{"id":3695,"date":"2025-05-09T07:02:24","date_gmt":"2025-05-09T07:02:24","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/05\/09\/clustering-eating-behaviors-in-time-a-machine-learning-approach-to-preventive-health\/"},"modified":"2025-05-09T07:02:24","modified_gmt":"2025-05-09T07:02:24","slug":"clustering-eating-behaviors-in-time-a-machine-learning-approach-to-preventive-health","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/05\/09\/clustering-eating-behaviors-in-time-a-machine-learning-approach-to-preventive-health\/","title":{"rendered":"Clustering Eating Behaviors in Time: A Machine Learning Approach to Preventive Health"},"content":{"rendered":"

Clustering Eating Behaviors in Time: A Machine Learning Approach to Preventive Health
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It\u2019s well known<\/mdspan> that\u00a0what<\/em>\u00a0we eat matters \u2014 but what if\u00a0when<\/em>\u00a0and\u00a0how often<\/em>\u00a0we eat matters just as much?<\/p>\n

In the midst of ongoing scientific debate around the benefits of\u00a0intermittent fasting<\/strong>, this question becomes even more intriguing. As someone passionate about machine learning and healthy living, I was inspired by a 2017 research paper[1] exploring this intersection. The authors introduced a novel distance metric called\u00a0Modified Dynamic Time Warping (MDTW)<\/strong>\u00a0\u2014 a technique designed to account not only for the nutritional content of meals but also their\u00a0timing<\/strong>\u00a0throughout the day.<\/p>\n

Motivated by their work[1], I built a full implementation of MDTW from scratch using Python. I applied it to cluster simulated individuals into\u00a0temporal dietary patterns<\/strong>, uncovering distinct behaviors like skippers, snackers, and night eaters.<\/p>\n

While MDTW may sound like a niche metric, it fills a critical gap in time-series comparison. Traditional distance measures \u2014 such as Euclidean distance or even classical Dynamic Time Warping (DTW) \u2014 struggle when applied to dietary data. People don\u2019t eat at fixed times or with consistent frequency. They skip meals, snack irregularly, or eat late at night.<\/p>\n

MDTW is designed for exactly this kind of temporal misalignment and behavioral variability.<\/strong>\u00a0By allowing flexible alignment while penalizing mismatches in both nutrient content and meal timing, MDTW reveals subtle but meaningful differences in how people eat.<\/p>\n

What this article covers:<\/h2>\n
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  1. \nMathematical foundation of MDTW<\/strong>\u00a0\u2014 explained intuitively.<\/li>\n
  2. \nFrom formula to code<\/strong>\u00a0\u2014 implementing MDTW in Python with dynamic programming.<\/li>\n
  3. \nGenerating synthetic dietary data<\/strong>\u00a0to simulate real-world eating behavior.<\/li>\n
  4. \nBuilding a distance matrix<\/strong>\u00a0between individual eating records.<\/li>\n
  5. \nClustering individuals<\/strong>\u00a0with K-Medoids and evaluating with silhouette and elbow methods.<\/li>\n
  6. \nVisualizing clusters<\/strong>\u00a0as scatter plots and joint distributions.<\/li>\n
  7. \nInterpreting temporal patterns<\/strong>\u00a0from clusters: who eats when and how much?<\/li>\n<\/ol>\n

    Quick Note on Classical Dynamic Time Warping (DTW)<\/h2>\n

    Dynamic Time Warping (DTW) is a classic algorithm used to measure similarity between two sequences that may vary in length or timing. It\u2019s widely used in speech recognition, gesture analysis, and time series alignment. Let\u2019s see a very simple example of the Sequence A is aligned to Sequence B (shifted version of B) with using traditional dynamic time warping algorithm using\u00a0fastdtw<\/em>\u00a0library. As input, we give a distance metric as Euclidean. Also, we put time series to calculate the distance between these time series and optimized aligned path.<\/p>\n

