Clustering Eating Behaviors in Time: A Machine Learning Approach to Preventive Health

It’s nicely that what we eat issues — however what if when and how typically we eat issues simply as a lot?

Within the midst of ongoing scientific debate round the advantages of intermittent fasting, this query turns into much more intriguing. As somebody enthusiastic about machine studying and wholesome dwelling, I used to be impressed by a 2017 analysis paper[1] exploring this intersection. The authors launched a novel distance metric referred to as Modified Dynamic Time Warping (MDTW) — a way designed to account not just for the dietary content material of meals but additionally their timing all through the day.

Motivated by their work[1], I constructed a full implementation of MDTW from scratch utilizing Python. I utilized it to cluster simulated people into temporal dietary patterns, uncovering distinct behaviors like skippers, snackers, and evening eaters.

Whereas MDTW might sound like a distinct segment metric, it fills a crucial hole in time-series comparability. Conventional distance measures — comparable to Euclidean distance and even classical Dynamic Time Warping (DTW) — wrestle when utilized to dietary information. Folks don’t eat at fastened instances or with constant frequency. They skip meals, snack irregularly, or eat late at evening.

MDTW is designed for precisely this sort of temporal misalignment and behavioral variability. By permitting versatile alignment whereas penalizing mismatches in each nutrient content material and meal timing, MDTW reveals delicate however significant variations in how individuals eat.

What this text covers:

1. Mathematical basis of MDTW — defined intuitively.
2. From method to code — implementing MDTW in Python with dynamic programming.
3. Producing artificial dietary information to simulate real-world consuming habits.
4. Constructing a distance matrix between particular person consuming information.
5. Clustering people with Okay-Medoids and evaluating with silhouette and elbow strategies.
6. Visualizing clusters as scatter plots and joint distributions.
7. Deciphering temporal patterns from clusters: who eats when and the way a lot?

Fast Be aware on Classical Dynamic Time Warping (DTW)

Dynamic Time Warping (DTW) is a traditional algorithm used to measure similarity between two sequences which will range in size or timing. It’s extensively utilized in speech recognition, gesture evaluation, and time sequence alignment. Let’s see a quite simple instance of the Sequence A is aligned to Sequence B (shifted model of B) with utilizing conventional dynamic time warping algorithm utilizing fastdtw library. As enter, we give a distance metric as Euclidean. Additionally, we put time sequence to calculate the gap between these time sequence and optimized aligned path.

import numpy as np
import matplotlib.pyplot as plt
from fastdtw import fastdtw
from scipy.spatial.distance import euclidean
# Pattern sequences (scalar values)
x = np.linspace(0, 3 * np.pi, 30)
y1 = np.sin(x)
y2 = np.sin(x+0.5)  # Shifted model
# Convert scalars to vectors (1D)
y1_vectors = [[v] for v in y1]
y2_vectors = [[v] for v in y2]
# Use absolute distance for scalars
distance, path = fastdtw(y1_vectors, y2_vectors, dist=euclidean)
#or for scalar 
# distance, path = fastdtw(y1, y2, dist=lambda x, y: np.abs(x-y))

distance, path = fastdtw(y1, y2,dist=lambda x, y: np.abs(x-y))
# Plot the alignment
plt.determine(figsize=(10, 4))
plt.plot(y1, label='Sequence A (sluggish)')
plt.plot(y2, label='Sequence B (shifted)')

# Draw alignment strains
for (i, j) in path:
    plt.plot([i, j], [y1[i], y2[j]], shade='grey', linewidth=0.5)

plt.title(f'Dynamic Time Warping Alignment (Distance = {distance:.2f})')
plt.xlabel('Time Index')
plt.legend()
plt.tight_layout()
plt.savefig('dtw_alignment.png')
plt.present()

The trail returned by fastdtw (or any DTW algorithm) is a sequence of index pairs (i, j) that signify the optimum alignment between two time sequence. Every pair signifies that component A[i] is matched with B[j]. By summing the distances between all these matched pairs, the algorithm computes the optimized cumulative value — the minimal whole distance required to warp one sequence to the opposite.

