8 " " C a m S o c " " C G " " C h M " " C h P " " C I P " " C I T Y " " C N P G " " C o m m " " C o m m L " " C o n " " C o r D " " C P A " " C S P " " C T D P " " C U R E " " D L a b " " D N a t " " D D P " " D U P " " E D " " E I P " " E P A " " F A W G " " F D P " " F F R " " G r n " " G S O T " " H u m " " I C H C " " I E A C " " I F E D " " I L E U " " I m p a c t " " I n d 1 " " I n d 2 " " I n d 3 " " I n d 4 " " I n d 5 " " I P T " " I S G B " " I S Q M " " I U K " " I V H " " I Z B " " J A C " " J o y " " J P " " L a b " " L a n d " " L D " " L i b " " L i b e r t " " L I N D " " L L P B " " L T T " " M A C I " " M C P " " M E D I " " M E P " " M I F " " M K " " M P E A " " M R L P " " M R P " " N a t L i b " " N C D V " " N D " " N e w " " N F " " N F P " " N I C F " " N o b o d y " " N S P S " " P B P " " P C " " P i r a t e " " P N D P " " P o e t " " P P B F " " P P E " " P P N V " " R e f o r m " " R e s p e c t " " R e s t " " R R G " " R T B P " " S A C L " " S c i " " S D L P " " S E P " " S F " " S I G " " S J P " " S K G P " " S M A " " S M R A " " S N P " " S o c " " S o c A l t " " S o c D e m " " S o c L a b " " S o u t h " " S p e a k e r " " S S P " " T F " " T O C " " T r u s t " " T U S C " " T U V " " U C U N F " " U K I P " " U P S " " U V " " V C C A " " V o t e " " W e s s e x R e g " " W R P " " Y o u " " Y o u t h " " Y R D P L " ]
12. ELECTORATE ( d e f n u k - e l e c t o r a t e [ ] ( - > > ( u k - d a t a ) ( i / $ " E l e c t o r a t e " ) ( r e m o v e n i l ? ) )
13. VARIANCE ( − 1 n ∑n i=1 x i μ x )2
14. …EXPLAINED is `(reduce + …)`. ∑ is "for all xs" ∑n i=1 is a function of x and the mean of x ( − x i μ x )2 ( d e f n v a r i a n c e [ x s ] ( l e t [ m ( m e a n x s ) n ( c o u n t x s ) s q u a r e - e r r o r ( f n [ x ] ( M a t h / p o w ( - x m ) 2 ) ) ] ( / ( r e d u c e + ( m a p s q u a r e - e r r o r x s ) ) n ) ) )
15. HISTOGRAM ( r e q u i r e ' [ i n c a n t e r . c h a r t s : a s c ] ) ( d e f n e x - 1 - 1 1 [ ] ( - > ( u k - e l e c t o r a t e ) ( c / h i s t o g r a m : n b i n s 2 0 ) ( i / v i e w ) ) )
16. DISTIBUTIONS AS MODELS [PDF] http://cljds.com/matura-2013
17. POINCARÉ'S BREAD Poincaré weighed his bread every day for a year. He discovered that the weights of the bread followed a normal distribution, but that the peak was at 950g, whereas loaves of bread were supposed to be regulated at 1kg. He reported his baker to the authorities. The next year Poincaré continued to weigh his bread from the same baker, who was now wary of giving him the lighter loaves. After a year the mean loaf weight was 1kg, but this time the distribution had a positive skew. This is consistent with the baker giving Poincaré only the heaviest of his loaves. The baker was reported to the authorities again
18. HONEST BAKER ( r e q u i r e ' [ i n c a n t e r . d i s t r i b u t i o n s : a s d ] ) ( d e f n h o n e s t - b a k e r [ ] ( l e t [ d i s t r i b u t i o n ( d / n o r m a l - d i s t r i b u t i o n 1 0 0 0 3 0 ) ] ( r e p e a t e d l y # ( d / d r a w d i s t r i b u t i o n ) ) ) ) ( d e f n e x - 1 - 1 6 [ ] ( - > ( t a k e 1 0 0 0 0 ( h o n e s t - b a k e r ) ) ( c / h i s t o g r a m : n b i n s 2 5 ) ( i / v i e w ) ) )
19. DISHONEST BAKER ( d e f n d i s h o n e s t - b a k e r [ ] ( l e t [ d i s t r i b u t i o n ( d / n o r m a l - d i s t r i b u t i o n 9 5 0 3 0 ) ] ( - > > ( r e p e a t e d l y # ( d / d r a w d i s t r i b u t i o n ) ) ( p a r t i t i o n 1 3 ) ( m a p ( p a r t i a l a p p l y m a x ) ) ) ) ) ( d e f n e x - 1 - 1 7 [ ] ( - > ( t a k e 1 0 0 0 0 ( d i s h o n e s t - b a k e r ) ) ( c / h i s t o g r a m : n b i n s 2 5 ) ( i / v i e w ) ) )
20. THE IMPORTANCE OF VISUALISATION Anscombe's Quartet: all have identical mean and variance.
21. SELECTION ( d e f n f i l t e r - e l e c t i o n - y e a r [ d a t a ] ( i / $ w h e r e { " E l e c t i o n Y e a r " { : $ n e n i l } } d a t a ) ) ( d e f n f i l t e r - v i c t o r - c o n s t i t u e n c i e s [ d a t a ] ( i / $ w h e r e { " C o n " { : $ f n n u m b e r ? } " L D " { : $ f n n u m b e r ? } } d a t a ) )
22. PROJECTION ( - > > ( u k - d a t a ) ( f i l t e r - e l e c t i o n - y e a r ) ( f i l t e r - v i c t o r - c o n s t i t u e n c i e s ) ( i / $ [ " R e g i o n " " E l e c t o r a t e " " C o n " " L D " ] ) ( i / a d d - d e r i v e d - c o l u m n " V i c t o r s " [ " C o n " " L D " ] + ) ( i / a d d - d e r i v e d - c o l u m n " V i c t o r s S h a r e " [ " V i c t o r s " " E l e c t o r a t e " ] / ) ( i / v i e w ) )
23. TWO VARIABLES: SCATTER PLOTS! ( d e f n e x - 1 - 3 3 [ ] ( l e t [ d a t a ( - > > ( u k - d a t a ) ( c l e a n - u k - d a t a ) ( d e r i v e - u k - d a t a ) ) ] ( - > ( s c a t t e r - p l o t ( $ " T u r n o u t " d a t a ) ( $ " V i c t o r s S h a r e " d a t a ) : x - l a b e l " T u r n o u t " : y - l a b e l " V i c t o r ' s S h a r e " ) ( v i e w ) ) ) )
24. UK VOTES SCATTER
25. RUSSIA IS A BIGGER COUNTRY
26. WE NEED A BETTER VISUALIZATION
