BSCDSCookbook.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Import necessary modules"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import string\n",
    "\n",
    "from HDVecSym import BSC #contains functions for MAP VSAs framework\n",
    "from HDVecSym import DS  #contains functions for representing data structures with VSAs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Basic set up "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Size of the item memory: (1000, 26)\n",
      "Content of the item memory:\n",
      "[array([[1, 1, 1, ..., 0, 0, 0],\n",
      "       [0, 0, 0, ..., 1, 1, 0],\n",
      "       [1, 0, 0, ..., 0, 1, 0],\n",
      "       ...,\n",
      "       [1, 1, 0, ..., 0, 0, 0],\n",
      "       [0, 0, 0, ..., 1, 1, 1],\n",
      "       [1, 0, 0, ..., 0, 0, 1]]), ['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r', 's', 't', 'u', 'v', 'w', 'x', 'y', 'z']]\n"
     ]
    }
   ],
   "source": [
    "N=1000 # dimensionality of HD vectors\n",
    "concepts=list(string.ascii_lowercase) # create the alphabet of lowercase letters\n",
    "itemMemory=BSC.item(concepts,  N=N) # create item memory for letters\n",
    "print(\"Size of the item memory:\",  itemMemory[0].shape)\n",
    "print(\"Content of the item memory:\")\n",
    "print(itemMemory)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Sets "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Similarity of the set to the codebook:\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "exSet=['a', 'b', 'c', 'd', 'e'] # set to represent\n",
    "HDset=DS.sethd(itemMemory, exSet, vsatype=\"BSC\", bundlingtype=\"majority\") # make representation\n",
    "\n",
    "#Calculate similarity between the representation of the set and the whole codebook\n",
    "similarity=BSC.similarity(itemMemory[0],HDset,stype=\"Hamming\")\n",
    "\n",
    "#Plot similarity\n",
    "plt.rcParams.update({'font.size': 22})\n",
    "plt.figure(figsize=(20,10))\n",
    "plt.stem(similarity, use_line_collection=True)\n",
    "plt.xticks([i for i in range(len(concepts))], concepts)  \n",
    "plt.grid()\n",
    "print(\"Similarity of the set to the codebook:\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Sequences "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bundling-based representation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Similarity of the fifth position in the sequence to the codebook:\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cosine similarity between replaced sequence and the sequence represented from the scratch: [[0.238]]\n"
     ]
    }
   ],
   "source": [
    "exSeq=['a', 'b', 'c', 'd', 'e'] # sequence to represent\n",
    "\n",
    "#\n",
    "HDseq_bundling=DS.sequence(itemMemory, exSeq, vsatype=\"BSC\", rerptype=\"bundling\", bundlingtype=\"majority\")\n",
    "\n",
    "#Calculate similarity between the representation of the sequence at 5th position and the whole codebook.\n",
    "#We expect to see similarity only to the fifth symbol in the sequence\n",
    "HDsymbol5=BSC.rotate(HDseq_bundling,rotateby=-4)\n",
    "similarity=BSC.similarity(itemMemory[0],HDsymbol5,stype=\"Hamming\")\n",
    "\n",
    "#Plot similarity\n",
    "plt.rcParams.update({'font.size': 22})\n",
    "plt.figure(figsize=(20,10))\n",
    "plt.stem(similarity, use_line_collection=True)\n",
    "plt.xticks([i for i in range(len(concepts))], concepts)  \n",
    "plt.grid()\n",
    "print(\"Similarity of the fifth position in the sequence to the codebook:\")\n",
    "plt.show()\n",
    "\n",
    "#Replacing \"e\" to \"z\" at 5th position in  the  sequence\n",
    "HDe=BSC.getitems(itemMemory, [\"e\"])\n",
    "HDz=BSC.getitems(itemMemory, [\"z\"])\n",
    "HDseq_replaced=HDseq_bundling - BSC.rotate(HDe[0],rotateby=4) + BSC.rotate(HDz[0],rotateby=4)\n",
    "\n",
