{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "2cbbd778",
   "metadata": {},
   "source": [
    "# Hidden Markov Model analysis of mouse behavioural syntax\n",
    "\n",
    "In this example, we fit and apply a Hidden Markov Model (HMM) to infer behavioural syllables from pre-processed mouse tracking data.\n",
    "\n",
    "The [sample dataset](../../downloads/hmm_example_mouse_pos.pkl) is a two-hour snippet of a single mouse in a foraging assay. \n",
    "The mouse was tracked using [SLEAP](sleap:) with key body parts annotated as follows:\n",
    "\n",
    ":::{image} ../../images/hmm-example-mouse-body-parts.png\n",
    ":alt: Mouse body part annotations\n",
    ":width: 50%\n",
    ":align: center\n",
    ":::\n",
    "\n",
    "The data includes:\n",
    "- raw centroid positions (`x`, `y`)\n",
    "- Kalman-filtered estimates of centroid positions, speed, and acceleration (`smoothed_x`, `smoothed_y`, `smoothed_speed`, `smoothed_acceleration`)\n",
    "- pairwise distances between key body parts (`head-spine3`, `left_ear-spine3`, `right_ear-spine3`, `spine1-spine3`)\n",
    "\n",
    "These pairwise distances were selected based on their contribution to overall variance in body shape (i.e. length and curvature), as determined by applying Singular Value Decomposition (SVD) to a standardised distance matrix. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3389234a",
   "metadata": {},
   "source": [
    "## Set up environment\n",
    "\n",
    "Create and activate a virtual environment named `hmm-example` using [uv](https://docs.astral.sh/uv/getting-started/installation/).\n",
    "```bash\n",
    "uv venv hmm-example --python \">=3.11\" \n",
    "source hmm-example/bin/activate   \n",
    "```\n",
    "\n",
    "Install the required [`ssm` package](https://github.com/lindermanlab/ssm) and its dependencies.\n",
    "```bash\n",
    "uv pip install setuptools wheel numpy cython && uv pip install --no-build-isolation \"git+https://github.com/lindermanlab/ssm#egg=ssm[plotting]\"\n",
    "```\n",
    "\n",
    "## Import libraries and define helper class"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7ac920ac",
   "metadata": {},
   "outputs": [],
   "source": [
    "import autograd.numpy as np\n",
    "import autograd.numpy.random as npr\n",
    "\n",
    "npr.seed(42)\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import pickle\n",
    "\n",
    "import seaborn as sns\n",
    "\n",
    "import ssm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "dd87407b",
   "metadata": {},
   "outputs": [],
   "source": [
    "class AeonHMM:\n",
    "    \"\"\"A class for training and analysing Hidden Markov Models (HMM) using the `ssm` library.\"\"\"\n",
    "\n",
    "    def __init__(self, n_state):\n",
    "        \"\"\"Initialise AeonHMM with the number of hidden states.\"\"\"\n",
    "        self.n_state = n_state  # Number of hidden states\n",
    "        self.features = [\n",
    "            \"smoothed_speed\",\n",
    "            \"smoothed_acceleration\",\n",
    "            \"head-spine3\",\n",
    "            \"left_ear-spine3\",\n",
    "            \"right_ear-spine3\",\n",
    "            \"spine1-spine3\",\n",
    "        ]  # Expected features in the input data\n",
    "        self.model = None  # HMM model instance\n",
    "        self.parameters = None  # Sorted model parameters (mean, variance, covariance)\n",
    "        self.transition_mat = None  # Sorted transition matrix\n",
    "        self.states = None  # Inferred states\n",
    "        self.connectivity_mat = None  # Connectivity matrix\n",
    "        self.test_lls = None  # Log-likelihoods of the test data\n",
    "        self.train_lls = None  # Log-likelihoods of the training data\n",
    "\n",
    "    def get_connectivity_matrix(self):\n",
    "        \"\"\"Compute the normalised connectivity matrix from the inferred states.\"\"\"\n",
    "        connectivity_mat = np.zeros((self.n_state, self.n_state))\n",
    "        states = self.states\n",
    "        # Count transitions between states\n",
    "        for i in range(len(states) - 1):\n",
    "            if states[i + 1] != states[i]:\n",
    "                connectivity_mat[states[i]][states[i + 1]] += 1\n",
    "        # Normalise to sum to 1\n",