27. BINNING DATA ( d e f n b i n [ n - b i n s x s ] ( l e t [ m i n - x ( a p p l y m i n x s ) r a n g e - x ( - ( a p p l y m a x x s ) m i n - x ) m a x - b i n ( d e c n - b i n s ) b i n - f n ( f n [ x ] ( - > x ( - m i n - x ) ( / r a n g e - x ) ( * n - b i n s ) i n t ( m i n m a x - b i n ) ) ) ] ( m a p b i n - f n x s ) ) ) ( d e f n e x - 1 - 1 0 [ ] ( - > > ( u k - e l e c t o r a t e ) ( b i n 1 0 ) ( f r e q u e n c i e s ) ) ) ; ; = > { 0 1 , 1 1 , 2 4 , 3 2 2 , 4 1 3 0 , 5 3 2 0 , 6 1 5 6 , 7 1 5 , 9 1 }
28. A 2D HISTOGRAM ( d e f n h i s t o g r a m - 2 d [ x s y s n - b i n s ] ( - > ( m a p v e c t o r ( b i n n - b i n s x s ) ( b i n n - b i n s y s ) ) ( f r e q u e n c i e s ) ) ) ( d e f n u k - h i s t o g r a m - 2 d [ ] ( l e t [ d a t a ( - > > ( u k - d a t a ) ( c l e a n - u k - d a t a ) ( d e r i v e - u k - d a t a ) ) ] ( h i s t o g r a m - 2 d ( $ " T u r n o u t " d a t a ) ( $ " V i c t o r s S h a r e " d a t a ) 5 ) ) ) ; ; = > { [ 2 1 ] 5 9 , [ 3 2 ] 9 1 , [ 4 3 ] 3 2 , [ 1 0 ] 8 , [ 2 2 ] 8 9 , [ 3 3 ] 1 0 1 , [ 4 4 ] 6 0 , [ 0 0 ] 2 , [ 1 1 ] 2 2 , [ 2 3 ] 1 9 , [ 3 4 ] 5 3 , [ 0 1 ] 6 , [ 1 2 ] 1 5 , [ 2 4 ] 5 , [ 1 3 ] 2 , [ 0 3 ] 1 , [ 3 0 ] 6 , [ 4 1 ] 3 , [ 3 1 ] 1 7 , [ 4 2 ] 1 7 , [ 2 0 ] 2 3 }
29. QUIL http://quil.info
30. VISUALIZATION WITH QUIL ( r e q u i r e ' [ q u i l . c o r e : a s q ] ) ( d e f n r a t i o - > g r a y s c a l e [ f ] ( - > f ( * 2 5 5 ) ( i n t ) ( m i n 2 5 5 ) ( m a x 0 ) ( q / c o l o r ) ) ) ( d e f n d r a w - h i s t o g r a m [ d a t a { : k e y s [ n - b i n s s i z e ] } ] ( l e t [ [ w i d t h h e i g h t ] s i z e x - s c a l e ( / w i d t h n - b i n s ) y - s c a l e ( / h e i g h t n - b i n s ) m a x - v a l u e ( a p p l y m a x ( v a l s d a t a ) ) s e t u p ( f n [ ] ( d o s e q [ x ( r a n g e n - b i n s ) y ( r a n g e n - b i n s ) ] ( l e t [ v ( g e t d a t a [ x y ] 0 ) x - p o s ( * x x - s c a l e ) y - p o s ( - h e i g h t ( * y y - s c a l e ) ) ] ( q / f i l l ( r a t i o - > g r a y s c a l e ( / v m a x - v a l u e ) ) ) ( q / r e c t x - p o s y - p o s x - s c a l e y - s c a l e ) ) ) ) ] ( q / s k e t c h : s e t u p s e t u p : s i z e s i z e ) ) )
31. A 2D HISTOGRAM
32. A COLOUR HEATMAP Interpolate between the colours of the spectrum. ( d e f n r a t i o - > h e a t [ f ] ( l e t [ c o l o r s [ ( q / c o l o r 0 0 2 5 5 ) ; ; b l u e ( q / c o l o r 0 2 5 5 2 5 5 ) ; ; t u r q u o i s e ( q / c o l o r 0 2 5 5 0 ) ; ; g r e e n ( q / c o l o r 2 5 5 2 5 5 0 ) ; ; y e l l o w ( q / c o l o r 2 5 5 0 0 ) ] ; ; r e d f ( - > f ( m a x 0 . 0 0 0 ) ( m i n 0 . 9 9 9 ) ( * ( d e c ( c o u n t c o l o r s ) ) ) ) ] ( q / l e r p - c o l o r ( n t h c o l o r s f ) ( n t h c o l o r s ( i n c f ) ) ( r e m f 1 ) ) ) )
33. A FINISHED HEATMAP $ > l e i n r u n - e 1 . 3 6
34. CREDIT Proceedings of the National Academy of Sciences, titled "Statistical Detection of Election Irregularities," a team led by Santa Fe Institute External Professor Stefan Thurner
35. INFERENCE
36. WHAT ARE STATISTICS ANYWAY? They are estimates of values, based on a sample.
37. WHAT ARE PARAMETERS? They are the true values, based on the entire population.
38. SAMPLING SIZE The values converge as the sample size increases. We can often only infer the population parameters. Sample Population n N X ¯ μ X S X σ X
39. REAGENT ( d e f p o p u l a t i o n - m e a n 1 0 0 ) ( d e f p o p u l a t i o n - s d 2 0 ) ( d e f s a m p l e - s i z e 1 0 )
40. REAGENT ATOMS ( r e q u i r e ' [ r e a g e n t . c o r e : a s r ] ) ( d e f n r a n d n [ m e a n s d ] ( . . j s / j S t a t - n o r m a l ( s a m p l e m e a n s d ) ) ) ( d e f n n o r m a l - d i s t r i b u t i o n [ m e a n s d ] ( r e p e a t e d l y # ( r a n d n m e a n s d ) ) ) ( d e f s t a t e ( r / a t o m { : s a m p l e [ ] } ) ) ( d e f n u p d a t e - s a m p l e ! [ s t a t e ] ( s w a p ! s t a t e a s s o c : s a m p l e ( - > > ( n o r m a l - d i s t r i b u t i o n p o p u l a t i o n - m e a n p o p u l a t i o n - s d ) ( m a p i n t ) ( t a k e s a m p l e - s i z e ) ) ) )
41. CREATE THE WIDGETS ( d e f n n e w - s a m p l e [ s t a t e ] [ : b u t t o n { : o n - c l i c k # ( u p d a t e - s a m p l e ! s t a t e ) } " N e w S a m p l e " ] ) ( d e f n s a m p l e - l i s t [ s t a t e ] [ : d i v ( l e t [ s a m p l e ( : s a m p l e @ s t a t e ) ] [ : d i v [ : u l ( f o r [ n s a m p l e ] [ : l i n ] ) ] [ : d l [ : d t " S a m p l e M e a n : " ] [ : d d ( m e a n s a m p l e ) ] ] ] ) ] )
42. LAY OUT THE INTERFACE ( d e f n l a y o u t - i n t e r f a c e [ ] [ : d i v [ : h 1 " N o r m a l S a m p l e " ] [ n e w - s a m p l e s t a t e ] [ s a m p l e - l i s t s t a t e ] ] ) ; ; R e n d e r t h e r o o t c o m p o n e n t ( d e f n r u n [ ] ( r / r e n d e r - c o m p o n e n t [ l a y o u t - i n t e r f a c e ] ( . g e t E l e m e n t B y I d j s / d o c u m e n t " r o o t " ) ) )
43. COMPILE THE CLJS $ > l e i n c l j s b u i l d o n c e
44. DEMO
45. STANDARD ERROR It's the standard deviation of the sample means. SE = σ X n √
46. STANDARD ERROR Let's see how the standard error changes with sample size.
47. DEMO
48. STANDARD DEVIATION PROPORTIONS
49. SMALL SAMPLES The standard error is calculated from the population standard deviation, but we don't know it! In practice they're assumed to be the same above around 30 samples, but there is another distribution that models the loss of precision with small samples.