    "#Calculate similarity between replaced sequence and the sequence represented from the scratch\n",
    "HDseq_scratch=DS.sequence(itemMemory, ['a', 'b', 'c', 'd', 'z'], vsatype=\"BSC\", rerptype=\"bundling\", bundlingtype=\"majority\")\n",
    "similarity=BSC.similarity(HDseq_replaced,HDseq_scratch,stype=\"Hamming\")\n",
    "print(\"Similarity between replaced sequence and the sequence represented from the scratch:\", similarity)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Shifting and concatenating two strings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Similarity of the fifth position in the shifted sequence to the codebook:\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cosine similarity between the concatenated sequence and the sequence represented from the scratch: [[0.257]]\n"
     ]
    }
   ],
   "source": [
    "HDseq_bundling_shifted=BSC.rotate(HDseq_bundling,rotateby=3) # shift the sequence by permutation\n",
    "\n",
    "#Calculate similarity between the representation of the shifted sequence at 5th position and the whole codebook.\n",
    "#We expect to see similarity only to the fifth symbol in the sequence\n",
    "HDsymbol5=BSC.rotate(HDseq_bundling_shifted,rotateby=-4)\n",
    "similarity=BSC.similarity(itemMemory[0],HDsymbol5,stype=\"Hamming\")\n",
    "\n",
    "#Plot similarity\n",
    "plt.rcParams.update({'font.size': 22})\n",
    "plt.figure(figsize=(20,10))\n",
    "plt.stem(similarity, use_line_collection=True)\n",
    "plt.xticks([i for i in range(len(concepts))], concepts)  \n",
    "plt.grid()\n",
    "print(\"Similarity of the fifth position in the shifted sequence to the codebook:\")\n",
    "plt.show()\n",
    "\n",
    "# Concatenation of two sequences\n",
    "exSeq2= ['x', 'y', 'z'] # the second sequence\n",
    "HDseq_bundling2=DS.sequence(itemMemory, exSeq2, vsatype=\"BSC\", rerptype=\"bundling\", bundlingtype=\"majority\")\n",
    "HDseq_bundling_concat=HDseq_bundling2 +  HDseq_bundling_shifted # concatenated sequence\n",
    "\n",
    "#Calculate similarity between concatenated sequence and the sequence represented from the scratch\n",
    "HDseq_scratch=DS.sequence(itemMemory, exSeq2 + exSeq, vsatype=\"BSC\", rerptype=\"bundling\", bundlingtype=\"majority\")\n",
    "similarity=BSC.similarity(HDseq_bundling_concat,HDseq_scratch,stype=\"Hamming\")\n",
    "print(\"Similarity between the concatenated sequence and the sequence represented from the scratch:\", similarity)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Binding-based representation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cosine similarity to another sequence, which differs in only one position: [[0.495]]\n",
      "Cosine similarity between replaced sequence and the sequence represented from the scratch: [[0.]]\n"
     ]
    }
   ],
   "source": [
    "exSeq=['a', 'b', 'c', 'd', 'e'] # sequence to represent\n",
    "HDseq_binding=DS.sequence(itemMemory, exSeq, vsatype=\"BSC\", rerptype=\"binding\")\n",
    "\n",
    "exSeq2=['a', 'b', 'c', 'd', 'd'] # very similar sequence \n",
    "HDseq_binding2=DS.sequence(itemMemory, exSeq2, vsatype=\"BSC\", rerptype=\"binding\")\n",
    "\n",
    "#Calculate similarity between very similar sequences\n",
    "similarity=BSC.similarity(HDseq_binding,HDseq_binding2,stype=\"Hamming\")\n",
    "print(\"Similarity to another sequence, which differs in only one position:\", similarity)\n",
    "\n",
    "#Replacing \"e\" to \"z\" at 5th position in  the  sequence\n",
    "HDe=BSC.getitems(itemMemory, [\"e\"])\n",
    "HDz=BSC.getitems(itemMemory, [\"z\"])\n",
    "HDseq_replaced=BSC.bind( BSC.unbind(HDseq_binding,BSC.rotate(HDe[0],rotateby=4)), BSC.rotate(HDz[0],rotateby=4)) \n",
    "\n",
    "#Calculate similarity between replaced sequence and the sequence represented from the scratch\n",