    "        for i in range(self.n_state):\n",
    "            total = np.sum(connectivity_mat[i])\n",
    "            if total > 0:\n",
    "                connectivity_mat[i] /= total\n",
    "\n",
    "        return connectivity_mat\n",
    "\n",
    "    def fit_model(self, train_data, num_iters=50):\n",
    "        \"\"\"Fit the HMM model to the training data using the EM algorithm.\"\"\"\n",
    "        fitting_input = np.array(train_data)\n",
    "        self.model = ssm.HMM(\n",
    "            self.n_state, len(fitting_input[0]), observations=\"gaussian\"\n",
    "        )\n",
    "        lls = self.model.fit(\n",
    "            fitting_input, method=\"em\", num_iters=num_iters, init_method=\"kmeans\"\n",
    "        )\n",
    "        self.train_lls = lls\n",
    "\n",
    "    def infer_states(self, test_data):\n",
    "        \"\"\"Infer states for the test data.\"\"\"\n",
    "        obs = np.array(test_data)\n",
    "        self.test_lls = self.model.log_likelihood(obs)\n",
    "        self.states = self.model.most_likely_states(obs)\n",
    "\n",
    "    def sort(self, sort_idx):\n",
    "        \"\"\"Sort the model parameters, transition matrix, and inferred states based on the provided indices.\"\"\"\n",
    "        # Sort Gaussian means: shape (n_features, n_state)\n",
    "        parameters_mean_sorted = self.model.observations.params[0][sort_idx].T\n",
    "        # Extract and sort variances: shape (n_features, n_state)\n",
    "        parameters_var = np.zeros((self.n_state, len(self.features)))\n",
    "        for i in range(self.n_state):\n",
    "            for j in range(len(self.features)):\n",
    "                # state i, feature j\n",
    "                parameters_var[i, j] = self.model.observations.params[1][i][j][j]\n",
    "        parameters_var_sorted = parameters_var[sort_idx].T\n",
    "        # Sort covariance matrices: shape (n_state, n_features, n_features)\n",
    "        parameters_covar_sorted = self.model.observations.params[1][sort_idx]\n",
    "        self.parameters = [\n",
    "            parameters_mean_sorted,\n",
    "            parameters_var_sorted,\n",
    "            parameters_covar_sorted,\n",
    "        ]\n",
    "        # Sort transition matrix: shape (n_state, n_state)\n",
    "        self.transition_mat = (\n",
    "            self.model.transitions.transition_matrix[sort_idx].T[sort_idx].T\n",
    "        )\n",
    "        # Compute connectivity matrix\n",
    "        self.connectivity_mat = self.get_connectivity_matrix()\n",
    "        # Reassign state labels to reflect new order\n",
    "        new_values = np.empty_like(self.states)\n",
    "        for i, val in enumerate(sort_idx):\n",
    "            new_values[self.states == val] = i\n",
    "        self.states = new_values"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e3ab438d",
   "metadata": {},
   "source": [
    "## Load sample data\n",
    "The sample dataset can be downloaded [here](../../downloads/hmm_example_mouse_pos.pkl). \n",
    "Please change the value of `file_path` to the location where you saved the file."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "id": "bc7c1d0d",
   "metadata": {},
   "outputs": [],
   "source": [
    "file_path = \"/path/to/hmm_example_mouse_pos.pkl\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "a1faf0c5",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>smoothed_speed</th>\n",
       "      <th>smoothed_acceleration</th>\n",
       "      <th>head-spine3</th>\n",
       "      <th>spine1-spine3</th>\n",
       "      <th>left_ear-spine3</th>\n",
       "      <th>right_ear-spine3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2024-02-01 07:00:00.080</th>\n",
       "      <td>6.765046</td>\n",
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       "      <th>2024-02-01 07:00:00.180</th>\n",
       "      <td>8.032855</td>\n",
       "      <td>13.389354</td>\n",
       "      <td>17.269546</td>\n",
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       "    <tr>\n",
       "      <th>2024-02-01 07:00:00.280</th>\n",
       "      <td>8.410684</td>\n",
       "      <td>7.612856</td>\n",
       "      <td>18.342884</td>\n",
       "      <td>12.943109</td>\n",