50. T-DISTRIBUTION
51. CALCULATING THE T-STATISTIC Based entirely on our sample statistics ( d e f n t - s t a t i s t i c [ s a m p l e t e s t - m e a n ] ( l e t [ s a m p l e - m e a n ( m e a n s a m p l e ) s a m p l e - s i z e ( c o u n t s a m p l e ) s a m p l e - s d ( s t a n d a r d - d e v i a t i o n s a m p l e ) ] ( / ( - s a m p l e - m e a n t e s t - m e a n ) ( / s a m p l e - s d ( M a t h / s q r t s a m p l e - s i z e ) ) ) ) )
52. DEMO
53. WHY THIS INTEREST IN MEANS? Because often when we want to know if a difference in populations is statistically significant, we'll compare the means.
54. HYPOTHESIS TESTING By convention the data is assumed not to support what the researcher is looking for. This conservative assumption is called the null hypothesis and denoted . h 0 The alternate hypothesis, , can then only be supported with a given confidence interval. h 1
55. SIGNIFICANCE The greater the significance of a result, the more certainty we have that the null hypothesis can be rejected. Let's use our range controller to adjust the significance threshold.
56. DEMO
57. PREDICTION
58. QUESTION What was Olympic swimmer Mark Spitz' competition weight?
59. POPULATION OF OLYMPIC SWIMMERS The Guardian has helpfully provided data on the vital statistics of Olympians http://www.theguardian.com/sport/datablog/2012/aug/07/olym 2012-athletes-age-weight-height#data
60. WEIGHT HISTOGRAM
61. LOG-WEIGHT HISTOGRAM
62. LOG-NORMAL DISTRIBUTION "A variable might be modeled as log-normal if it can be thought of as the multiplicative product of many independent random variables, each of which is positive. This is justified by considering the central limit theorem in the log-domain."
63. SCATTER PLOT
64. WHAT IS CORRELATION ANYWAY? We've talked about variance in the context of the normal distribution.
65. COVARIANCE How much things vary together! COV(X, Y) = ( − )( − ) 1 n ∑n i=1 x i μ x y i μ y
66. CORRELATION A few ways of measuring it, depending on whether your data is continuous or discrete http://xkcd.com/552/
67. PEARSON'S CORRELATION Covariance divided by the product of standard deviations. It measures linear correlation. ρX, Y = COV(X,Y) σ X σ Y ( d e f n p e a r s o n s - c o r r e l a t i o n [ x y ] ( / ( c o v a r i a n c e x y ) ( * ( s t a n d a r d - d e v i a t i o n x ) ( s t a n d a r d - d e v i a t i o n y ) ) ) )
68. PEARSON'S CORRELATION If is 0, it doesn’t necessarily mean that the variables are not correlated. Pearson’s correlation only measures linear relationships. r
69. THIS IS A STATISTIC The unknown population parameter for correlation is the Greek letter . We are only able to calculate the sample statistic . ρ r How far we can trust as an estimate of will depend on two factors: r ρ the size of the coefficient the size of the sample rX, Y = COV(X,Y) sX sY
70. SIMPLE LINEAR REGRESSION y = α + βx
71. SIMPLE LINEAR REGRESSION ( d e f n s l o p e [ x y ] ( / ( c o v a r i a n c e x y ) ( v a r i a n c e x ) ) ) ( d e f n i n t e r c e p t [ x y ] ( - ( m e a n y ) ( * ( m e a n x ) ( s l o p e x y ) ) ) ) ( d e f n p r e d i c t [ a b x ] ( + a ( * b x ) ) )
72. TRAINING A MODEL ( d e f n s w i m m e r - d a t a [ ] ( - > > ( a t h l e t e - d a t a ) ( $ w h e r e { " H e i g h t , c m " { : $ n e n i l } " W e i g h t " { : $ n e n i l } " S p o r t " { : $ e q " S w i m m i n g " } } ) ) ) ( d e f n e x - 3 - 1 2 [ ] ( l e t [ d a t a ( s w i m m e r - d a t a ) h e i g h t s ( $ " H e i g h t , c m " d a t a ) w e i g h t s ( l o g ( $ " W e i g h t " d a t a ) ) a ( i n t e r c e p t h e i g h t s w e i g h t s ) b ( s l o p e h e i g h t s w e i g h t s ) ] ( p r i n t l n " I n t e r c e p t : " a ) ( p r i n t l n " S l o p e : " b ) ) )
73. MAKING A PREDICTION ( p r e d i c t 1 . 6 9 1 0 . 0 1 4 3 1 8 5 ) ; ; = > 4 . 3 3 6 5 ( i / e x p ( p r e d i c t 1 . 6 9 1 0 . 0 1 4 3 1 8 5 ) ) ; ; = > 7 6 . 4 4 Corresponding to a predicted weight of 76.4kg In 1979, Mark Spitz was 79kg. http://www.topendsports.com/sport/swimming/profiles/spitz- mark.htm
74. MORE DATA! ( d e f n f e a t u r e s [ d a t a s e t c o l - n a m e s ] ( - > > ( i / $ c o l - n a m e s d a t a s e t ) ( i / t o - m a t r i x ) ) ) ( d e f n g e n d e r - d u m m y [ g e n d e r ] ( i f ( = g e n d e r " F " ) 0 . 0 1 . 0 ) ) ( d e f n e x - 3 - 2 6 [ ] ( l e t [ d a t a ( - > > ( s w i m m e r - d a t a ) ( i / a d d - d e r i v e d - c o l u m n " G e n d e r D u m m y " [ " S e x " ] g e n d e r - d u m m y ) ) x ( f e a t u r e s d a t a [ " H e i g h t , c m " " A g e " " G e n d e r D u m m y " ] ) y ( i / l o g ( $ " W e i g h t " d a t a ) ) m o d e l ( s / l i n e a r - m o d e l y x ) ] ( : c o e f s m o d e l ) ) ) ; ; = > [ 2 . 2 3 0 7 5 2 9 4 3 1 4 2 2 6 3 7 0 . 0 1 0 7 1 4 6 9 7 8 2 7 1 2 1 0 8 9 0 . 0 0 2 3 7 2 1 8 8 7 4 9 4 0 8 5 7 4 0 . 0 9 7 5 4 1 2 5 3 2 4 9 2 0 2 6 ]
75. MULTIVARIABLE LINEAR REGRESSION y = + +. . . + θ 0 θ 1 x 1 θ n x n
76. LEAST SQUARES
77. MAKING PREDICTIONS y = x θT ( d e f n p r e d i c t [ t h e t a x ] ( - > ( c l / t t h e t a ) ( c l / * x ) ( f i r s t ) ) ) ( d e f n e x - 3 - 2 7 [ ] ( l e t [ d a t a ( - > > ( s w i m m e r - d a t a ) ( i / a d d - d e r i v e d - c o l u m n " G e n d e r D u m m y " [ " S e x " ] g e n d e r - d u m m y ) ) x ( f e a t u r e s d a t a [ " H e i g h t , c m " " A g e " " G e n d e r D u m m y " ] ) y ( i / l o g ( $ " W e i g h t " d a t a ) ) m o d e l ( s / l i n e a r - m o d e l y x ) ] ( i / e x p ( p r e d i c t ( i / m a t r i x ( : c o e f s m o d e l ) ) ( i / m a t r i x [ 1 1 8 5 2 2 1 ] ) ) ) ) ) ; ; = > 7 8 . 4 6 8 8 2 7 7 2 6 3 1 6 9 7