    "HDseq_scratch=DS.sequence(itemMemory, ['a', 'b', 'c', 'd', 'z'], vsatype=\"BSC\", rerptype=\"binding\")\n",
    "similarity=BSC.similarity(HDseq_replaced,HDseq_scratch,stype=\"Hamming\")\n",
    "print(\"Similarity between replaced sequence and the sequence represented from the scratch:\", similarity)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tuples "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cosine similarity between the composite representation and a tuple present in the representation: [[0.406]]\n",
      "Cosine similarity between the composite representation and a tuple not present in the representation: [[0.49]]\n"
     ]
    }
   ],
   "source": [
    "exSet1=['a', 'b', 'c', 'd', 'e'] # 1st set to represent\n",
    "exSet2=['x', 'y', 'z'] # 2nd set to represent\n",
    "HDset1=DS.sethd(itemMemory, exSet1, vsatype=\"BSC\", bundlingtype=\"majority\") # make representation\n",
    "HDset2=DS.sethd(itemMemory, exSet2, vsatype=\"BSC\", bundlingtype=\"majority\") # make representation\n",
    "HDtuples=BSC.bind( HDset1 , BSC.rotate(HDset2,rotateby=1)) # composite representation of all tuples \n",
    "\n",
    "#Calculate similarity between the representation of the tuples and some of the tuples\n",
    "tuple_pres=DS.sequence(itemMemory, ['a', 'x'], vsatype=\"BSC\", rerptype=\"binding\")\n",
    "similarity_pres=BSC.similarity(HDtuples,tuple_pres,stype=\"Hamming\")\n",
    "print(\"Similarity between the composite representation and a tuple present in the representation:\", similarity_pres)\n",
    "\n",
    "tuple_no_pres=DS.sequence(itemMemory, ['a', 'b'], vsatype=\"BSC\", rerptype=\"binding\")\n",
    "similarity_no_pres=BSC.similarity(HDtuples,tuple_no_pres,stype=\"Hamming\")\n",
    "print(\"Similarity between the composite representation and a tuple not present in the representation:\", similarity_no_pres)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Graphs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Undirected graphs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Similarity of the vertices connected to 'a' in the graph to the codebook:\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "edges=[(\"a\",\"b\"),(\"a\",\"e\"),(\"c\",\"b\"),(\"d\",\"c\"),(\"e\",\"d\")] # edges of the graph to be represented\n",
    "\n",
    "HDundir=DS.graph(itemMemory, edges, vsatype=\"BSC\", graphtype=\"undirected\", bundlingtype=\"majority\") # make representation\n",
    "#print(HDundir)\n",
    "#Check verteces connected to \"a\"\n",
    "HDa=BSC.getitems(itemMemory, [\"a\"])\n",
    "approx_verteces=BSC.unbind(HDundir,HDa[0])\n",
    "\n",
    "#We expect to see similarity only to \"b\" and \"e\" symbols \n",
    "similarity=BSC.similarity(itemMemory[0],approx_verteces,stype=\"Hamming\")\n",
    "\n",
    "#Plot similarity\n",
    "plt.rcParams.update({'font.size': 22})\n",
    "plt.figure(figsize=(20,10))\n",
    "plt.stem(similarity, use_line_collection=True)\n",
    "plt.xticks([i for i in range(len(concepts))], concepts)  \n",
    "plt.grid()\n",
    "print(\"Similarity of the vertices connected to 'a' in the graph to the codebook:\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Directed graphs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Similarity of the outgoing connections from 'a' to the codebook:\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Similarity of the incoming connections to 'b' to the codebook:\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "edges=[(\"a\",\"b\"),(\"a\",\"e\"),(\"c\",\"b\"),(\"d\",\"c\"),(\"e\",\"d\")] # edges of the graph to be represented\n",
    "\n",
    "HDundir=DS.graph(itemMemory, edges, vsatype=\"BSC\", graphtype=\"directed\", bundlingtype=\"majority\") # make representation\n",
    "\n",
    "#Check outgoing connections from \"a\"\n",
    "HDa=BSC.getitems(itemMemory, [\"a\"])\n",
    "approx_outgoing=BSC.rotate( BSC.unbind(HDundir,HDa[0]),  rotateby=-1)\n",
