;; gorilla-repl.fileformat = 1

;; **
;;; # Stochastic Neighbour Embedding
;;; implementing the original [Stochastic Neighbour Embedding](http://www.cs.nyu.edu/~roweis/papers/sne_final.pdf) without mixtures and with a Gaussian distribution over neighbours in low-dimensional space (not t-SNE). σ is variance over all other data-points, binary search not yet understood/ implemented.
;; **

;; @@
(ns stochastic-neighbour-embedding
  (:refer-clojure :exclude [* - + == /])
  (:use clojure.core.matrix.operators)
  (:require [gorilla-plot.core :as plot]
            [gg4clj.core :as gg4clj]
            [clojure.math.combinatorics :refer [cartesian-product]]
            [cnc.analytics :as a]
            [incanter.stats :as s]
            [cnc.execute :as exe]
            [clojure.pprint :refer [pprint]]
            [hasch.core :refer [uuid]]
            [boltzmann.matrix :refer [full-matrix]]
            [clojure.java.shell :refer [sh]]
            [cnc.core :refer [state]]
            [cnc.execute :refer [slurp-bytes]]
            [clj-hdf5.core :as hdf5]
            [konserve.protocols :refer [-get-in -bget -exists?]]
            [geschichte.platform :refer [<!?]]
            [boltzmann.core :refer [train-cd sample-gibbs]]
            [boltzmann.theoretical :refer [create-theoretical-rbm]]
            [boltzmann.formulas :as f]
            [boltzmann.protocols :refer [-weights -biases]]
            [boltzmann.visualize :as v]
            [clojure.core.matrix :refer [dot matrix] :as mat]
            [datomic.api :as d]
            [clojure.core.async :refer [chan] :as async]
            [quil.core :as q]))
(def store (get-in @state [:repo :store]))
(def states (apply cartesian-product (repeat 9 [0 1])))
(def conn (a/conn "train current rbms4"))
(defn exp [x] (Math/exp x))
(defn ² [x] (Math/pow x 2))
(def r# (comp range count))
;; @@
;; =>
;;; {"type":"html","content":"<span class='clj-var'>#&#x27;stochastic-neighbour-embedding/r#</span>","value":"#'stochastic-neighbour-embedding/r#"}
;; <=

;; **
;;; ## Import Iris as dataset
;; **

;; @@
(require '[incanter.core :as ic]
         '[incanter.datasets :as ds])
(def iris (ds/get-dataset :iris))
#_(ic/view iris)
(def iris-mat (ic/to-matrix iris))
#_(ic/view iris-mat)
(def data (matrix iris-mat))
(def ys (mapv vec (take (count data) (repeatedly #(s/sample-normal 2 :sd 1e-4)))))
;; @@
;; =>
;;; {"type":"html","content":"<span class='clj-var'>#&#x27;stochastic-neighbour-embedding/ys</span>","value":"#'stochastic-neighbour-embedding/ys"}
;; <=

;; **
;;; ## Formulas
;;; 
;;; Section 1, 1-5.
;; **

;; @@
(def ∑ (partial apply mat/add))
;; @@
;; =>
;;; {"type":"html","content":"<span class='clj-var'>#&#x27;stochastic-neighbour-embedding/∑</span>","value":"#'stochastic-neighbour-embedding/∑"}
;; <=

;; @@
(def p 
  (memoize (fn [d i j]
 (let [dvar (mapv s/variance d)]
  (/ (exp (- (/ (² ((d i) j)) 
                (* 6 (dvar i)))))
     (∑ (for [k (r# d) :when (not= k i)]
          (exp (- (/ (² ((d i) k)) 
                     (* 6 (dvar i))))))))))))
;; @@
;; =>
;;; {"type":"html","content":"<span class='clj-var'>#&#x27;stochastic-neighbour-embedding/p</span>","value":"#'stochastic-neighbour-embedding/p"}
;; <=

;; @@
(defn q [yd i j]
  (/ (exp (- (² ((yd i) j))))
     (∑ (for [k (r# yd) :when (not= k i)]
          (exp (- (² ((yd i) k))))))))
;; @@
;; =>
;;; {"type":"html","content":"<span class='clj-var'>#&#x27;stochastic-neighbour-embedding/q</span>","value":"#'stochastic-neighbour-embedding/q"}
;; <=

