nyc-taxi-knn.clj

;; gorilla-repl.fileformat = 1

;; **
;;; # Forecasting NYC taxi passengers
;; **

;; **
;;; _Felix Andrews_
;;; 
;;; Adapted from part of Marcus Lewis' [Predicting power consumptions with HTM](http://mrcslws.com/gorilla/?path=hotgym.clj).
;;; 
;;; This is just an extra comparison on the case study presented in the paper
;;; * [Continuous online sequence learning with an unsupervised neural network model](http://arxiv.org/abs/1512.05463).
;;; 
;;; I show results from a weighted running/sliding average by hour (k-NN) method.
;;; 
;; **

;; @@
(ns comportex.notebook.nyc-taxi
  (:require [clj-time.core :as t]
            [clj-time.format :as f]
            [clj-time.predicates :as pr]
            [clojure.data.csv :as csv]
            [clojure.java.io :as io]
            [clojure.set :as set]
            [gorilla-plot.core :as plot]
            [gorilla-repl.table :refer [table-view]]
            [gorilla-renderable.core :as renderable])
  (:use [clojure.pprint]
        [clojure.stacktrace]))
;; @@
;; =>
;;; {"type":"html","content":"<span class='clj-nil'>nil</span>"}
;; <=

;; **
;;; ## <a name="the_data" /> The data
;; **

;; **
;;; Load in the NYC taxi (perturbed) dataset.
;; **

;; @@
(def the-data
  (with-open [in-file (io/reader "data/nyc_taxi_perturb.csv")]
    (doall (->> (csv/read-csv in-file)
                (drop 3)
                (map (fn [[timestamp-str val-str]]
                       [timestamp-str
                        (int (Double/parseDouble val-str))]))))))

(def perturbed-at (* 24 2 274))

(pprint (take 10 the-data))
;; @@
;; ->
;;; ([&quot;2014-07-01 00:00:00&quot; 10844]
;;;  [&quot;2014-07-01 00:30:00&quot; 8127]
;;;  [&quot;2014-07-01 01:00:00&quot; 6210]
;;;  [&quot;2014-07-01 01:30:00&quot; 4656]
;;;  [&quot;2014-07-01 02:00:00&quot; 3820]
;;;  [&quot;2014-07-01 02:30:00&quot; 2873]
;;;  [&quot;2014-07-01 03:00:00&quot; 2369]
;;;  [&quot;2014-07-01 03:30:00&quot; 2064]
;;;  [&quot;2014-07-01 04:00:00&quot; 2221]
;;;  [&quot;2014-07-01 04:30:00&quot; 2158])
;;; 
;; <-
;; =>
;;; {"type":"html","content":"<span class='clj-nil'>nil</span>"}
;; <=

;; **
;;; Each row is a `[timestamp passenger-count]` pair.
;;; 
;;; Here's some data around the point of perturbation:
;; **

;; @@
(let [[n-drop n-take] [0 (* 24 2 10)]]
  (plot/list-plot (->> (map-indexed (fn [i [timestamp passengers]]
                                        [i passengers])
                                      the-data)
                         (drop n-drop)
                         (take n-take))
                :joined true
                :color "red"))
;; @@
;; =>
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;; <=

;; **
;;; It covers every half hour between the dates:
;; **

;; @@
[(first the-data)
 (last the-data)]
;; @@
;; =>
;;; {"type":"list-like","open":"<span class='clj-vector'>[</span>","close":"<span class='clj-vector'>]</span>","separator":" ","items":[{"type":"list-like","open":"<span class='clj-vector'>[</span>","close":"<span class='clj-vector'>]</span>","separator":" ","items":[{"type":"html","content":"<span class='clj-string'>&quot;2014-07-01 00:00:00&quot;</span>"},{"type":"html","content":"<span class='clj-unkown'>10844</span>"}]},{"type":"list-like","open":"<span class='clj-vector'>[</span>","close":"<span class='clj-vector'>]</span>","separator":" ","items":[{"type":"html","content":"<span class='clj-string'>&quot;2015-06-30 23:30:00&quot;</span>"},{"type":"html","content":"<span class='clj-unkown'>17090</span>"}]}]}
;; <=

;; **
;;; Let's shape the data into the sequence of inputs that will go into our model. Just fetch everything we might use.
;; **