    "\n",
    "#We expect to see high similarity only to \"b\" and \"e\" symbols \n",
    "similarity=BSC.similarity(itemMemory[0],approx_outgoing,stype=\"Hamming\")\n",
    "\n",
    "#Plot similarity\n",
    "plt.rcParams.update({'font.size': 22})\n",
    "plt.figure(figsize=(20,10))\n",
    "plt.stem(similarity, use_line_collection=True)\n",
    "plt.xticks([i for i in range(len(concepts))], concepts)  \n",
    "plt.grid()\n",
    "print(\"Similarity of the outgoing connections from 'a' to the codebook:\")\n",
    "plt.show()\n",
    "\n",
    "#Check incoming connections to \"b\"\n",
    "HDb=BSC.getitems(itemMemory, [\"b\"])\n",
    "approx_incoming=BSC.unbind(HDundir, BSC.rotate( HDb[0], rotateby=1) )  \n",
    "\n",
    "#We expect to see high similarity only to \"a\" and \"c\" symbols \n",
    "similarity=BSC.similarity(itemMemory[0],approx_incoming,stype=\"Hamming\")\n",
    "\n",
    "#Plot similarity\n",
    "plt.rcParams.update({'font.size': 22})\n",
    "plt.figure(figsize=(20,10))\n",
    "plt.stem(similarity, use_line_collection=True)\n",
    "plt.xticks([i for i in range(len(concepts))], concepts)  \n",
    "plt.grid()\n",
    "print(\"Similarity of the incoming connections to 'b' to the codebook:\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Binary trees"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Similarity of the symbol at path ['r','r','l'] to the codebook:\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cosine similarity to the correct path: [[0.352]]\n",
      "Cosine similarity to the wrong path: [[0.522]]\n"
     ]
    }
   ],
   "source": [
    "#Tree to be represented\n",
    "treelist=[[\"a\",[\"l\",\"l\",\"l\"]], [\"b\",[\"l\",\"r\",\"l\"]], [\"c\",[\"r\",\"r\",\"l\"]], [\"d\",[\"r\",\"r\",\"r\",\"l\"]], [\"e\",[\"r\",\"r\",\"r\",\"r\"]], [\"f\",[\"l\",\"r\",\"r\",\"l\",\"l\"]], [\"g\",[\"l\",\"r\",\"r\",\"l\",\"r\"]]]\n",
    "\n",
    "itemroles=BSC.item([\"l\",\"r\"],  N) # Item memory for roles\n",
    " \n",
    "HDtree=DS.tree(itemroles, itemMemory, treelist, vsatype=\"BSC\", bundlingtype=\"majority\") # make representation\n",
    "\n",
    "# Check symbol at path [\"r\",\"r\",\"l\"]\n",
    "HDpath=DS.sequence(itemroles, treelist[2][1], vsatype=\"BSC\", rerptype=\"binding\") # HD vector for [\"r\",\"r\",\"l\"]\n",
    "HDapprox=BSC.unbind(HDtree,HDpath) # Get approximate representation for the sybmol at [\"r\",\"r\",\"l\"]\n",
    "\n",
    "#Calculate similarity between the approximate representation of the set and the whole codebook\n",
    "similarity=BSC.similarity(itemMemory[0],HDapprox,stype=\"Hamming\")\n",
    "\n",
    "#Plot similarity\n",
    "plt.rcParams.update({'font.size': 22})\n",
    "plt.figure(figsize=(20,10))\n",
    "plt.stem(similarity, use_line_collection=True)\n",
    "plt.xticks([i for i in range(len(concepts))], concepts)  \n",
    "plt.grid()\n",
    "print(\"Similarity of the symbol at path ['r','r','l'] to the codebook:\")\n",
    "plt.show()\n",
    "\n",
    "# Check path of symbol \"c\"\n",
    "HDc=BSC.getitems(itemMemory, [\"c\"]) # HD vector for \"c\"\n",
    "HDapprox=BSC.unbind(HDtree,HDc[0]) # Get approximate representation of the path for sybmol \"c\"\n",
    "\n",
    "#Calculate similarity to the correct path\n",
    "similarity_cor=BSC.similarity(HDpath,HDapprox,stype=\"Hamming\")\n",
    "print(\"Similarity to the correct path:\", similarity_cor)\n",
    "\n",
    "#Calculate similarity to the wrong path\n",
    "HDpath_wrong=DS.sequence(itemroles, treelist[0][1], vsatype=\"BSC\", rerptype=\"binding\") # HD vector for [\"r\",\"r\",\"l\"]\n",
    "similarity_wrong=BSC.similarity(HDpath_wrong,HDapprox,stype=\"Hamming\")\n",