       "      <td>18.868068</td>\n",
       "      <td>15.568200</td>\n",
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       "    <tr>\n",
       "      <th>2024-02-01 07:00:00.380</th>\n",
       "      <td>7.863123</td>\n",
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       "      <td>18.010769</td>\n",
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       "      <td>18.209636</td>\n",
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       "    <tr>\n",
       "      <th>2024-02-01 07:00:00.480</th>\n",
       "      <td>6.422148</td>\n",
       "      <td>15.558013</td>\n",
       "      <td>18.457386</td>\n",
       "      <td>12.783098</td>\n",
       "      <td>18.527658</td>\n",
       "      <td>15.594391</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      ],
      "text/plain": [
       "                         smoothed_speed  smoothed_acceleration  head-spine3  \\\n",
       "2024-02-01 07:00:00.080        6.765046              19.325969    17.767353   \n",
       "2024-02-01 07:00:00.180        8.032855              13.389354    17.269546   \n",
       "2024-02-01 07:00:00.280        8.410684               7.612856    18.342884   \n",
       "2024-02-01 07:00:00.380        7.863123               9.032341    18.010769   \n",
       "2024-02-01 07:00:00.480        6.422148              15.558013    18.457386   \n",
       "\n",
       "                         spine1-spine3  left_ear-spine3  right_ear-spine3  \n",
       "2024-02-01 07:00:00.080      12.744590        17.301722         15.257318  \n",
       "2024-02-01 07:00:00.180      12.521794        18.267784         15.036750  \n",
       "2024-02-01 07:00:00.280      12.943109        18.868068         15.568200  \n",
       "2024-02-01 07:00:00.380      12.811849        18.209636         14.367178  \n",
       "2024-02-01 07:00:00.480      12.783098        18.527658         15.594391  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "with open(file_path, \"rb\") as file:\n",
    "    mouse_pos = pickle.load(file)\n",
    "\n",
    "# Select only the required features for the HMM\n",
    "mouse_pos = mouse_pos[\n",
    "    [\n",
    "        \"smoothed_speed\",\n",
    "        \"smoothed_acceleration\",\n",
    "        \"head-spine3\",\n",
    "        \"spine1-spine3\",\n",
    "        \"left_ear-spine3\",\n",
    "        \"right_ear-spine3\",\n",
    "    ]\n",
    "]\n",
    "mouse_pos.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e8c63cf5",
   "metadata": {},
   "source": [
    "## Training and inference\n",
    "\n",
    "In this two-hour example, we use the data in the first hour to train the model, \n",
    "and use the model to infer the hidden states of the mouse in the second hour."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "aa6475e4",
   "metadata": {},
   "outputs": [],
   "source": [
    "start = mouse_pos.index[0]\n",
    "train_mouse_pos = mouse_pos[start : start + pd.Timedelta(\"1h\")]\n",
    "test_mouse_pos = mouse_pos[start + pd.Timedelta(\"1h\") : start + pd.Timedelta(\"2h\")]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c72d31a6",
   "metadata": {},
   "source": [
    "We initialise the model with 10 hidden states and train it using the Expectation-Maximisation (EM) algorithm over 50 iterations on the 6 selected features:\n",
    "- smoothed centroid speed,\n",
    "- smoothed acceleration\n",
    "- distance between `head` and `spine3`\n",
    "- distance between `spine1` and `spine3`\n",
    "- distance between `left_ear` and `spine3`\n",
    "- distance between `right_ear` and `spine3`\n",
    "\n",
    "We then use the trained model to infer the hidden states of the mouse in the test data (the second hour)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "04dcbe11",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "955f0f87cec448239da3586322734a4a",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/50 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mouse_hmm = AeonHMM(n_state=10)\n",
    "mouse_hmm.fit_model(train_mouse_pos)  # Set `num_iters` as needed\n",
    "mouse_hmm.infer_states(test_mouse_pos)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7e129c45",
   "metadata": {},
   "source": [
    "## Parameter sorting\n",
    "\n",