;; @@
(def inputs
  (->> the-data
       (map (fn [[timestamp-string passengers]]
              (let [timestamp (f/parse timestamp-string)]
                {:timestamp timestamp-string
                 :day-of-week (t/day-of-week timestamp)
                 :hour-of-day (t/hour timestamp)
                 :is-weekend? (pr/weekend? timestamp)
                 :passengers passengers})))))
;; @@
;; =>
;;; {"type":"html","content":"<span class='clj-var'>#&#x27;comportex.notebook.nyc-taxi/inputs</span>"}
;; <=

;; @@
(table-view
  (->> inputs
       (drop (- perturbed-at (* 24 2 1)))
       (take-nth 24)
       (take 10)
       (map (juxt :timestamp :day-of-week :hour-of-day :is-weekend? :passengers)))
  :columns [:timestamp :day-of-week :hour-of-day :is-weekend? :passengers]
)
;; @@
;; =>
;;; {"type":"list-like","open":"<center><table>","close":"</table></center>","separator":"\n","items":[{"type":"list-like","open":"<tr><th>","close":"</th></tr>","separator":"</th><th>","items":[{"type":"html","content":"<span class='clj-keyword'>:timestamp</span>"},{"type":"html","content":"<span class='clj-keyword'>:day-of-week</span>"},{"type":"html","content":"<span class='clj-keyword'>:hour-of-day</span>"},{"type":"html","content":"<span class='clj-keyword'>:is-weekend?</span>"},{"type":"html","content":"<span class='clj-keyword'>:passengers</span>"}]},{"type":"list-like","open":"<tr><td>","close":"</td></tr>","separator":"</td><td>","items":[{"type":"html","content":"<span class='clj-string'>&quot;2015-03-31 00:00:00&quot;</span>"},{"type":"html","content":"<span class='clj-unkown'>2</span>"},{"type":"html","content":"<span class='clj-unkown'>0</span>"},{"type":"html","content":"<span class='clj-unkown'>false</span>"},{"type":"html","content":"<span class='clj-unkown'>10141</span>"}]},{"type":"list-like","open":"<tr><td>","close":"</td></tr>","separator":"</td><td>","items":[{"type":"html","content":"<span class='clj-string'>&quot;2015-03-31 12:00:00&quot;</span>"},{"type":"html","content":"<span class='clj-unkown'>2</span>"},{"type":"html","content":"<span class='clj-unkown'>12</span>"},{"type":"html","content":"<span class='clj-unkown'>false</span>"},{"type":"html","content":"<span class='clj-unkown'>17433</span>"}]},{"type":"list-like","open":"<tr><td>","close":"</td></tr>","separator":"</td><td>","items":[{"type":"html","content":"<span class='clj-string'>&quot;2015-04-01 00:00:00&quot;</span>"},{"type":"html","content":"<span class='clj-unkown'>3</span>"},{"type":"html","content":"<span class='clj-unkown'>0</span>"},{"type":"html","content":"<span class='clj-unkown'>false</span>"},{"type":"html","content":"<span class='clj-unkown'>11660</span>"}]},{"type":"list-like","open":"<tr><td>","close":"</td></tr>","separator":"</td><td>","items":[{"type":"html","content":"<span class='clj-string'>&quot;2015-04-01 12:00:00&quot;</span>"},{"type":"html","content":"<span class='clj-unkown'>3</span>"},{"type":"html","content":"<span class='clj-unkown'>12</span>"},{"type":"html","content":"<span class='clj-unkown'>false</span>"},{"type":"html","content":"<span class='clj-unkown'>18087</span>"}]},{"type":"list-like","open":"<tr><td>","close":"</td></tr>","separator":"</td><td>","items":[{"type":"html","content":"<span class='clj-string'>&quot;2015-04-02 00:00:00&quot;</span>"},{"type":"html","content":"<span class='clj-unkown'>4</span>"},{"type":"html","content":"<span class='clj-unkown'>0</span>"},{"type":"html","content":"<span class='clj-unkown'>false</span>"},{"type":"html","content":"<span class='clj-unkown'>13647</span>"}]},{"type":"list-like","open":"<tr><td>","close":"</td></tr>","separator":"</td><td>","items":[{"type":"html","content":"<span class='clj-string'>&quot;2015-04-02 12:00:00&quot;</span>"},{"type":"html","content":"<span class='clj-unkown'>4</span>"},{"type":"html","content":"<span class='clj-unkown'>12</span>"},{"type":"html","content":"<span class='clj-unkown'>false</span>"},{"type":"html","content":"<span class='clj-unkown'>18037</span>"}]},{"type":"list-like","open":"<tr><td>","close":"</td></tr>","separator":"</td><td>","items":[{"type":"html","content":"<span class='clj-string'>&quot;2015-04-03 00:00:00&quot;</span>"},{"type":"html","content":"<span class='clj-unkown'>5</span>"},{"type":"html","content":"<span class='clj-unkown'>0</span>"},{"type":"html","content":"<span class='clj-unkown'>false</span>"},{"type":"html","content":"<span class='clj-unkown'>18876</span>"}]},{"type":"list-like","open":"<tr><td>","close":"</td></tr>","separator":"</td><td>","items":[{"type":"html","content":"<span class='clj-string'>&quot;2015-04-03 12:00:00&quot;</span>"},{"type":"html","content":"<span class='clj-unkown'>5</span>"},{"type":"html","content":"<span class='clj-unkown'>12</span>"},{"type":"html","content":"<span class='clj-unkown'>false</span>"},{"type":"html","content":"<span class='clj-unkown'>20660</span>"}]},{"type":"list-like","open":"<tr><td>","close":"</td></tr>","separator":"</td><td>","items":[{"type":"html","content":"<span class='clj-string'>&quot;2015-04-04 00:00:00&quot;</span>"},{"type":"html","content":"<span class='clj-unkown'>6</span>"},{"type":"html","content":"<span class='clj-unkown'>0</span>"},{"type":"html","content":"<span class='clj-unkown'>true</span>"},{"type":"html","content":"<span class='clj-unkown'>20851</span>"}]},{"type":"list-like","open":"<tr><td>","close":"</td></tr>","separator":"</td><td>","items":[{"type":"html","content":"<span class='clj-string'>&quot;2015-04-04 12:00:00&quot;</span>"},{"type":"html","content":"<span class='clj-unkown'>6</span>"},{"type":"html","content":"<span class='clj-unkown'>12</span>"},{"type":"html","content":"<span class='clj-unkown'>true</span>"},{"type":"html","content":"<span class='clj-unkown'>19010</span>"}]}]}
;; <=