    import numpy as np\nimport matplotlib.pyplot as plt\nfrom fastdtw import fastdtw\nfrom scipy.spatial.distance import euclidean\n# Sample sequences (scalar values)\nx = np.linspace(0, 3 * np.pi, 30)\ny1 = np.sin(x)\ny2 = np.sin(x+0.5)  # Shifted version\n# Convert scalars to vectors (1D)\ny1_vectors = [[v] for v in y1]\ny2_vectors = [[v] for v in y2]\n# Use absolute distance for scalars\ndistance, path = fastdtw(y1_vectors, y2_vectors, dist=euclidean)\n#or for scalar \n# distance, path = fastdtw(y1, y2, dist=lambda x, y: np.abs(x-y))\n\ndistance, path = fastdtw(y1, y2,dist=lambda x, y: np.abs(x-y))\n# Plot the alignment\nplt.figure(figsize=(10, 4))\nplt.plot(y1, label='Sequence A (slow)')\nplt.plot(y2, label='Sequence B (shifted)')\n\n# Draw alignment lines\nfor (i, j) in path:\n    plt.plot([i, j], [y1[i], y2[j]], color='gray', linewidth=0.5)\n\nplt.title(f'Dynamic Time Warping Alignment (Distance = {distance:.2f})')\nplt.xlabel('Time Index')\nplt.legend()\nplt.tight_layout()\nplt.savefig('dtw_alignment.png')\nplt.show()\n<\/code><\/pre>\n
    \"\"
    Illustration of the application of dynamic time warping to two time series (Image by author)<\/figcaption><\/figure>\n
    The path returned by fastdtw<\/code> (or any DTW algorithm) is a sequence of index pairs (i, j)<\/code> that represent the optimal alignment between two time series. Each pair indicates that element A[i]<\/code> is matched with B[j]<\/code>. By summing the distances between all these matched pairs, the algorithm computes the optimized cumulative cost<\/strong>\u200a\u2014\u200athe minimum total distance required to warp one sequence to the other.<\/p>\n
    \"\"<\/figure>\n
    Modified Dynamic\u00a0Warping<\/h3>\n
    The key challenge when applying dynamic time warping (DTW)<\/strong> to dietary data<\/strong> (vs. simple examples like sine waves or fixed-length sequences) lies in the complexity and variability<\/strong> of real-world eating behaviors. Some challenges and the proposed solution in the paper[1] as a response to each challenge are as follows:<\/p>\n
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    1. Irregular Time Steps: MDTW accounts for this by explicitly incorporating the time difference in the distance function.<\/li>\n
    2. Multidimensional Nutrients: MDTW supports multidimensional vectors to represent nutrients such as calories, fat etc. and uses a weight matrix to handle differing units and the importance of nutrients,<\/li>\n
    3. Unequal number of meals: MDTW allows for matching with empty eating events<\/strong>, penalizing skipped or unmatched meals appropriately.<\/li>\n
    4. Time Sensitivity: MDTW includes a time difference penalty<\/strong>, weighting eating events far apart in time even if the nutrients are similar.<\/li>\n<\/ol>\n
      Eating Occasion Data Representation<\/h4>\n
      According to the modified dynamic time warping proposed in the paper[1], each person\u2019s diet can be thought of as a sequence of eating events<\/strong>, where each event has:<\/p>\n
      \"\"<\/figure>\n
      To illustrate how eating records appear in real data, I created three synthetic dietary profiles<\/strong> only considering calorie consumption\u200a\u2014\u200aSkipper<\/strong>, Night Eater<\/strong>, and Snacker. <\/strong>Let\u2019s assume if we ingest the raw data from an API in this format:<\/p>\n
      skipper={\n    'person_id': 'skipper_1',\n    'records': [\n        {'time': 12, 'nutrients': [300]},  # Skipped breakfast, large lunch\n        {'time': 19, 'nutrients': [600]},  # Large dinner\n    ]\n}\nnight_eater={\n    'person_id': 'night_eater_1',\n    'records': [\n        {'time': 9, 'nutrients': [150]},   # Light breakfast\n        {'time': 14, 'nutrients': [250]},  # Small lunch\n        {'time': 22, 'nutrients': [700]},  # Large late dinner\n    ]\n}\nsnacker=  {\n    'person_id': 'snacker_1',\n    'records': [\n        {'time': 8, 'nutrients': [100]},   # Light morning snack\n        {'time': 11, 'nutrients': [150]},  # Late morning snack\n        {'time': 14, 'nutrients': [200]},  # Afternoon snack\n        {'time': 17, 'nutrients': [100]},  # Early evening snack\n        {'time': 21, 'nutrients': [200]},  # Night snack\n    ]\n}\nraw_data = [skipper, night_eater, snacker]<\/code><\/pre>\n
      As suggested in the paper, the nutritional values should be normalized by the total calorie consumptions.<\/p>\n