Modified Dynamic Warping

The important thing problem when making use of dynamic time warping (DTW) to dietary information (vs. easy examples like sine waves or fixed-length sequences) lies within the complexity and variability of real-world consuming behaviors. Some challenges and the proposed answer within the paper[1] as a response to every problem are as follows:

1. Irregular Time Steps: MDTW accounts for this by explicitly incorporating the time distinction within the distance operate.
2. Multidimensional Vitamins: MDTW helps multidimensional vectors to signify vitamins comparable to energy, fats and so forth. and makes use of a weight matrix to deal with differing models and the significance of vitamins,
3. Unequal variety of meals: MDTW permits for matching with empty consuming occasions, penalizing skipped or unmatched meals appropriately.
4. Time Sensitivity: MDTW consists of a time distinction penalty, weighting consuming occasions far aside in time even when the vitamins are comparable.

Consuming Event Information Illustration

In accordance with the modified dynamic time warping proposed within the paper[1], every individual’s weight loss program may be regarded as a sequence of consuming occasions, the place every occasion has:

For example how consuming information seem in actual information, I created three artificial dietary profiles solely contemplating calorie consumption — Skipper, Night time Eater, and Snacker. Let’s assume if we ingest the uncooked information from an API on this format:

skipper={
    'person_id': 'skipper_1',
    'information': [
        {'time': 12, 'nutrients': [300]},  # Skipped breakfast, massive lunch
        {'time': 19, 'vitamins': [600]},  # Giant dinner
    ]
}
night_eater={
    'person_id': 'night_eater_1',
    'information': [
        {'time': 9, 'nutrients': [150]},   # Gentle breakfast
        {'time': 14, 'vitamins': [250]},  # Small lunch
        {'time': 22, 'vitamins': [700]},  # Giant late dinner
    ]
}
snacker=  {
    'person_id': 'snacker_1',
    'information': [
        {'time': 8, 'nutrients': [100]},   # Gentle morning snack
        {'time': 11, 'vitamins': [150]},  # Late morning snack
        {'time': 14, 'vitamins': [200]},  # Afternoon snack
        {'time': 17, 'vitamins': [100]},  # Early night snack
        {'time': 21, 'vitamins': [200]},  # Night time snack
    ]
}
raw_data = [skipper, night_eater, snacker]

As prompt within the paper, the dietary values must be normalized by the whole calorie consumptions.

import numpy as np
import matplotlib.pyplot as plt
def create_time_series_plot(information,save_path=None):
    plt.determine(figsize=(10, 5))
    for individual,report in information.objects():
        #in case the nutrient vector has a couple of dimension
        information=[[time, float(np.mean(np.array(value)))] for time,worth in report.objects()]

        time = [item[0] for merchandise in information]
        nutrient_values = [item[1] for merchandise in information]
        # Plot the time sequence
        plt.plot(time, nutrient_values, label=individual, marker='o')

    plt.title('Time Collection Plot for Nutrient Information')
    plt.xlabel('Time')
    plt.ylabel('Normalized Nutrient Worth')
    plt.legend()
    plt.grid(True)
    if save_path:
        plt.savefig(save_path)

def prepare_person(individual):
    
    # Examine if all vitamins have identical size
    nutrients_lengths = [len(record['nutrients']) for report in individual["records"]]
    
    if len(set(nutrients_lengths)) != 1:
        elevate ValueError(f"Inconsistent nutrient vector lengths for individual {individual['person_id']}.")

    sorted_records = sorted(individual["records"], key=lambda x: x['time'])

    vitamins = np.stack([np.array(record['nutrients']) for report in sorted_records])
    total_nutrients = np.sum(vitamins, axis=0)

    # Examine to keep away from division by zero
    if np.any(total_nutrients == 0):
        elevate ValueError(f"Zero whole vitamins for individual {individual['person_id']}.")

    normalized_nutrients = vitamins / total_nutrients

    # Return a dictionary {time: [normalized nutrients]}
    person_dict = {
        report['time']: normalized_nutrients[i].tolist()
        for i, report in enumerate(sorted_records)
    }

    return person_dict
prepared_data = {individual['person_id']: prepare_person(individual) for individual in raw_data}
create_time_series_plot(prepared_data)

Calculation Distance of Pairs

The computation of distance measure between pair of people are outlined within the method under. The primary time period signify an Euclidean distance of nutrient vectors whereas the second takes into consideration the time penalty.