    "print(\"Similarity to the wrong path:\", similarity_wrong)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Frequency distributions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Simality of the representation of the frequency distribution to the codebook:\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# distribution to represent\n",
    "conc=['a', 'b', 'c'] \n",
    "frequency=[3,2,1]\n",
    "HDfreq=DS.frequency(itemMemory, conc, frequency, vsatype=\"BSC\", bundlingtype=\"majority\") # make representation\n",
    "\n",
    "#Calculate similarity between the representation of the frequency distribution and the whole codebook\n",
    "similarity=BSC.similarity(itemMemory[0],HDfreq,stype=\"Hamming\")\n",
    "\n",
    "#Plot similarity\n",
    "plt.rcParams.update({'font.size': 22})\n",
    "plt.figure(figsize=(20,10))\n",
    "plt.stem(similarity, use_line_collection=True)\n",
    "plt.xticks([i for i in range(len(concepts))], concepts)  \n",
    "plt.grid()\n",
    "print(\"Simality of the representation of the frequency distribution to the codebook:\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# n-gram statistics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['h', 'e', 'l', 'l', 'o', 'w', 'o', 'r', 'l', 'd']\n",
      "Cosine similarity to very similar data: [[0.003]]\n",
      "Cosine similarity to rather different data: [[0.002]]\n",
      "Cosine similarity to n-gram 'ell' present in data: [[0.48]]\n",
      "Cosine similarity to n-gram 'abc' not present in data: [[0.512]]\n"
     ]
    }
   ],
   "source": [
    "data=list(\"helloworld\") # data to represent\n",
    "n=3 # size of n-gram\n",
    "HDgram=DS.ngram(itemMemory, data, n, vsatype=\"BSC\", bundlingtype=\"majority\") # make representation\n",
    "print(data)\n",
    "\n",
    "#Calculate similarity to very similar data\n",
    "data2=list(\"felloworld\") # data to represent\n",
    "HDgram2=DS.ngram(itemMemory, data2, n, vsatype=\"BSC\", bundlingtype=\"majority\") # make representation\n",
    "similarity=BSC.similarity(HDgram,HDgram2,stype=\"Hamming\")\n",
    "print(\"Cosine similarity to very similar data:\", similarity)\n",
    "\n",
    "#Calculate similarity to rather different data\n",
    "data2=list(\"hejvarlden\") # data to represent\n",
    "HDgram2=DS.ngram(itemMemory, data2, n, vsatype=\"BSC\", bundlingtype=\"majority\") # make representation\n",
    "similarity=BSC.similarity(HDgram,HDgram2,stype=\"Hamming\")\n",
    "print(\"Cosine similarity to rather different data:\", similarity)\n",
    "\n",
    "#Calculate similarity to n-gram present in data\n",
    "HDgram2=DS.ngram(itemMemory, list(\"ell\"), n, vsatype=\"BSC\", bundlingtype=\"majority\") # make representation\n",
    "similarity=BSC.similarity(HDgram,HDgram2,stype=\"Hamming\")\n",
    "print(\" similarity to n-gram 'ell' present in data:\", similarity)\n",
    "\n",
    "#Calculate similarity to n-gram not present in data\n",
    "HDgram2=DS.ngram(itemMemory, list(\"abc\"), n, vsatype=\"BSC\", bundlingtype=\"majority\") # make representation\n",
    "similarity=BSC.similarity(HDgram,HDgram2,stype=\"Hamming\")\n",
    "print(\"Similarity to n-gram 'abc' not present in data:\", similarity)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Stacks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cosine similarity between the representation of the stack and the codebook:\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cosine similarity between the representation of the stack and the codebook after adding 'a':\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Identified symbol to pop: g\n",
      "Cosine similarity between the manipulated stack and the initial one: [[0.365]]\n"
     ]
    }
   ],
   "source": [
    "exStack=['b', 'c', 'd'] # current stack to represent\n",
    "\n",
    "\n",
    "HDstack=DS.sequence(itemMemory, exStack, vsatype=\"BSC\", rerptype=\"bundling\", bundlingtype=\"majority\") # make representation\n",
    "\n",