78. HOW CLOSE? The result is around 78.47kg. Compared to 79kg, we were pretty close!
79. SUMMARY Distributions Statistics Visualisation with Quil Correlation Linear regression Multivariate linear regression with Incanter
80. INTERLUDE
81. CLASSIFICATION
82. QUESTION Did all passengers on the Titanic have an equal chance of survival?
83. ON THE DATA Data is based on Thomas Cason's Titanic3 dataset.
84. INSPECT THE DATA Class Survived Name Sex Age 1 1 Allen, Miss. Elisabeth Walton female 29 1 0 Allison, Mr. Hudson Joshua Creighton male 30
85. CATEGORICAL VARIABLES Survived Perished Male 161 682 Female 339 127
86. STANDARD ERROR FOR A PROPORTION SE = p(1 − p) n ‾ ‾ ‾‾‾‾‾‾‾ √ ( d e f n s t a n d a r d - e r r o r - p r o p o r t i o n [ p n ] ( - > ( - 1 p ) ( * p ) ( / n ) ( M a t h / s q r t ) ) ) = = 0.61 161 + 339 682 + 127 500 809 SE = 0.013
87. HOW SIGNIFICANT? z = − p 1 p 2 SE P1: the proportion of women who survived is = 0.76 339 446 P2: the proportion of men who survived = = 0.19 161 843 SE: 0.013 z = 20.36 This is essentially impossible.
88. MORE CATEGORIES Survived Perished First Class 200 123 Second Class 119 158 Third Class 181 528
89. OUR APPROACH DOESN'T SCALE We can use a test. χ2 ( d e f n e x - 5 - 5 [ ] ( l e t [ o b s e r v a t i o n s ( i / m a t r i x [ [ 2 0 0 1 1 9 1 8 1 ] [ 1 2 3 1 5 8 5 2 8 ] ] ) ] ( s / c h i s q - t e s t : t a b l e o b s e r v a t i o n s ) ) ) How likely is that this distribution occurred via chance? { : X - s q 1 2 7 . 8 5 9 1 5 6 4 3 9 3 0 3 2 6 , : c o l - l e v e l s ( 0 1 2 ) , : r o w - m a r g i n s { 0 5 0 0 . 0 , 1 8 0 9 . 0 } , : t a b l e [ m a t r i x ] , : p - v a l u e 1 . 7 2 0 8 2 5 9 5 8 8 2 5 6 1 7 5 E - 2 8 , : d f 2 , : p r o b s n i l , : c o l - m a r g i n s { 0 3 2 3 . 0 , 1 2 7 7 . 0 , 2 7 0 9 . 0 } , : E ( 1 2 3 . 3 7 6 6 2 3 3 7 6 6 2 3 3 7 1 9 9 . 6 2 3 3 7 6 6 2 3 3 7 6 6 3 1 0 5 . 8 0 5 9 5 8 7 4 7 1 3 5 2 2 1 7 1 . 1 9 4 0 4 1 2 5 2 8 6 4 8 2 7 0 . 8 1 7 4 1 7 8 7 6 2 4 1 4 4 3 8 . 1 8 2 5 8 2 1 2 3 7 5 8 6 ) , : r o w - l e v e l s ( 0 1 ) , : t w o - s a m p ? t r u e , : N 1 3 0 9 . 0 }
90. P-VALUE "The estimated probability of rejecting the null hypothesis of a study question when that hypothesis is true." h 0
91. PROBABILITY https://xkcd.com/1132/
92. BAYES RULE P(A|B) = P(B|A)P(A) P(B) initial degree of belief in A (the prior) P(A)
93. BAYES TITANIC P(survive|f emale) = P(f emale|survive)P(survive) P(f emale) P(survive|f emale) = = 339 500 500 1309 446 1309 339 446
94. BAYES CLASSIFICATION P(survive|third, male) = P(survive)P(third|survive)P(male| P(third, male) P(perish|third, male) = P(perish)P(third|perish)P(male|per P(third, male) Because the evidence is the same for all classes, we can cancel this out.
95. PARSE THE DATA ( t i t a n i c - s a m p l e s ) ; ; = > ( { : s u r v i v e d t r u e , : g e n d e r : f e m a l e , : c l a s s : f i r s t , : e m b a r k e d " S " , : a g e " 2 0 - 3 0 " } { : s u r v i v e d t r u e , : g e n d e r : m a l e , : c l a s s : f i r s t , : e m b a r k e d " S " , : a g e " 3 0 - 4 0 " } . . . )
96. IMPLEMENTING A NAIVE BAYES MODEL ( d e f n s a f e - i n c [ v ] ( i n c ( o r v 0 ) ) ) ( d e f n i n c - c l a s s - t o t a l [ m o d e l c l a s s ] ( u p d a t e - i n m o d e l [ c l a s s : t o t a l ] s a f e - i n c ) ) ( d e f n i n c - p r e d i c t o r s - c o u n t - f n [ r o w c l a s s ] ( f n [ m o d e l a t t r ] ( l e t [ v a l ( g e t r o w a t t r ) ] ( u p d a t e - i n m o d e l [ c l a s s a t t r v a l ] s a f e - i n c ) ) ) )
97. IMPLEMENTING A NAIVE BAYES MODEL ( d e f n a s s o c - r o w - f n [ c l a s s - a t t r p r e d i c t o r s ] ( f n [ m o d e l r o w ] ( l e t [ c l a s s ( g e t r o w c l a s s - a t t r ) ] ( r e d u c e ( i n c - p r e d i c t o r s - c o u n t - f n r o w c l a s s ) ( i n c - c l a s s - t o t a l m o d e l c l a s s ) p r e d i c t o r s ) ) ) ) ( d e f n n a i v e - b a y e s [ d a t a c l a s s - a t t r p r e d i c t o r s ] ( r e d u c e ( a s s o c - r o w - f n c l a s s - a t t r p r e d i c t o r s ) { } d a t a ) )
98. NAIVE BAYES MODEL ( d e f n e x - 5 - 6 [ ] ( l e t [ d a t a ( t i t a n i c - s a m p l e s ) ] ( p p r i n t ( n a i v e - b a y e s d a t a : s u r v i v e d [ : g e n d e r : c l a s s ] ) ) ) ) …produces the following output… ; ; { f a l s e ; ; { : c l a s s { : t h i r d 5 2 8 , : s e c o n d 1 5 8 , : f i r s t 1 2 3 } , ; ; : g e n d e r { : m a l e 6 8 2 , : f e m a l e 1 2 7 } , ; ; : t o t a l 8 0 9 } , ; ; t r u e ; ; { : c l a s s { : t h i r d 1 8 1 , : s e c o n d 1 1 9 , : f i r s t 1 9 8 } , ; ; : g e n d e r { : m a l e 1 6 1 , : f e m a l e 3 3 7 } , ; ; : t o t a l 4 9 8 } }
99. MAKING PREDICTIONS ( d e f n n [ m o d e l ] ( - > > ( v a l s m o d e l ) ( m a p : t o t a l ) ( a p p l y + ) ) ) ( d e f n c o n d i t i o n a l - p r o b a b i l i t y [ m o d e l t e s t c l a s s ] ( l e t [ e v i d e n c e ( g e t m o d e l c l a s s ) p r i o r ( / ( : t o t a l e v i d e n c e ) ( n m o d e l ) ) ] ( a p p l y * p r i o r ( f o r [ k v t e s t ] ( / ( g e t - i n e v i d e n c e k v ) ( : t o t a l e v i d e n c e ) ) ) ) ) ) ( d e f n b a y e s - c l a s s i f y [ m o d e l t e s t ] ( l e t [ p r o b s ( m a p ( f n [ c l a s s ] [ c l a s s ( c o n d i t i o n a l - p r o b a b i l i t y m o d e l t e s t c l a s s ) ] ) ( k e y s m o d e l ) ) ] ( - > ( s o r t - b y s e c o n d > p r o b s ) ( f f i r s t ) ) ) )
100. DOES IT WORK? ( d e f n e x - 5 - 7 [ ] ( l e t [ d a t a ( t i t a n i c - s a m p l e s ) m o d e l ( n a i v e - b a y e s d a t a : s u r v i v e d [ : g e n d e r : c l a s s ] ) ] ( b a y e s - c l a s s i f y m o d e l { : g e n d e r : m a l e : c l a s s : t h i r d } ) ) ) ; ; = > f a l s e ( d e f n e x - 5 - 8 [ ] ( l e t [ d a t a ( t i t a n i c - s a m p l e s ) m o d e l ( n a i v e - b a y e s d a t a : s u r v i v e d [ : g e n d e r : c l a s s ] ) ] ( b a y e s - c l a s s i f y m o d e l { : g e n d e r : f e m a l e : c l a s s : f i r s t } ) ) ) ; ; = > t r u e
101. WHY NAIVE? Because it assumes all variables are independent. We know they are not (e.g. being male and in third class) but naive bayes weights all attributes equally. In practice it works surprisingly well, particularly where there are large numbers of features.