;; @@
(defn dists [y]
  (vec (for [i (r# y)]
         (vec (for [j (r# y)]
                (s/euclidean-distance (y i) (y j)))))))
;; @@
;; =>
;;; {"type":"html","content":"<span class='clj-var'>#&#x27;stochastic-neighbour-embedding/dists</span>","value":"#'stochastic-neighbour-embedding/dists"}
;; <=

;; @@
(q (dists ys) 1 2)

;; @@
;; =>
;;; {"type":"html","content":"<span class='clj-double'>0.006711409829452413</span>","value":"0.006711409829452413"}
;; <=

;; @@
(defn ∂C [d y yd i]
  (* 2 (∑ (for [j (r# d)]
            (* (- (y i) (y j))
               (+ (p d i j) 
                  (- (q yd i j))
                  (p d j i)
                  (- (q yd j i))))))))
;; @@
;; =>
;;; {"type":"html","content":"<span class='clj-var'>#&#x27;stochastic-neighbour-embedding/∂C</span>","value":"#'stochastic-neighbour-embedding/∂C"}
;; <=

;; @@
(defn norm-update [up]
  (∑ (map #(s/euclidean-distance
             % (mat/zero-vector 2)) up)))
;; @@
;; =>
;;; {"type":"html","content":"<span class='clj-var'>#&#x27;stochastic-neighbour-embedding/norm-update</span>","value":"#'stochastic-neighbour-embedding/norm-update"}
;; <=

;; @@
(defn random-matrix [rows columns 
                     & {:keys [sd mean] 
                        :or {sd 1 mean 0}}]
  (->> (repeatedly 
         #(s/sample-normal columns 
                           :sd sd :mean mean))
        (take rows)
        matrix))
;; @@
;; =>
;;; {"type":"html","content":"<span class='clj-var'>#&#x27;stochastic-neighbour-embedding/random-matrix</span>","value":"#'stochastic-neighbour-embedding/random-matrix"}
;; <=

;; @@
(defn train [init dd rate epochs]
  (let [dc (count dd)
        dr (range dc)]
(reduce (fn [yss r] 
          (let [[[ys oup]] yss
                yd (dists ys)
                up (time (mapv #(∂C dd ys yd %) dr))
                ar (/ (+ 30 rate) (+ (inc r) 30))
                upr (+ (* 0.5 up)
                       (* 0.5 oup)
                       (random-matrix dc
                                      2
                                      :sd (/ 1e-3 (inc r))))
                ys' (- ys (* ar upr))]
            (println "Step:" r "rate: " ar ", update size:" (norm-update upr))
            (conj yss [ys' upr])))
        (list [init (mat/zero-matrix dc 2)])
        (range epochs))))
;; @@
;; =>
;;; {"type":"html","content":"<span class='clj-var'>#&#x27;stochastic-neighbour-embedding/train</span>","value":"#'stochastic-neighbour-embedding/train"}
;; <=