This method is carried out within the local_distance operate with the prompt values:

import numpy as np

def local_distance(eo_i, eo_j,delta=23, beta=1, alpha=2):
    """
    Calculate the native distance between two occasions.
    Args:
        eo_i (tuple): Occasion i (time, vitamins).
        eo_j (tuple): Occasion j (time, vitamins).
        delta (float): Time scaling issue.
        beta (float): Weighting issue for time distinction.
        alpha (float): Exponent for time distinction scaling.
    Returns:
        float: Native distance.
    """
    ti, vi = eo_i
    tj, vj = eo_j
   
    vi = np.array(vi)
    vj = np.array(vj)

    if vi.form != vj.form:
        elevate ValueError("Mismatch in function dimensions.")
    if np.any(vi 1 ) or np.any(vj>1):
        elevate ValueError("Nutrient values should be within the vary [0, 1].")   
    W = np.eye(len(vi))  # Assume W = id for now
    value_diff = (vi - vj).T @ W @ (vi - vj) 
    time_diff = (np.abs(ti - tj) / delta) ** alpha
    scale = 2 * beta * (vi.T @ W @ vj)
    distance = value_diff + scale * time_diff
  
    return distance

We assemble a neighborhood distance matrix deo(i,j) for every pair of people being in contrast. The variety of rows and columns on this matrix corresponds to the variety of consuming events for every particular person.

As soon as the native distance matrix deo(i,j) is constructed — capturing the pairwise distances between all consuming events of two people — the following step is to compute the international value matrix dER(i,j). This matrix accumulates the minimal alignment value by contemplating three attainable transitions at every step: matching two consuming events, skipping an event within the first report (aligning to an empty), or skipping an event within the second report.

To compute the total distance between two sequences of consuming events, we construct:

A native distance matrix deo crammed utilizing local_distance.

• A international value matrix dER utilizing dynamic programming, minimizing over:
• Match
• Skip within the first sequence (align to empty)
• Skip within the second sequence

These straight implement the recurrence:

import numpy as np

def mdtw_distance(ER1, ER2, delta=23, beta=1, alpha=2):
    """
    Calculate the modified DTW distance between two sequences of occasions.
    Args:
        ER1 (listing): First sequence of occasions (time, vitamins).
        ER2 (listing): Second sequence of occasions (time, vitamins).
        delta (float): Time scaling issue.
        beta (float): Weighting issue for time distinction.
        alpha (float): Exponent for time distinction scaling.
    
    Returns:
        float: Modified DTW distance.
    """
    m1 = len(ER1)
    m2 = len(ER2)
   
    # Native distance matrix together with matching with empty
    deo = np.zeros((m1 + 1, m2 + 1))

    for i in vary(m1 + 1):
        for j in vary(m2 + 1):
            if i == 0 and j == 0:
                deo[i, j] = 0
            elif i == 0:
                tj, vj = ER2[j-1]
                deo[i, j] = np.dot(vj, vj)  
            elif j == 0:
                ti, vi = ER1[i-1]
                deo[i, j] = np.dot(vi, vi)
            else:
                deo[i, j]=local_distance(ER1[i-1], ER2[j-1], delta, beta, alpha)

    # # World value matrix
    dER = np.zeros((m1 + 1, m2 + 1))
    dER[0, 0] = 0

    for i in vary(1, m1 + 1):
        dER[i, 0] = dER[i-1, 0] + deo[i, 0]
    for j in vary(1, m2 + 1):
        dER[0, j] = dER[0, j-1] + deo[0, j]

    for i in vary(1, m1 + 1):
        for j in vary(1, m2 + 1):
            dER[i, j] = min(
                dER[i-1, j-1] + deo[i, j],   # Match i and j
                dER[i-1, j] + deo[i, 0],     # Match i to empty
                dER[i, j-1] + deo[0, j]      # Match j to empty
            )
   
    
    return dER[m1, m2]  # Return the ultimate value

ERA = listing(prepared_data['skipper_1'].objects())
ERB = listing(prepared_data['night_eater_1'].objects())
distance = mdtw_distance(ERA, ERB)
print(f"Distance between skipper_1 and night_eater_1: {distance}")