102. LOGISTIC REGRESSION
103. LOGISTIC REGRESSION Logistic regression uses similar techniques to linear regression but guarantees an output only between 0 and 1. (x) = x hθ θT (x) = g( x) hθ θT Where the sigmoid function is g(z) = 1 1 + e −z
104. THE LOGISTIC FUNCTION
105. THE LOGISTIC FUNCTION ( d e f n l o g i s t i c - f u n c t i o n [ t h e t a ] ( l e t [ t t ( m a t r i x / t r a n s p o s e ( v e c t h e t a ) ) z ( f n [ x ] ( - ( m a t r i x / m m u l t t ( v e c x ) ) ) ) ] ( f n [ x ] ( / 1 ( + 1 ( M a t h / e x p ( z x ) ) ) ) ) ) )
106. INTERPRETATION ( l e t [ f ( l o g i s t i c - f u n c t i o n [ 0 ] ) ] ( f [ 1 ] ) ; ; = > 0 . 5 ( f [ - 1 ] ) ; ; = > 0 . 5 ( f [ 4 2 ] ) ; ; = > 0 . 5 ) ( l e t [ f ( l o g i s t i c - f u n c t i o n [ 0 . 2 ] ) g ( l o g i s t i c - f u n c t i o n [ - 0 . 2 ] ) ] ( f [ 5 ] ) ; ; = > 0 . 7 3 ( g [ 5 ] ) ; ; = > 0 . 2 7 )
107. COST FUNCTION Cost varies between 0 and (a big number). ( d e f n c o s t - f u n c t i o n [ y y - h a t ] ( - ( i f ( z e r o ? y ) ( M a t h / l o g ( m a x ( - 1 y - h a t ) D o u b l e / M I N _ V A L U E ) ) ( M a t h / l o g ( m a x y - h a t ( D o u b l e / M I N _ V A L U E ) ) ) ) ) ) ( d e f n l o g i s t i c - c o s t [ y s y - h a t s ] ( a v g ( m a p c o s t - f u n c t i o n y s y - h a t s ) ) )
108. CONVERTING TITANIC DATA TO FEATURES ( d e f n t i t a n i c - f e a t u r e s [ ] ( r e m o v e ( p a r t i a l s o m e n i l ? ) ( f o r [ r o w ( t i t a n i c - d a t a ) ] [ ( : s u r v i v e d r o w ) ( : p c l a s s r o w ) ( : s i b s p r o w ) ( : p a r c h r o w ) ( i f ( n i l ? ( : a g e r o w ) ) 3 0 ( : a g e r o w ) ) ( i f ( = ( : s e x r o w ) " f e m a l e " ) 1 . 0 0 . 0 ) ( i f ( = ( : e m b a r k e d r o w ) " S " ) 1 . 0 0 . 0 ) ( i f ( = ( : e m b a r k e d r o w ) " C " ) 1 . 0 0 . 0 ) ( i f ( = ( : e m b a r k e d r o w ) " Q " ) 1 . 0 0 . 0 ) ] ) ) )
109. CALCULATING THE GRADIENT ( d e f n g r a d i e n t - f n [ h - t h e t a x s y s ] ( l e t [ g ( f n [ x y ] ( m a t r i x / m m u l ( - ( h - t h e t a x ) y ) x ) ) ] ( - > > ( m a p g x s y s ) ( m a t r i x / t r a n s p o s e ) ( m a p a v g ) ) ) ) We transpose to calculate the average for each feature across all xs rather than average for each x across all features.
110. GRADIENT DESCENT The cost function will be lowest when the parameters are at their optimum.
111. APACHE COMMONS MATH Provides heavy-lifting for running tasks like gradient descent. ( : i m p o r t [ o r g . a p a c h e . c o m m o n s . m a t h 3 . a n a l y s i s M u l t i v a r i a t e F u n c t i o n M u l t i v a r i a t e V e c t o r F u n c t i o n ] [ o r g . a p a c h e . c o m m o n s . m a t h 3 . o p t i m I n i t i a l G u e s s M a x E v a l S i m p l e B o u n d s O p t i m i z a t i o n D a t a S i m p l e V a l u e C h e c k e r P o i n t V a l u e P a i r ] [ o r g . a p a c h e . c o m m o n s . m a t h 3 . o p t i m . n o n l i n e a r . s c a l a r O b j e c t i v e F u n c t i o n O b j e c t i v e F u n c t i o n G r a d i e n t G o a l T y p e ] [ o r g . a p a c h e . c o m m o n s . m a t h 3 . o p t i m . n o n l i n e a r . s c a l a r . g r a d i e n t N o n L i n e a r C o n j u g a t e G r a d i e n t O p t i m i z e r N o n L i n e a r C o n j u g a t e G r a d i e n t O p t i m i z e r $ F o r m u l a ] )
112. CLOJURE'S JAVA INTEROP An object wrapper to represent a function: too many levels of indirection?! ( d e f n o b j e c t i v e - f u n c t i o n [ f ] ( O b j e c t i v e F u n c t i o n . ( r e i f y M u l t i v a r i a t e F u n c t i o n ( v a l u e [ _ v ] ( a p p l y f ( v e c v ) ) ) ) ) ) ( d e f n o b j e c t i v e - f u n c t i o n - g r a d i e n t [ f ] ( O b j e c t i v e F u n c t i o n G r a d i e n t . ( r e i f y M u l t i v a r i a t e V e c t o r F u n c t i o n ( v a l u e [ _ v ] ( d o u b l e - a r r a y ( a p p l y f ( v e c v ) ) ) ) ) ) )
113. GRADIENT DESCENT ( d e f n m a k e - n c g - o p t i m i z e r [ ] ( N o n L i n e a r C o n j u g a t e G r a d i e n t O p t i m i z e r . N o n L i n e a r C o n j u g a t e G r a d i e n t O p t i m i z e r $ F o r m u l a / F L E T C H E R _ R E E V E S ( S i m p l e V a l u e C h e c k e r . ( d o u b l e 1 e - 6 ) ( d o u b l e 1 e - 6 ) ) ) ) ( d e f n i n i t i a l - g u e s s [ g u e s s ] ( I n i t i a l G u e s s . ( d o u b l e - a r r a y g u e s s ) ) ) ( d e f n m a x - e v a l u a t i o n s [ n ] ( M a x E v a l . n ) ) ( d e f n g r a d i e n t - d e s c e n t [ f g e s t i m a t e n ] ( l e t [ o p t i o n s ( i n t o - a r r a y O p t i m i z a t i o n D a t a [ ( o b j e c t i v e - f u n c t i o n f ) ( o b j e c t i v e - f u n c t i o n - g r a d i e n t g ) ( i n i t i a l - g u e s s e s t i m a t e ) ( m a x - e v a l u a t i o n s n ) G o a l T y p e / M I N I M I Z E ] ) ] ( - > ( m a k e - n c g - o p t i m i z e r ) ( . o p t i m i z e o p t i o n s ) ( . g e t P o i n t ) ( v e c ) ) ) )