;; @@
(def trained (train ys (dists data) 1 50))
;; @@
;; ->
;;; &quot;Elapsed time: 970623.897766 msecs&quot;
;;; Step: 0 rate:  1 , update size: 0.20349844425375815
;;; &quot;Elapsed time: 2140.600539 msecs&quot;
;;; Step: 1 rate:  31/32 , update size: 0.14935646321197252
;;; &quot;Elapsed time: 2070.214548 msecs&quot;
;;; Step: 2 rate:  31/33 , update size: 0.24726590163614495
;;; &quot;Elapsed time: 2153.699529 msecs&quot;
;;; Step: 3 rate:  31/34 , update size: 0.709908794071409
;;; &quot;Elapsed time: 2064.950084 msecs&quot;
;;; Step: 4 rate:  31/35 , update size: 2.1685550763945547
;;; &quot;Elapsed time: 2144.17178 msecs&quot;
;;; Step: 5 rate:  31/36 , update size: 6.638502305875773
;;; &quot;Elapsed time: 2082.465975 msecs&quot;
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;;; &quot;Elapsed time: 2161.334876 msecs&quot;
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;;; &quot;Elapsed time: 2140.087315 msecs&quot;
;;; Step: 8 rate:  31/39 , update size: 106.48447819455984
;;; &quot;Elapsed time: 2184.564186 msecs&quot;
;;; Step: 9 rate:  31/40 , update size: 81.87612375363132
;;; &quot;Elapsed time: 2110.570531 msecs&quot;
;;; Step: 10 rate:  31/41 , update size: 56.570389244910835
;;; &quot;Elapsed time: 2167.059524 msecs&quot;
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;;; &quot;Elapsed time: 2116.231455 msecs&quot;
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;;; &quot;Elapsed time: 2202.947634 msecs&quot;
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;;; &quot;Elapsed time: 2160.181625 msecs&quot;
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;;; &quot;Elapsed time: 2155.919288 msecs&quot;
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;;; &quot;Elapsed time: 2199.277205 msecs&quot;
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;;; &quot;Elapsed time: 2269.64549 msecs&quot;
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;;; &quot;Elapsed time: 2252.916041 msecs&quot;
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;;; &quot;Elapsed time: 2176.26221 msecs&quot;
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;;; &quot;Elapsed time: 2347.644644 msecs&quot;
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;;; &quot;Elapsed time: 2340.596084 msecs&quot;
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;;; &quot;Elapsed time: 2237.852993 msecs&quot;
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;;; &quot;Elapsed time: 2367.28864 msecs&quot;
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;;; &quot;Elapsed time: 2263.103034 msecs&quot;
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;;; &quot;Elapsed time: 2187.804049 msecs&quot;
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;;; &quot;Elapsed time: 2341.73089 msecs&quot;
;;; Step: 28 rate:  31/59 , update size: 1.67961348790605
;;; &quot;Elapsed time: 2425.047722 msecs&quot;
;;; Step: 29 rate:  31/60 , update size: 1.6005805642311535
;;; &quot;Elapsed time: 2299.980374 msecs&quot;
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;;; &quot;Elapsed time: 2289.752708 msecs&quot;
;;; Step: 31 rate:  1/2 , update size: 1.4678018784261375
;;; &quot;Elapsed time: 2377.630002 msecs&quot;
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;;; &quot;Elapsed time: 2316.510919 msecs&quot;
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;;; &quot;Elapsed time: 2252.314376 msecs&quot;
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;;; &quot;Elapsed time: 2318.648433 msecs&quot;
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;;; &quot;Elapsed time: 2270.793427 msecs&quot;
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;;; &quot;Elapsed time: 2325.553928 msecs&quot;
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;;; &quot;Elapsed time: 2155.810853 msecs&quot;
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;;; &quot;Elapsed time: 2200.011834 msecs&quot;
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;;; &quot;Elapsed time: 2189.60727 msecs&quot;
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;;; &quot;Elapsed time: 2216.78097 msecs&quot;
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;;; &quot;Elapsed time: 2255.209571 msecs&quot;
;;; Step: 49 rate:  31/80 , update size: 0.9985296897226674
;;; 
;; <-
;; =>
;;; {"type":"html","content":"<span class='clj-var'>#&#x27;stochastic-neighbour-embedding/trained</span>","value":"#'stochastic-neighbour-embedding/trained"}
;; <=

;; @@
(apply plot/compose
(map #(plot/compose 
        (plot/list-plot (take 50 %1) :color "red"
                        :plot-range [[-3 3] [-3 3]] :opacity 0.2 :plot-size 1024)
        (plot/list-plot (take 50 (drop 50 %1)) :color "blue" :opacity 0.2)
        (plot/list-plot (take 50 (drop 100 %1)) :color "green" :opacity 0.2))
     (map first (take 10 trained))))
;; @@
;; =>
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;; <=

;; **
;;; ## Compare p and q
;;; 
;;; The gradient descent optimizes the difference between the softmax distribution p over pair-wise distances in high-dimensional space and the distribution q over pair-wise distances in the low-dimensional (2D) space. Hence one can see how the descent approximates the original distribution. This also depends on the choice of σ.
;; **

;; @@
(plot/list-plot (map #(p (dists data) 6 %) (range (count data))))
;; @@
;; =>
;;; 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;; <=

;; @@
(map (fn [t]
       (let [dt (dists t)]
       (plot/list-plot (map #(q dt 6 %) (range (count data)))))) (map first (take-nth 10 (reverse trained))))
;; @@
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;; <=

;; **
;;; ## MNIST
;;; Try with three classes 50 data-points each on MNIST.
;; **