    "To make it easier to interpret the model, we can sort the inferred states by the mean centroid speed (`smoothed_speed`) in ascending order.\n",
    "The model parameters, transition matrix, and inferred states can then be reordered using `AeonHmm.sort()`, such that state 0 corresponds to the slowest, state 1 to the next slowest, and so on."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a4d46642",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8ee10860",
   "metadata": {},
   "outputs": [],
   "source": [
    "state_mean_speed = mouse_hmm.model.observations.params[0].T[0]\n",
    "sort_idx = np.argsort(state_mean_speed, -1)\n",
    "mouse_hmm.sort(sort_idx)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "06f54557",
   "metadata": {},
   "source": [
    "## Visualise inferred states\n",
    "\n",
    "Below we colour-code the inferred states and plot these over time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "91a8820c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1400x300 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(14, 3))\n",
    "# Plot the state color bars\n",
    "states_colored = mouse_hmm.states.reshape(1, -1)\n",
    "im = ax.imshow(\n",
    "    states_colored,\n",
    "    aspect=\"auto\",\n",
    "    vmin=0,\n",
    "    vmax=mouse_hmm.n_state - 1,\n",
    "    extent=[0, len(mouse_hmm.states), 0, 0.2],\n",
    ")\n",
    "ax.set_xlim(0, len(mouse_hmm.states))\n",
    "ax.set_yticks([])\n",
    "ax.set_xlabel(\"Time (frame index)\")\n",
    "ax.set_title(\"Hidden states over time\")\n",
    "# Add colorbar with state labels\n",
    "cbar = plt.colorbar(im, ax=ax, orientation=\"horizontal\", pad=0.2, shrink=0.8)\n",
    "cbar.set_label(\"State\")\n",
    "cbar.set_ticks(range(mouse_hmm.n_state))\n",
    "cbar.set_ticklabels([f\"$S_{i + 1}$\" for i in range(mouse_hmm.n_state)])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "89a9c939",
   "metadata": {},
   "source": [
    "We can also visualise how key behavioural features differ across the 10 hidden states by plotting the mean and 95% confidence interval for each state, as estimated from the training data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "id": "6e390478",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x1200 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Define feature labels\n",
    "features = [\"Speed (m/s)\", \"Acceleration (m/s$^2$)\", \"Body length (mm)\"]\n",
    "scale = 2e-3  # Scale for speed and acceleration\n",
    "n_features = len(features)\n",
    "n_state = mouse_hmm.n_state\n",
    "params = mouse_hmm.parameters\n",
    "fig, axs = plt.subplots(n_features, 1, figsize=(6, 12))\n",
    "for i in range(n_features):\n",
    "    if i > 1:\n",
    "        scale = 2  # Body length is in mm, no scaling needed\n",
    "    axs[i].bar(\n",
    "        range(n_state),\n",
    "        params[0][i] * scale,\n",
    "        yerr=1.65 * (params[1][i] ** 0.5) * scale,  # 95% CI = ±1.65*std\n",
    "        capsize=8,  # Size of error bar caps\n",
    "    )\n",
    "    axs[i].set_xticks(range(0, n_state), [str(j + 1) for j in range(n_state)])\n",
    "    axs[i].set_ylabel(features[i])\n",
    "axs[2].set_xlabel(\"State\")\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "092d7828",
   "metadata": {},
   "source": [
    "The transition matrix can be visualised as a heatmap, where the diagonal entries indicate the probability of remaining in the same state, while off-diagonal entries represent transitions between different states."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "id": "34a9180a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "matrix = mouse_hmm.transition_mat\n",
    "annot_array = np.array([[round(item, 3) for item in row] for row in matrix])\n",
    "labels = [\"$S_{\" + str(i + 1) + \"}$\" for i in range(len(matrix))]\n",
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "sns.heatmap(\n",
    "    matrix,\n",
    "    cmap=\"RdBu\",\n",
    "    ax=ax,\n",
    "    square=\"True\",\n",
    "    cbar=True,\n",
    "    annot=annot_array,\n",
    ")\n",
    "ax.set_title(\"Transition Matrix\")\n",
    "ax.set_xticklabels(labels)\n",
    "ax.set_yticklabels(labels, rotation=0)\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
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