From Pairwise Comparisons to a Distance Matrix

As soon as we outline the right way to calculate the gap between two people’ consuming patterns utilizing MDTW, the following pure step is to compute distances throughout the whole dataset. To do that, we assemble a distance matrix the place every entry (i,j) represents the MDTW distance between individual i and individual j.

That is carried out within the operate under:

import numpy as np

def calculate_distance_matrix(prepared_data):
    """
    Calculate the gap matrix for the ready information.
    
    Args:
        prepared_data (dict): Dictionary containing ready information for every individual.
        
    Returns:
        np.ndarray: Distance matrix.
    """
    n = len(prepared_data)
    distance_matrix = np.zeros((n, n))
    
    # Compute pairwise distances
    for i, (id1, records1) in enumerate(prepared_data.objects()):
        for j, (id2, records2) in enumerate(prepared_data.objects()):
            if i 

After computing the pairwise Modified Dynamic Time Warping (MDTW) distances, we will visualize the similarities and variations between people’ dietary patterns utilizing a heatmap. Every cell (i,j) within the matrix represents the MDTW distance between individual i and individual j— decrease values point out extra comparable temporal consuming profiles.

This heatmap presents a compact and interpretable view of dietary dissimilarities, making it simpler to establish clusters of comparable consuming behaviors.

This means that skipper_1 shares extra similarity with night_eater_1 than with snacker_1. The reason being that each skipper and evening eater have fewer, bigger meals concentrated later within the day, whereas the snacker distributes smaller meals extra evenly throughout the complete timeline.

Clustering Temporal Dietary Patterns

After calculating the pairwise distances utilizing Modified Dynamic Time Warping (MDTW), we’re left with a distance matrix that displays how dissimilar every particular person’s consuming sample is from the others. However this matrix alone doesn’t inform us a lot at a look — to disclose construction within the information, we have to go one step additional.

Earlier than making use of any Clustering Algorithm, we first want a dataset that displays real looking dietary behaviors. Since entry to large-scale dietary consumption datasets may be restricted or topic to utilization restrictions, I generated artificial consuming occasion information that simulate various day by day patterns. Every report represents an individual’s calorie consumption at particular hours all through a 24-hour interval.

import numpy as np

def generate_synthetic_data(num_people=5, min_meals=1, max_meals=5,min_calories=200,max_calories=800):
    """
    Generate artificial information for a given variety of individuals.
    Args:
        num_people (int): Variety of individuals to generate information for.
        min_meals (int): Minimal variety of meals per individual.
        max_meals (int): Most variety of meals per individual.
        min_calories (int): Minimal energy per meal.
        max_calories (int): Most energy per meal.
    Returns:
        listing: Record of dictionaries containing artificial information for every individual.
    """
    information = []
    np.random.seed(42)  # For reproducibility
    for person_id in vary(1, num_people + 1):
        num_meals = np.random.randint(min_meals, max_meals + 1)  # random variety of meals between min and max
        meal_times = np.type(np.random.alternative(vary(24), num_meals, change=False))  # random instances sorted

        raw_calories = np.random.randint(min_calories, max_calories, dimension=num_meals)  # random energy between min and max

        person_record = {
            'person_id': f'person_{person_id}',
            'information': [
                {'time': float(time), 'nutrients': [float(cal)]} for time, cal in zip(meal_times, raw_calories)
            ]
        }

        information.append(person_record)
    return information

raw_data=generate_synthetic_data(num_people=1000, min_meals=1, max_meals=5,min_calories=200,max_calories=800)
prepared_data = {individual['person_id']: prepare_person(individual) for individual in raw_data}
distance_matrix = calculate_distance_matrix(prepared_data)

Selecting the Optimum Variety of Clusters

To find out the suitable variety of clusters for grouping dietary patterns, I evaluated two widespread strategies: the Elbow Technique and the Silhouette Rating.