;; **
;;; ## Shift (baseline) forecast
;; **

;; @@
(def lagged-inputs
  (concat (repeat 5 (assoc (first inputs) :passengers 0))
          (drop-last 5 inputs)))

(println "lagged values corresponding")
(pprint (map (fn [i in lagged]
               {:i i, :in (:passengers in), :lagged (:passengers lagged)})
             (range 10) inputs lagged-inputs))

;; @@
;; ->
;;; lagged values corresponding
;;; ({:i 0, :in 10844, :lagged 0}
;;;  {:i 1, :in 8127, :lagged 0}
;;;  {:i 2, :in 6210, :lagged 0}
;;;  {:i 3, :in 4656, :lagged 0}
;;;  {:i 4, :in 3820, :lagged 0}
;;;  {:i 5, :in 2873, :lagged 10844}
;;;  {:i 6, :in 2369, :lagged 8127}
;;;  {:i 7, :in 2064, :lagged 6210}
;;;  {:i 8, :in 2221, :lagged 4656}
;;;  {:i 9, :in 2158, :lagged 3820})
;;; 
;; <-
;; =>
;;; {"type":"html","content":"<span class='clj-nil'>nil</span>"}
;; <=

;; @@
(def shift-forecast
  (map :passengers inputs))
;; @@
;; =>
;;; {"type":"html","content":"<span class='clj-var'>#&#x27;comportex.notebook.nyc-taxi/shift-forecast</span>"}
;; <=

;; **
;;; ### Running average by hour
;;; 
;;; Simply calculate the average 5-step-ahead value for this `hour-of-day` + `is-weekend?` combination.
;;; 
;;; In other words, "It's hour 12 on a Tuesday. What usually happens after this?"
;; **

;; @@
(def avg-by-hour-forecast
  (first
    (reduce
      (fn [[output average-builder] [i input prev-input]]
        (when (zero? (mod i 1000)) (print "."))
        (let [{:keys [is-weekend? hour-of-day passengers]} input
              average-builder (update average-builder [(:is-weekend? prev-input )
                                                       (:hour-of-day prev-input)]
                                      #(if-let [[total n] %]
                                         [(+ total passengers) (inc n)]
                                         [passengers 1]))
              prediction (if-let [[total n] (get average-builder
                                                 [is-weekend? hour-of-day])]
                           (quot total n)
                           passengers)]
          [(conj output prediction) average-builder]))
      [[] {}]
      (map vector (range) inputs lagged-inputs))))
(println)
;; @@
;; ->
;;; ..................
;;; 
;; <-
;; =>
;;; {"type":"html","content":"<span class='clj-nil'>nil</span>"}
;; <=