      import numpy as np\nimport matplotlib.pyplot as plt\ndef create_time_series_plot(data,save_path=None):\n    plt.figure(figsize=(10, 5))\n    for person,record in data.items():\n        #in case the nutrient vector has more than one dimension\n        data=[[time, float(np.mean(np.array(value)))] for time,value in record.items()]\n\n        time = [item[0] for item in data]\n        nutrient_values = [item[1] for item in data]\n        # Plot the time series\n        plt.plot(time, nutrient_values, label=person, marker='o')\n\n    plt.title('Time Series Plot for Nutrient Data')\n    plt.xlabel('Time')\n    plt.ylabel('Normalized Nutrient Value')\n    plt.legend()\n    plt.grid(True)\n    if save_path:\n        plt.savefig(save_path)\n\ndef prepare_person(person):\n    \n    # Check if all nutrients have same length\n    nutrients_lengths = [len(record['nutrients']) for record in person[\"records\"]]\n    \n    if len(set(nutrients_lengths)) != 1:\n        raise ValueError(f\"Inconsistent nutrient vector lengths for person {person['person_id']}.\")\n\n    sorted_records = sorted(person[\"records\"], key=lambda x: x['time'])\n\n    nutrients = np.stack([np.array(record['nutrients']) for record in sorted_records])\n    total_nutrients = np.sum(nutrients, axis=0)\n\n    # Check to avoid division by zero\n    if np.any(total_nutrients == 0):\n        raise ValueError(f\"Zero total nutrients for person {person['person_id']}.\")\n\n    normalized_nutrients = nutrients \/ total_nutrients\n\n    # Return a dictionary {time: [normalized nutrients]}\n    person_dict = {\n        record['time']: normalized_nutrients[i].tolist()\n        for i, record in enumerate(sorted_records)\n    }\n\n    return person_dict\nprepared_data = {person['person_id']: prepare_person(person) for person in raw_data}\ncreate_time_series_plot(prepared_data)<\/code><\/pre>\n
      \"\"
      Plot of eating occasion of three different profiles (Image by author)<\/figcaption><\/figure>\n
      Calculation Distance of\u00a0Pairs<\/h4>\n
      The computation of distance measure between pair of individuals are defined in the formula below. The first term represent an Euclidean distance of nutrient vectors whereas the second one takes into account the time penalty.<\/p>\n
      \"\"<\/figure>\n
      This formula is implemented in the local_distance<\/code> function with the suggested values:<\/p>\n
      import numpy as np\n\ndef local_distance(eo_i, eo_j,delta=23, beta=1, alpha=2):\n    \"\"\"\n    Calculate the local distance between two events.\n    Args:\n        eo_i (tuple): Event i (time, nutrients).\n        eo_j (tuple): Event j (time, nutrients).\n        delta (float): Time scaling factor.\n        beta (float): Weighting factor for time difference.\n        alpha (float): Exponent for time difference scaling.\n    Returns:\n        float: Local distance.\n    \"\"\"\n    ti, vi = eo_i\n    tj, vj = eo_j\n   \n    vi = np.array(vi)\n    vj = np.array(vj)\n\n    if vi.shape != vj.shape:\n        raise ValueError(\"Mismatch in feature dimensions.\")\n    if np.any(vi < 0) or np.any(vj < 0):\n        raise ValueError(\"Nutrient values must be non-negative.\")\n    if np.any(vi>1 ) or np.any(vj>1):\n        raise ValueError(\"Nutrient values must be in the range [0, 1].\")   \n    W = np.eye(len(vi))  # Assume W = identity for now\n    value_diff = (vi - vj).T @ W @ (vi - vj) \n    time_diff = (np.abs(ti - tj) \/ delta) ** alpha\n    scale = 2 * beta * (vi.T @ W @ vj)\n    distance = value_diff + scale * time_diff\n  \n    return distance<\/code><\/pre>\n
      We construct a local distance matrix deo<\/em>(i<\/em>,j<\/em>) for each pair of individuals being compared. The number of rows and columns in this matrix corresponds to the number of eating occasions for each individual.<\/p>\n
      Once the local distance matrix deo(i,j) is constructed\u200a\u2014\u200acapturing the pairwise distances between all eating occasions of two individuals\u200a\u2014\u200athe next step is to compute the global cost matrix<\/strong> dER(i,j). This matrix accumulates the minimal alignment cost by considering three possible transitions at each step: matching two eating occasions, skipping an occasion in the first record (aligning to an empty), or skipping an occasion in the second record.<\/p>\n
      \"\"<\/figure>\n
      To compute the overall distance<\/strong> between two sequences of eating occasions, we build:<\/p>\n
      A local distance matrix<\/strong> deo<\/code> filled using local_distance<\/code>.<\/p>\n