    "#Calculate cosine similarity between the top most symbol in the stack and the whole codebook\n",
    "similarity=BSC.similarity(itemMemory[0],HDstack,stype=\"Hamming\")\n",
    "\n",
    "#Plot similarity\n",
    "plt.rcParams.update({'font.size': 22})\n",
    "plt.figure(figsize=(20,10))\n",
    "plt.stem(similarity, use_line_collection=True)\n",
    "plt.xticks([i for i in range(len(concepts))], concepts)  \n",
    "plt.grid()\n",
    "print(\"Cosine similarity between the representation of the stack and the codebook:\")\n",
    "plt.show()\n",
    "\n",
    "\n",
    "#Add \"a\" to the stack\n",
    "HDa=BSC.getitems(itemMemory, [\"a\"]) # HD vector for \"c\"\n",
    "HDstack_w_a= HDa[0] + BSC.rotate(HDstack,rotateby=1)\n",
    "\n",
    "#Calculate cosine similarity between the top most symbol in the stack and the whole codebook after adding 'a'\n",
    "similarity=BSC.similarity(itemMemory[0],HDstack_w_a,stype=\"Hamming\")\n",
    "\n",
    "#Plot similarity\n",
    "plt.rcParams.update({'font.size': 22})\n",
    "plt.figure(figsize=(20,10))\n",
    "plt.stem(similarity, use_line_collection=True)\n",
    "plt.xticks([i for i in range(len(concepts))], concepts)  \n",
    "plt.grid()\n",
    "print(\"Cosine similarity between the representation of the stack and the codebook after adding 'a':\")\n",
    "plt.show()\n",
    "\n",
    "#Pop \"a\" from the stack\n",
    "#Step 1: identify the topmost symbol \n",
    "HDpop=BSC.probe(itemMemory, HDstack_w_a, searchtype=\"nearest\", simtype=\"dot\")\n",
    "print(\"Identified symbol to pop:\", HDpop[1])\n",
    "\n",
    "#Step 2 remove the topmost symbol \n",
    "HDstack_w_a=BSC.rotate(HDstack_w_a-HDpop[0],rotateby=-1)\n",
    "\n",
    "#Calculate cosine similarity between the manipulated stack and the initial one\n",
    "similarity=BSC.similarity(HDstack,HDstack_w_a,stype=\"Hamming\")\n",
    "print(\"Cosine similarity between the manipulated stack and the initial one:\", similarity)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Finite State Automata"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Identified next state: L\n",
      "Identified next state: U\n"
     ]
    }
   ],
   "source": [
    "transitions=[[\"L\",\"L\",\"P\"],[\"L\",\"U\",\"T\"],[\"U\",\"U\",\"T\"],[\"U\",\"L\",\"P\"]] # transition of the automaton\n",
    "itemmemstates=BSC.item([\"L\",\"U\"],  N) # Item memory for states\n",
    "itemmeminput=BSC.item([\"P\",\"T\"],  N) # Item memory for input symbols\n",
    "\n",
    "HDfsa=DS.fsa(itemmemstates, itemmeminput, transitions, vsatype=\"BSC\", bundlingtype=\"majority\") # make representation\n",
    "    \n",
    "# Query automaton: Example 1\n",
    "HDL=BSC.getitems(itemmemstates, [\"L\"]) # HD vector for state \"Lock\"\n",
    "HDP=BSC.getitems(itemmeminput, [\"P\"]) # HD vector for input \"Push\"\n",
    "\n",
    "#Perform query \n",
    "HDapprox= BSC.rotate( BSC.unbind(BSC.unbind(HDfsa, HDP[0]), HDL[0] )      ,rotateby=-1) # approximate representation of the next state    \n",
    "\n",
    "#Item memory search    \n",
    "HDnextState=BSC.probe(itemmemstates, HDapprox, searchtype=\"nearest\", simtype=\"Hamming\")\n",
    "print(\"Identified next state:\", HDnextState[1])    \n",
    "\n",
    "# Query automaton: Example 2\n",
    "HDT=BSC.getitems(itemmeminput, [\"T\"]) # HD vector for state \"Lock\"\n",
    "\n",
    "#Perform query \n",
    "HDapprox= BSC.rotate( BSC.unbind(BSC.unbind(HDfsa, HDT[0]), HDL[0] )      ,rotateby=-1) # approximate representation of the next state    \n",
    "\n",
    "#Item memory search    \n",
    "HDnextState=BSC.probe(itemmemstates, HDapprox, searchtype=\"nearest\", simtype=\"Hamming\")\n",
    "print(\"Identified next state:\", HDnextState[1])    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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