;; **
;;; ### Weighted running average by hour (k-NN)
;;; 
;;; A k-Nearest-Neighbors estimator. It simply calculates the weighted average next value for this `hour-of-day` + `day-of-week` combination, weighted by the nearness of the data points' current passenger count.
;;; 
;;; In other words, "It's hour 12 on a Tuesday, and the current passenger count is 3200. What usually happens after this?"
;; **

;; @@
(defn weighted-mean
  [weighted-xs]
  (let [[total weight-sum] (reduce (fn [[total weight-sum] [x weight]]
                                     [(+ total (* weight x))
                                      (+ weight-sum weight)])
                                   [0 0]
                                   weighted-xs)]
    (when-not (zero? weight-sum)
      (/ total weight-sum))))


(def knn-by-hour-forecast
  (let [k 10]
  (first
    (reduce
      (fn [[output average-builder] [i input prev-input]]
        (when (zero? (mod i 1000)) (print ".") (flush))
        (let [{:keys [is-weekend? day-of-week hour-of-day passengers]} input
              average-builder (update average-builder [(:day-of-week prev-input)
                                                       (:hour-of-day prev-input)]
                                      #(assoc (or % (sorted-map))
                                              (:passengers prev-input) passengers))
              ordered-obs (get average-builder [day-of-week
                                                hour-of-day])
              closest-index (if (seq ordered-obs)
                              (dec
                                (Math/abs
                                  (java.util.Collections/binarySearch (keys ordered-obs) passengers
                                                                    compare)))
                              0)
              predictions (->> ordered-obs
                               (drop (- closest-index k))
                               (take (* k 2))
                               (sort-by (fn [[old-passengers _]]
                                          (Math/abs (int (- old-passengers passengers)))))
                               (take k))
              aggregated (if (empty? predictions)
                           passengers
                           (->> predictions
                                (map (fn [[old-passengers v]]
                                       [v
                                        (/ 1 (-> (- old-passengers passengers)
                                                 int Math/abs
                                                 (+ 0.01)))]))
                                weighted-mean))]
          [(conj output aggregated) average-builder]))
      [[] {}]
      (map vector (range) inputs lagged-inputs)))))

;; @@
;; ->
;;; ..................
;; <-
;; =>
;;; {"type":"html","content":"<span class='clj-var'>#&#x27;comportex.notebook.nyc-taxi/knn-by-hour-forecast</span>"}
;; <=

;; **
;;; ### Weighted sliding average by hour (k-NN)
;; **

;; @@
(defn knn-by-hour-sliding
  [k window-steps]
  (first
    (reduce
      (fn [[output average-builder] [i input prev-input]]
        (when (zero? (mod i 1000)) (print ".") (flush))
        (let [{:keys [is-weekend? day-of-week hour-of-day passengers]} input
              average-builder (update average-builder [(:day-of-week prev-input)
                                                       (:hour-of-day prev-input)]
                                      #(assoc (or % (sorted-map))
                                              i [(:passengers prev-input) passengers]))
              indexed-obs (get average-builder [day-of-week
                                                hour-of-day] (sorted-map))
              predictions (->> (subseq indexed-obs > (- i window-steps))
                               (vals)
                               (sort-by (fn [[old-passengers _]]
                                          (Math/abs (int (- old-passengers passengers)))))
                               (take k))
              aggregated (if (empty? predictions)
                           passengers
                           (->> predictions
                                (map (fn [[old-passengers v]]
                                       [v
                                        (/ 1 (-> (- old-passengers passengers)
                                                 int Math/abs
                                                 (+ 0.01)))]))
                                weighted-mean))]
          [(conj output aggregated) average-builder]))
      [[] {}]
      (map vector (range) inputs lagged-inputs))))

(def knn-by-hour-sliding-forecast-1000 (knn-by-hour-sliding 10 1000))
(def knn-by-hour-sliding-forecast-3000 (knn-by-hour-sliding 10 3000))

;; @@
;; ->
;;; ....................................
;; <-
;; =>
;;; {"type":"html","content":"<span class='clj-var'>#&#x27;comportex.notebook.nyc-taxi/knn-by-hour-sliding-forecast-3000</span>"}
;; <=

;; **
;;; ## Forecast results
;; **

;; @@
(defn mean [xs] (/ (reduce + xs) (count xs)))
(defn abs [x] (if (neg? x) (- x) x))

(defn mae
  "mean absolute error"
  [predicted observed]
  (mean (map (comp abs -) observed predicted)))

(defn mape
  "mean absolute error divided by mean actual value."
  [predicted observed]
  (double
    (/ (mae predicted observed)
       (mean observed))))