114. RUNNING GRADIENT DESCENT ( d e f n r u n - l o g i s t i c - r e g r e s s i o n [ d a t a i n i t i a l - g u e s s ] ( l e t [ p o i n t s ( t i t a n i c - f e a t u r e s ) x s ( - > > p o i n t s ( m a p r e s t ) ( m a p # ( c o n s 1 % ) ) ) y s ( m a p f i r s t p o i n t s ) ] ( g r a d i e n t - d e s c e n t ( f n [ & t h e t a ] ( l e t [ f ( l o g i s t i c - f u n c t i o n t h e t a ) ] ( l o g i s t i c - c o s t ( m a p f x s ) y s ) ) ) ( f n [ & t h e t a ] ( g r a d i e n t - f n ( l o g i s t i c - f u n c t i o n t h e t a ) x s y s ) ) i n i t i a l - g u e s s 2 0 0 0 ) ) )
115. PRODUCING A MODEL ( d e f n e x - 5 - 1 1 [ ] ( l e t [ d a t a ( t i t a n i c - f e a t u r e s ) i n i t i a l - g u e s s ( - > d a t a f i r s t c o u n t ( t a k e ( r e p e a t e d l y r a n d ) ) ) ] ( r u n - l o g i s t i c - r e g r e s s i o n d a t a i n i t i a l - g u e s s ) ) )
116. MAKING PREDICTIONS ( d e f t h e t a [ 0 . 6 9 0 8 0 7 8 2 4 6 2 3 4 0 4 - 0 . 9 0 3 3 8 2 8 0 0 1 3 6 9 4 3 5 - 0 . 3 1 1 4 3 7 5 2 7 8 6 9 8 7 6 6 - 0 . 0 1 8 9 4 3 1 9 6 7 3 2 8 7 2 1 9 - 0 . 0 3 1 0 0 3 1 5 5 7 9 7 6 8 6 6 1 2 . 5 8 9 4 8 5 8 3 6 6 0 3 3 2 7 3 0 . 7 9 3 9 1 9 0 7 0 8 1 9 3 3 7 4 1 . 3 7 1 1 3 3 4 8 8 7 9 4 7 3 8 8 0 . 6 6 7 2 5 5 5 2 5 7 8 2 8 9 1 9 ] ) ( d e f n r o u n d [ x ] ( M a t h / r o u n d x ) ) ( d e f l o g i s t i c - m o d e l ( l o g i s t i c - f u n c t i o n t h e t a ) ) ( d e f n e x - 5 - 1 3 [ ] ( l e t [ d a t a ( t i t a n i c - f e a t u r e s ) t e s t ( f n [ x ] ( = ( r o u n d ( l o g i s t i c - m o d e l ( c o n s 1 ( r e s t x ) ) ) ) ( r o u n d ( f i r s t x ) ) ) ) r e s u l t s ( f r e q u e n c i e s ( m a p t e s t d a t a ) ) ] ( / ( g e t r e s u l t s t r u e ) ( a p p l y + ( v a l s r e s u l t s ) ) ) ) ) ; ; = > 1 0 3 0 / 1 3 0 9
117. EVALUATING THE CLASSIFIER Cross-validation: we want to separate our test and training data sets Bias vs variance: your model may fail to generalise
118. CLUSTERING
119. CLUSTERING Find a grouping of a set of objects such that objects in the same group are more similar to each other than those in other groups.
120. SIMILARITY MEASURES Many to choose from: Jaccard, Euclidean. For text documents the Cosine measure is often chosen. Good for high-dimensional spaces Positive spaces the similarity is between 0 and 1.
121. COSINE SIMILARITY cos( θ) = A ⋅ B ∥A ∥∥B ∥ ( d e f n c o s i n e [ a b ] ( l e t [ d o t - p r o d u c t ( - > > ( m a p * a b ) ( a p p l y + ) ) m a g n i t u d e ( f n [ d ] ( - > > ( m a p # ( M a t h / p o w % 2 ) d ) ( a p p l y + ) M a t h / s q r t ) ) ] ( / d o t - p r o d u c t ( * ( m a g n i t u d e a ) ( m a g n i t u d e b ) ) ) ) )
122. CREATING SPARSE VECTORS ( d e f d i c t i o n a r y ( a t o m { : c o u n t 0 : w o r d s { } } ) ) ( d e f n a d d - w o r d - t o - d i c t [ d i c t w o r d ] ( i f ( g e t - i n d i c t [ : w o r d s w o r d ] ) d i c t ( - > d i c t ( u p d a t e - i n [ : w o r d s ] a s s o c w o r d ( g e t d i c t : c o u n t ) ) ( u p d a t e - i n [ : c o u n t ] i n c ) ) ) ) ( d e f n u p d a t e - w o r d s [ d i c t d o c w o r d ] ( l e t [ w o r d - i d ( - > ( s w a p ! d i c t a d d - w o r d - t o - d i c t w o r d ) ( g e t - i n [ : w o r d s w o r d ] ) ) ] ( u p d a t e - i n d o c [ w o r d - i d ] # ( i n c ( o r % 0 ) ) ) ) ) ( d e f n d o c u m e n t - v e c t o r [ d i c t n g r a m s ] ( r / r e d u c e ( p a r t i a l u p d a t e - w o r d s d i c t ) { } n g r a m s ) )
123. EXAMPLE ( - > > ( s p l i t " t h e q u i c k b r o w n f o x j u m p s o v e r t h e l a z y d o g " # " \ W + " ) ( d o c u m e n t - v e c t o r d i c t i o n a r y ) ) ; ; = > { 7 1 , 6 1 , 5 1 , 4 1 , 3 1 , 2 1 , 1 1 , 0 2 } @ d i c t i o n a r y ; ; = > { : w o r d s { " d o g " 7 , " l a z y " 6 , " o v e r " 5 , " j u m p s " 4 , " f o x " 3 , " b r o w n " 2 , " q u i c k " 1 , " t h e " 0 } , : c o u n t 8 }
124. STEMMING / STOPWORDS http://clojars.org/stemmers ( s t e m m e r / s t e m s " i t ' s l o v e l y t h a t y o u ' r e m u s i c a l " ) ; ; = > ( " l o v e " " m u s i c " )
125. WHY? ( c o s i n e - s p a r s e ( - > > " m u s i c i s t h e f o o d o f l o v e " s t e m m e r / s t e m s ( d o c u m e n t - v e c t o r d i c t i o n a r y ) ) ( - > > " w a r i s t h e l o c o m o t i v e o f h i s t o r y " s t e m m e r / s t e m s ( d o c u m e n t - v e c t o r d i c t i o n a r y ) ) ) ; ; = > 0 . 0 ( c o s i n e - s p a r s e ( - > > " m u s i c i s t h e f o o d o f l o v e " s t e m m e r / s t e m s ( d o c u m e n t - v e c t o r d i c t i o n a r y ) ) ( - > > " i t ' s l o v e l y t h a t y o u ' r e m u s i c a l " s t e m m e r / s t e m s ( d o c u m e n t - v e c t o r d i c t i o n a r y ) ) ) ; ; = > 0 . 8 1 6 4 9 6 5 8 0 9 2 7 7 2 5 9
126. EXAMPLE ( - > > " i t ' s l o v e l y t h a t y o u ' r e m u s i c a l " s t e m m e r / s t e m s ( d o c u m e n t - v e c t o r d i c t i o n a r y ) ) ; ; = > { 0 1 , 2 1 } @ d i c t i o n a r y ; ; = > { : c o u n t 6 , : w o r d s { " h i s t o r i " 5 , " l o c o m o t " 4 , " w a r " 3 , " l o v e " 2 , " f o o d " 1 , " m u s i c " 0 } }
127. MAHOUT http://mahout.apache.org/ "The Apache Mahout™ project's goal is to build an environment for quickly creating scalable preformant machine learning applications."