;; @@
(require '[boltzmann.mnist :as mnist]
         '[boltzmann.visualize :as visu])
;; @@
;; =>
;;; {"type":"html","content":"<span class='clj-var'>#&#x27;stochastic-neighbour-embedding/images</span>","value":"#'stochastic-neighbour-embedding/images"}
;; <=

;; @@
(def images (boltzmann.mnist/read-images "/usr/src/boltzmann/resources/train-images-idx3-ubyte"))
;; @@

;; @@
(def labels (mnist/read-labels "/usr/src/boltzmann/resources/train-labels-idx1-ubyte"))
;; @@
;; =>
;;; {"type":"html","content":"<span class='clj-var'>#&#x27;stochastic-neighbour-embedding/labels</span>","value":"#'stochastic-neighbour-embedding/labels"}
;; <=

;; @@
(defn filter-class [c]
(apply concat (map-indexed (fn [i l] (if (= l c) 
                                 [(images i)]
                                 [])) labels)))
;; @@
;; =>
;;; {"type":"html","content":"<span class='clj-var'>#&#x27;stochastic-neighbour-embedding/filter-class</span>","value":"#'stochastic-neighbour-embedding/filter-class"}
;; <=

;; @@
(->> (filter-class 4) 
     (take 100 )
     (map #(partition 28 %))
     (visu/tile 10)
     (visu/render-float-matrix (fn [v] [0 0 v]))
     visu/view)
;; @@
;; =>
;;; {"type":"html","content":"<span class='clj-unkown'>#&lt;JFrame javax.swing.JFrame[frame11,0,24,280x280,layout=java.awt.BorderLayout,title=No title,normal,defaultCloseOperation=HIDE_ON_CLOSE,rootPane=javax.swing.JRootPane[,5,25,270x250,layout=javax.swing.JRootPane$RootLayout,alignmentX=0.0,alignmentY=0.0,border=,flags=16777673,maximumSize=,minimumSize=,preferredSize=],rootPaneCheckingEnabled=true]&gt;</span>","value":"#<JFrame javax.swing.JFrame[frame11,0,24,280x280,layout=java.awt.BorderLayout,title=No title,normal,defaultCloseOperation=HIDE_ON_CLOSE,rootPane=javax.swing.JRootPane[,5,25,270x250,layout=javax.swing.JRootPane$RootLayout,alignmentX=0.0,alignmentY=0.0,border=,flags=16777673,maximumSize=,minimumSize=,preferredSize=],rootPaneCheckingEnabled=true]>"}
;; <=

;; @@
(def threes (take 50 (filter-class 3)))
(def fours (take 50 (filter-class 4)))
(def fives (take 50 (filter-class 5)))
;; @@
;; =>
;;; {"type":"html","content":"<span class='clj-var'>#&#x27;stochastic-neighbour-embedding/fives</span>","value":"#'stochastic-neighbour-embedding/fives"}
;; <=

;; @@
(def mnist-data (matrix (concat threes fours fives)))
;; @@
;; =>
;;; {"type":"html","content":"<span class='clj-var'>#&#x27;stochastic-neighbour-embedding/mnist-data</span>","value":"#'stochastic-neighbour-embedding/mnist-data"}
;; <=

;; @@
(plot/list-plot (map #(if (= % 125) 0 (p mnist-dist 125 %)) (r# mnist-data)))
;; @@
;; =>
;;; 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;; <=

;; @@
(count mnist-data)
;; @@
;; =>
;;; {"type":"html","content":"<span class='clj-unkown'>150</span>","value":"150"}
;; <=

;; @@
(def mnist-dist (time (dists mnist-data)))
;; @@
;; ->
;;; &quot;Elapsed time: 17045.336261 msecs&quot;
;;; 
;; <-
;; =>
;;; {"type":"html","content":"<span class='clj-var'>#&#x27;stochastic-neighbour-embedding/mnist-dist</span>","value":"#'stochastic-neighbour-embedding/mnist-dist"}
;; <=

;; @@
(s/mean (map #(s/variance (mnist-dist %)) (r# mnist-data)))
;; @@
;; =>
;;; {"type":"html","content":"<span class='clj-double'>2.374790431829107</span>","value":"2.374790431829107"}
;; <=