• The Elbow Technique analyzes the clustering value (inertia) because the variety of clusters will increase. As proven within the plot, the price decreases sharply as much as 4 clusters, after which the speed of enchancment slows considerably. This “elbow” suggests diminishing returns past 4 clusters.
• The Silhouette Rating, which measures how nicely every object lies inside its cluster, confirmed a comparatively excessive rating at 4 clusters (≈0.50), even when it wasn’t absolutely the peak.

The next code computes the clustering value and silhouette scores for various values of okay (variety of clusters), utilizing the Okay-Medoids algorithm and a precomputed distance matrix derived from the MDTW metric:

from sklearn.metrics import silhouette_score
from sklearn_extra.cluster import KMedoids
import matplotlib.pyplot as plt

prices = []
silhouette_scores = []
for okay in vary(2, 10):
    mannequin = KMedoids(n_clusters=okay, metric='precomputed', random_state=42)
    labels = mannequin.fit_predict(distance_matrix)
    prices.append(mannequin.inertia_)
    rating = silhouette_score(distance_matrix, mannequin.labels_, metric='precomputed')
    silhouette_scores.append(rating)

# Plot
ks = listing(vary(2, 10))
fig, ax1 = plt.subplots(figsize=(8, 5))

color1 = 'tab:blue'
ax1.set_xlabel('Variety of Clusters (okay)')
ax1.set_ylabel('Value (Inertia)', shade=color1)
ax1.plot(ks, prices, marker='o', shade=color1, label='Value')
ax1.tick_params(axis='y', labelcolor=color1)

# Create a second y-axis that shares the identical x-axis
ax2 = ax1.twinx()
color2 = 'tab:pink'
ax2.set_ylabel('Silhouette Rating', shade=color2)
ax2.plot(ks, silhouette_scores, marker='s', shade=color2, label='Silhouette Rating')
ax2.tick_params(axis='y', labelcolor=color2)

# Elective: mix legends
lines1, labels1 = ax1.get_legend_handles_labels()
lines2, labels2 = ax2.get_legend_handles_labels()
ax1.legend(lines1 + lines2, labels1 + labels2, loc='higher proper')
ax1.vlines(x=4, ymin=min(prices), ymax=max(prices), shade='grey', linestyle='--', linewidth=0.5)

plt.title('Value and Silhouette Rating vs Variety of Clusters')
plt.tight_layout()
plt.savefig('clustering_metrics_comparison.png')
plt.present()

Deciphering the Clustered Dietary Patterns

As soon as the optimum variety of clusters (okay=4) was decided, every particular person within the dataset was assigned to certainly one of these clusters utilizing the Okay-Medoids mannequin. Now, we have to perceive what characterizes every cluster.

To take action, I adopted the strategy prompt within the unique MDTW paper [1]: analyzing the largest consuming event for each particular person, outlined by each the time of day it occurred and the fraction of whole day by day consumption it represented. This supplies perception into when individuals devour probably the most energy and how a lot they devour throughout that peak event.

# Kmedoids clustering with the optimum variety of clusters
from sklearn_extra.cluster import KMedoids
import seaborn as sns
import pandas as pd

okay=4
mannequin = KMedoids(n_clusters=okay, metric='precomputed', random_state=42)
labels = mannequin.fit_predict(distance_matrix)

# Discover the time and fraction of their largest consuming event
def get_largest_event(report):
    whole = sum(v[0] for v in report.values())
    largest_time, largest_value = max(report.objects(), key=lambda x: x[1][0])
    fractional_value = largest_value[0] / whole if whole > 0 else 0
    return largest_time, fractional_value