128. GET THE DATA We're going to be clustering the Reuters dataset. Follow the readme instructions: b r e w i n s t a l l m a h o u t s c r i p t / d o w n l o a d - r e u t e r s . s h l e i n r u n - e 6 . 7 m a h o u t s e q d i r e c t o r y - i d a t a / r e u t e r s - t x t - o d a t a / r e u t e r s - s e q u e n c e f i l e
129. VECTOR REPRESENTATION Each document is converted into a vector representation. All vectors share a dictionary providing a unique index for each word.
130. SEQUENCEFILES Input: org.apache.hadoop.io.Text org.apache.hadoop.io.Text Output (Vectors): org.apache.hadoop.io.Text org.apache.mahout.math.VectorWritable Output (Dictionary): org.apache.hadoop.io.Text org.apache.mahout.math.IntWritable
131. PARKOUR Parkour is a Clojure library for interacting with Hadoop. It provides a thinner layer of abstraction than PigPen and Cascalog.
132. TF-IDF Term frequency, inverse document frenquency. tf idf (t, d, D) = tf (t, d) ⋅ idf (t, D)
133. WE NEED A UNIQUE ID And we need to compute it in parallel.
134. PARKOUR MAPPING ( r e q u i r e ' [ c l o j u r e . c o r e . r e d u c e r s : a s r ] ' [ p a r k o u r . m a p r e d u c e : a s m r ] ) ( d e f n d o c u m e n t - > t e r m s [ d o c ] ( c l o j u r e . s t r i n g / s p l i t d o c # " \ W + " ) ) ( d e f n d o c u m e n t - c o u n t - m " E m i t s t h e u n i q u e w o r d s f r o m e a c h d o c u m e n t " { : : m r / s o u r c e - a s : v a l s } [ d o c u m e n t s ] ( - > > d o c u m e n t s ( r / m a p c a t ( c o m p d i s t i n c t d o c u m e n t - > t e r m s ) ) ( r / m a p # ( v e c t o r % 1 ) ) ) )
135. SHAPE METADATA : k e y v a l s ; ; R e - s h a p e a s v e c t o r s o f k e y - v a l s p a i r s . : k e y s ; ; J u s t t h e k e y s f r o m e a c h k e y - v a l u e p a i r . : v a l s ; ; J u s t t h e v a l u e s f r o m e a c h k e y - v a l u e p a i r .
136. PLAIN OLD FUNCTIONS ( - > > ( d o c u m e n t - c o u n t - m [ " i t ' s l o v e l y t h a t y o u ' r e m u s i c a l " " m u s i c i s t h e f o o d o f l o v e " " w a r i s t h e l o c o m o t i v e o f h i s t o r y " ] ) ( i n t o [ ] ) ) ; ; = > [ [ " l o v e " 1 ] [ " m u s i c " 1 ] [ " m u s i c " 1 ] [ " f o o d " 1 ] [ " l o v e " 1 ] [ " w a r " 1 ] [ " l o c o m o t " 1 ] [ " h i s t o r i " 1 ] ]
137. AND REDUCING… ( r e q u i r e ' [ p a r k o u r . i o . d u x : a s d u x ] ' [ t r a n s d u c e . r e d u c e r s : a s t r ] ) ( d e f n u n i q u e - i n d e x - r { : : m r / s o u r c e - a s : k e y v a l g r o u p s , : : m r / s i n k - a s d u x / n a m e d - k e y v a l s } [ c o l l ] ( l e t [ g l o b a l - o f f s e t ( c o n f / g e t - l o n g m r / * c o n t e x t * " m a p r e d . t a s k . p a r t i t i o n " - 1 ) ] ( t r / m a p c a t - s t a t e ( f n [ l o c a l - o f f s e t [ w o r d c o u n t s ] ] [ ( i n c l o c a l - o f f s e t ) ( i f ( i d e n t i c a l ? : : f i n i s h e d w o r d ) [ [ : c o u n t s [ g l o b a l - o f f s e t l o c a l - o f f s e t ] ] ] [ [ : d a t a [ w o r d [ [ g l o b a l - o f f s e t l o c a l - o f f s e t ] ( a p p l y + c o u n t s ) ] ] ] ] ) ] ) 0 ( r / m a p c a t i d e n t i t y [ c o l l [ [ : : f i n i s h e d n i l ] ] ] ) ) ) )
138. CREATING A JOB ( r e q u i r e ' [ p a r k o u r . g r a p h : a s p g ] ' [ p a r k o u r . a v r o : a s m r a ] ' [ a b r a c a d . a v r o : a s a v r o ] ) ( d e f l o n g - p a i r ( a v r o / t u p l e - s c h e m a [ : l o n g : l o n g ] ) ) ( d e f i n d e x - v a l u e ( a v r o / t u p l e - s c h e m a [ l o n g - p a i r : l o n g ] ) ) ( d e f n d f - j [ d s e q ] ( - > ( p g / i n p u t d s e q ) ( p g / m a p # ' d o c u m e n t - c o u n t - m ) ( p g / p a r t i t i o n ( m r a / s h u f f l e [ : s t r i n g : l o n g ] ) ) ( p g / r e d u c e # ' u n i q u e - i n d e x - r ) ( p g / o u t p u t : d a t a ( m r a / d s i n k [ : s t r i n g i n d e x - v a l u e ] ) : c o u n t s ( m r a / d s i n k [ : l o n g : l o n g ] ) ) ) )
139. WRITING TO DISTRIBUTED CACHE ( r e q u i r e ' [ p a r k o u r . i o . d v a l : a s d v a l ] ) ( d e f n c a l c u l a t e - o f f s e t s " B u i l d m a p o f o f f s e t s f r o m d s e q o f c o u n t s . " [ d s e q ] ( - > > d s e q ( i n t o [ ] ) ( s o r t - b y f i r s t ) ( r e d u c t i o n s ( f n [ [ _ t ] [ i n ] ] [ ( i n c i ) ( + t n ) ] ) [ 0 0 ] ) ( i n t o { } ) ) ) ( d e f n d f - e x e c u t e [ c o n f d s e q ] ( l e t [ [ d f - d a t a d f - c o u n t s ] ( p g / e x e c u t e ( d f - j d s e q ) c o n f ` d f ) o f f s e t s - d v a l ( d v a l / e d n - d v a l ( c a l c u l a t e - o f f s e t s d f - c o u n t s ) ) ] . . . ) )