(defn mape-excluding-warmup
  [forecast warmup-steps]
  (mape (drop warmup-steps forecast)
        (drop (+ warmup-steps 5) (map :passengers inputs))))

;; @@
;; =>
;;; {"type":"html","content":"<span class='clj-var'>#&#x27;comportex.notebook.nyc-taxi/mape-excluding-warmup</span>"}
;; <=

;; **
;;; ### Shift
;; **

;; @@
(mape-excluding-warmup shift-forecast (* 24 2 7))
;; @@
;; =>
;;; {"type":"html","content":"<span class='clj-double'>0.3265029292302994</span>"}
;; <=

;; **
;;; ### Running average by hour
;; **

;; @@
(mape-excluding-warmup avg-by-hour-forecast (* 24 2 7))
;; @@
;; =>
;;; {"type":"html","content":"<span class='clj-double'>0.1521830792015254</span>"}
;; <=

;; @@
(mape-excluding-warmup avg-by-hour-forecast perturbed-at)
;; @@
;; =>
;;; {"type":"html","content":"<span class='clj-double'>0.1481880237819002</span>"}
;; <=

;; **
;;; ### Weighted running KNN by hour
;; **

;; @@
(mape-excluding-warmup knn-by-hour-forecast (* 24 2 7))
;; @@
;; =>
;;; {"type":"html","content":"<span class='clj-double'>0.09039234737451765</span>"}
;; <=

;; @@
(mape-excluding-warmup knn-by-hour-forecast perturbed-at)
;; @@
;; =>
;;; {"type":"html","content":"<span class='clj-double'>0.10309088173334977</span>"}
;; <=

;; **
;;; ### Weighted sliding KNN by hour (1000 steps)
;; **

;; @@
(mape-excluding-warmup knn-by-hour-sliding-forecast-1000 (* 24 2 7))
;; @@
;; =>
;;; {"type":"html","content":"<span class='clj-double'>0.0914515448043314</span>"}
;; <=

;; @@
(mape-excluding-warmup knn-by-hour-sliding-forecast-1000 perturbed-at)
;; @@
;; =>
;;; {"type":"html","content":"<span class='clj-double'>0.07595319209615771</span>"}
;; <=

;; **
;;; ### Weighted sliding KNN by hour (3000 steps)
;; **

;; @@
(mape-excluding-warmup knn-by-hour-sliding-forecast-3000 (* 24 2 7))
;; @@
;; =>
;;; {"type":"html","content":"<span class='clj-double'>0.08553116118479587</span>"}
;; <=

;; @@
(mape-excluding-warmup knn-by-hour-sliding-forecast-3000 perturbed-at)
;; @@
;; =>
;;; {"type":"html","content":"<span class='clj-double'>0.08106487414326526</span>"}
;; <=

;; @@
(let [[n-drop n-take] [(- perturbed-at (* 24 2 7)) (* 24 2 14)]]
  (plot/compose
    (plot/list-plot (->> (map-indexed (fn [i v]
                                        [i (:passengers v)])
                                      inputs)
                         (drop n-drop)
                         (take n-take))
                    :joined true
                    :color "black"
                    :plot-size 700)
    (plot/list-plot (->> (map-indexed (fn [i v]
                                        [(+ i 5) v])
                                      knn-by-hour-sliding-forecast-1000)
                         (drop n-drop)
                         (take n-take))
                    :joined true
                    :color "blue"
                    :plot-size 700)
    ))
;; @@
;; =>
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;; <=

;; @@
(let [[n-drop n-take] [(- perturbed-at (* 24 2 7)) (* 24 2 14)]]
  (plot/compose
    (plot/list-plot (->> (map (fn [i v x]
                                 [i (- v x)])
                              (range)
                              (drop 5 (map :passengers inputs))
                              knn-by-hour-forecast)
                         (drop n-drop)
                         (take n-take))
                    :joined true
                    :color "blue"
                    :opacity 0.5
                    :plot-size 700)
    (plot/list-plot (->> (map (fn [i v x]
                                 [i (- v x)])
                              (range)
                              (drop 5 (map :passengers inputs))
                              knn-by-hour-sliding-forecast-1000)
                         (drop n-drop)
                         (take n-take))
                    :joined true
                    :color "red"
                    :opacity 0.5
                    :plot-size 700)
    (plot/list-plot [[n-drop 0] [(+ n-drop n-take) 0]]
                    :joined true
                    :color "black"
                    )
    ))
;; @@
;; =>
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