;; @@
(def trained-mnist (train ys mnist-dist 1 100))
;; @@
;; ->
;;; &quot;Elapsed time: 960673.94673 msecs&quot;
;;; Step: 0 rate:  1 , update size: 0.18535718460290973
;;; &quot;Elapsed time: 2271.39812 msecs&quot;
;;; Step: 1 rate:  31/32 , update size: 0.17601530148667954
;;; &quot;Elapsed time: 2286.745636 msecs&quot;
;;; Step: 2 rate:  31/33 , update size: 0.2932062039745418
;;; &quot;Elapsed time: 2266.317717 msecs&quot;
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;;; &quot;Elapsed time: 2281.361707 msecs&quot;
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;;; &quot;Elapsed time: 2285.404602 msecs&quot;
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;;; &quot;Elapsed time: 2282.815188 msecs&quot;
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;;; &quot;Elapsed time: 2304.496892 msecs&quot;
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;;; &quot;Elapsed time: 2295.22271 msecs&quot;
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;;; &quot;Elapsed time: 2289.540128 msecs&quot;
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;;; &quot;Elapsed time: 2289.326543 msecs&quot;
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;;; &quot;Elapsed time: 2305.961504 msecs&quot;
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;;; &quot;Elapsed time: 2276.226564 msecs&quot;
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;;; &quot;Elapsed time: 2275.397932 msecs&quot;
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;;; &quot;Elapsed time: 2279.091783 msecs&quot;
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;;; &quot;Elapsed time: 2293.782117 msecs&quot;
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;;; &quot;Elapsed time: 2270.653109 msecs&quot;
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;;; &quot;Elapsed time: 2277.123858 msecs&quot;
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;;; &quot;Elapsed time: 2271.027021 msecs&quot;
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;;; &quot;Elapsed time: 2273.447178 msecs&quot;
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;;; &quot;Elapsed time: 2262.592168 msecs&quot;
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;;; &quot;Elapsed time: 2275.404649 msecs&quot;
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;;; &quot;Elapsed time: 2268.777433 msecs&quot;
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;;; &quot;Elapsed time: 2276.924541 msecs&quot;
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;;; &quot;Elapsed time: 2262.131305 msecs&quot;
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;;; &quot;Elapsed time: 2269.827622 msecs&quot;
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;;; &quot;Elapsed time: 2263.941814 msecs&quot;
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;;; &quot;Elapsed time: 2275.718011 msecs&quot;
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;;; &quot;Elapsed time: 2276.011912 msecs&quot;
;;; Step: 28 rate:  31/59 , update size: 2.9970484051328055
;;; &quot;Elapsed time: 2292.563221 msecs&quot;
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;;; &quot;Elapsed time: 2268.160774 msecs&quot;
;;; Step: 30 rate:  31/61 , update size: 2.170225490157318
;;; &quot;Elapsed time: 2272.662443 msecs&quot;
;;; Step: 31 rate:  1/2 , update size: 1.8594769234684358
;;; &quot;Elapsed time: 2264.928012 msecs&quot;
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;;; &quot;Elapsed time: 2280.17349 msecs&quot;
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;;; &quot;Elapsed time: 2271.382276 msecs&quot;
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;;; &quot;Elapsed time: 2269.834941 msecs&quot;
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;;; &quot;Elapsed time: 2275.617586 msecs&quot;
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;;; 
;; <-
;; =>
;;; {"type":"html","content":"<span class='clj-var'>#&#x27;stochastic-neighbour-embedding/trained-mnist</span>","value":"#'stochastic-neighbour-embedding/trained-mnist"}
;; <=

;; @@
(apply plot/compose
(map #(plot/compose 
        (plot/list-plot (take 50 %1) :color "red"
                        :plot-range [[-3 3] [-3 3]] :opacity 0.2 :plot-size 1024)
        (plot/list-plot (take 50 (drop 50 %1)) :color "blue" :opacity 0.2)
        (plot/list-plot (take 50 (drop 100 %1)) :color "green" :opacity 0.2))
     (map first (take 10 trained-mnist))))
;; @@
;; =>
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;; <=

;; @@
(map (fn [t]
       (let [dt (dists t)]
       (plot/list-plot (map #(q dt 60 %) (r# mnist-data))))) 
     (map first (take-nth 10 (reverse trained-mnist))))
;; @@
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;; <=

;; @@

;; @@