140. READING FROM DISTRIBUTED CACHE ( d e f n g l o b a l - i d " U s e o f f s e t s t o c a l c u l a t e u n i q u e i d f r o m g l o b a l a n d l o c a l o f f s e t " [ o f f s e t s [ g l o b a l - o f f s e t l o c a l - o f f s e t ] ] ( + l o c a l - o f f s e t ( g e t o f f s e t s g l o b a l - o f f s e t ) ) ) ( d e f n w o r d s - i d f - m " C a l c u l a t e t h e u n i q u e i d a n d i n v e r s e d o c u m e n t f r e q u e n c y f o r e a c h w o r d " { : : m r / s i n k - a s : k e y s } [ o f f s e t s - d v a l n c o l l ] ( l e t [ o f f s e t s @ o f f s e t s - d v a l ] ( r / m a p ( f n [ [ w o r d [ w o r d - o f f s e t d f ] ] ] [ w o r d ( g l o b a l - i d o f f s e t s w o r d - o f f s e t ) ( M a t h / l o g ( / n d f ) ) ] ) c o l l ) ) ) ( d e f n m a k e - d i c t i o n a r y [ c o n f d f - d a t a d f - c o u n t s d o c - c o u n t ] ( l e t [ o f f s e t s - d v a l ( d v a l / e d n - d v a l ( c a l c u l a t e - o f f s e t s d f - c o u n t s ) ) ] ( - > ( p g / i n p u t d f - d a t a ) ( p g / m a p # ' w o r d s - i d f - m o f f s e t s - d v a l d o c - c o u n t ) ( p g / o u t p u t ( m r a / d s i n k [ w o r d s ] ) ) ( p g / f e x e c u t e c o n f ` i d f ) ( - > > ( r / m a p p a r s e - i d f ) ( i n t o { } ) ) ( d v a l / e d n - d v a l ) ) ) )
141. CREATING TEXT VECTORS ( i m p o r t ' [ o r g . a p a c h e . m a h o u t . m a t h R a n d o m A c c e s s S p a r s e V e c t o r ] ) ( d e f n c r e a t e - s p a r s e - v e c t o r [ d i c t i o n a r y [ i d d o c ] ] ( l e t [ v e c t o r ( R a n d o m A c c e s s S p a r s e V e c t o r . ( c o u n t d i c t i o n a r y ) ) ] ( d o s e q [ [ t e r m f r e q ] ( - > d o c d o c u m e n t - > t e r m s f r e q u e n c i e s ) ] ( l e t [ t e r m - i n f o ( g e t d i c t i o n a r y t e r m ) ] ( . s e t Q u i c k v e c t o r ( : i d t e r m - i n f o ) ( * f r e q ( : i d f t e r m - i n f o ) ) ) ) ) [ i d v e c t o r ] ) ) ( d e f n c r e a t e - v e c t o r s - m [ d i c t i o n a r y c o l l ] ( l e t [ d i c t i o n a r y @ d i c t i o n a r y ] ( r / m a p # ( c r e a t e - s p a r s e - v e c t o r d i c t i o n a r y % ) c o l l ) ) )
142. THE FINISHED JOB ( i m p o r t ' [ o r g . a p a c h e . h a d o o p . i o T e x t ] ' [ o r g . a p a c h e . m a h o u t . m a t h V e c t o r W r i t a b l e ] ) ( d e f n t f i d f [ c o n f d s e q d i c t i o n a r y - p a t h v e c t o r - p a t h ] ( l e t [ d o c - c o u n t ( - > > d s e q ( i n t o [ ] ) c o u n t ) [ d f - d a t a d f - c o u n t s ] ( p g / e x e c u t e ( d f - j d s e q ) c o n f ` d f ) d i c t i o n a r y - d v a l ( m a k e - d i c t i o n a r y c o n f d f - d a t a d f - c o u n t s d o c - c o u n t ) ] ( w r i t e - d i c t i o n a r y d i c t i o n a r y - p a t h d i c t i o n a r y - d v a l ) ( - > ( p g / i n p u t d s e q ) ( p g / m a p # ' c r e a t e - v e c t o r s - m d i c t i o n a r y - d v a l ) ( p g / o u t p u t ( s e q f / d s i n k [ T e x t V e c t o r W r i t a b l e ] v e c t o r - p a t h ) ) ( p g / f e x e c u t e c o n f ` v e c t o r i z e ) ) ) ) ( d e f n t o o l [ c o n f i n p u t o u t p u t ] ( l e t [ d s e q ( s e q f / d s e q i n p u t ) d i c t i o n a r y - p a t h ( d o t o ( s t r o u t p u t " / d i c t i o n a r y " ) f s / p a t h - d e l e t e ) v e c t o r - p a t h ( d o t o ( s t r o u t p u t " / v e c t o r s " ) f s / p a t h - d e l e t e ) ] ( t f i d f c o n f d s e q d i c t i o n a r y - p a t h v e c t o r - p a t h ) ) ) ( d e f n - m a i n [ & a r g s ] ( S y s t e m / e x i t ( t o o l / r u n t o o l a r g s ) ) )
143. RUN THE JOB ( d e f n e x - 6 - 1 4 [ ] ( l e t [ i n p u t " d a t a / r e u t e r s - s e q u e n c e f i l e " o u t p u t " d a t a / p a r k o u r - v e c t o r s " ] ( t o o l / r u n v e c t o r i z e r / t o o l [ i n p u t o u t p u t ] ) ) )
144. K-MEANS
145. K-MEANS
146. RUNNING CLUSTERING script/run-kmeans.sh # ! / b i n / b a s h W O R K _ D I R = d a t a I N P U T _ D I R = $ { W O R K _ D I R } / p a r k o u r - v e c t o r s m a h o u t k m e a n s \ - i $ { I N P U T _ D I R } / v e c t o r s \ - c $ { W O R K _ D I R } / c l u s t e r s - o u t \ - o $ { W O R K _ D I R } / k m e a n s - o u t \ - d m o r g . a p a c h e . m a h o u t . c o m m o n . d i s t a n c e . C o s i n e D i s t a n c e M e a s u r e \ - x 2 0 - k 5 - c d 0 . 0 1 - o w - - c l u s t e r i n g m a h o u t c l u s t e r d u m p \ - i $ { W O R K _ D I R } / k m e a n s - o u t / c l u s t e r s - * - f i n a l \ - o $ { W O R K _ D I R } / c l u s t e r d u m p . t x t \ - d $ { I N P U T _ D I R } / d i c t i o n a r y / p a r t - r - 0 0 0 0 0 \ - d t s e q u e n c e f i l e \ - d m o r g . a p a c h e . m a h o u t . c o m m o n . d i s t a n c e . C o s i n e D i s t a n c e M e a s u r e \ - - p o i n t s D i r $ { W O R K _ D I R } / k m e a n s - o u t / c l u s t e r e d P o i n t s \ - b 1 0 0 - n 2 0 - s p 0 - e
147. HOW MANY CLUSTERS?
148. WHAT DID I LEAVE OUT? Cluster quality measures Spectral and LDA clustering Collaborative filtering with Mahout Random forests Spark for movie recommendations with Sparkling Graph data with Loom and Datomic MapReduce with Cascalog and PigPen Adapting algorithms for massive scale Time series and forecasting Dimensionality reduction, feature selection More visualisation techniques Lots more…
149. BOOK Clojure for Data Science will be available in the second half of the year from . http://packtpub.com http://cljds.com
150. SLIDES http://github.com/henrygarner/clojure-data-science
151. THANK YOU! Henry Garner @henrygarner