# Create a largest meal information per cluster
data_per_cluster = {i: [] for i in vary(okay)}
for i, person_id in enumerate(prepared_data.keys()):
    cluster_id = labels[i]
    t, v = get_largest_event(prepared_data[person_id])
    data_per_cluster[cluster_id].append((t, v))

import seaborn as sns
import matplotlib.pyplot as plt
import pandas as pd

# Convert to pandas DataFrame
rows = []
for cluster_id, values in data_per_cluster.objects():
    for hour, fraction in values:
        rows.append({"Hour": hour, "Fraction": fraction, "Cluster": f"Cluster {cluster_id}"})
df = pd.DataFrame(rows)
plt.determine(figsize=(10, 6))
sns.scatterplot(information=df, x="Hour", y="Fraction", hue="Cluster", palette="tab10")
plt.title("Consuming Occasions Throughout Clusters")
plt.xlabel("Hour of Day")
plt.ylabel("Fraction of Each day Consumption (largest meal)")
plt.grid(True)
plt.tight_layout()
plt.present()

Whereas the scatter plot presents a broad overview, a extra detailed understanding of every cluster’s consuming habits may be gained by analyzing their joint distributions.
By plotting the joint histogram of the hour and fraction of day by day consumption for the most important meal, we will establish attribute patterns, utilizing the code under:

# Plot every cluster utilizing seaborn.jointplot
for cluster_label in df['Cluster'].distinctive():
    cluster_data = df[df['Cluster'] == cluster_label]
    g = sns.jointplot(
        information=cluster_data,
        x="Hour",
        y="Fraction",
        sort="scatter",
        top=6,
        shade=sns.color_palette("deep")[int(cluster_label.split()[-1])]
    )
    g.fig.suptitle(cluster_label, fontsize=14)
    g.set_axis_labels("Hour of Day", "Fraction of Each day Consumption (largest meal)", fontsize=12)
    g.fig.tight_layout()
    g.fig.subplots_adjust(high=0.95)  # modify title spacing
    plt.present()

To grasp how people had been distributed throughout clusters, I visualized the variety of individuals assigned to every cluster. The bar plot under exhibits the frequency of people grouped by their temporal dietary sample. This helps assess whether or not sure consuming behaviors — comparable to skipping meals, late-night consuming, or frequent snacking — are extra prevalent within the inhabitants.

Based mostly on the joint distribution plots, distinct temporal dietary behaviors emerge throughout clusters:

Cluster 0 (Versatile or Irregular Eater) reveals a broad dispersion of the most important consuming events throughout each the 24-hour day and the fraction of day by day caloric consumption.

Cluster 1 (Frequent Gentle Eaters) shows a extra evenly distributed consuming sample, the place no single consuming event exceeds 30% of the whole day by day consumption, reflecting frequent however smaller meals all through the day. That is the cluster that almost certainly represents “regular eaters” — those that devour three comparatively balanced meals unfold all through the day. That’s due to low variance in timing and fraction per consuming occasion.

Cluster 2 (Early Heavy Eaters) is outlined by a really distinct and constant sample: people on this group devour virtually their whole day by day caloric consumption (near 100%) in a single meal, predominantly in the course of the early hours of the day (midnight to midday).

Cluster 3 (Late Night time Heavy Eaters) is characterised by people who devour almost all of their day by day energy in a single meal in the course of the late night or evening hours (between 6 PM and midnight). Like Cluster 2, this group displays a unimodal consuming sample with a very excessive fractional consumption (~1.0), indicating that almost all members eat as soon as per day, however not like Cluster 2, their consuming window is considerably delayed.

CONCLUSION

On this venture, I explored how Modified Dynamic Time Warping (MDTW) may also help uncover temporal dietary patterns — focusing not simply on what we eat, however when and how a lot. Utilizing artificial information to simulate real looking consuming behaviors, I demonstrated how MDTW can cluster people into distinct profiles like irregular or versatile eaters, frequent gentle eaters, early heavy eaters and later evening eaters primarily based on the timing and magnitude of their meals.

Whereas the outcomes present that MDTW mixed with Okay-Medoids can reveal significant patterns in consuming behaviors, this strategy isn’t with out its challenges. For the reason that dataset was synthetically generated and clustering was primarily based on a single initialization, there are a number of caveats value noting:

• The clusters seem messy, probably as a result of the artificial information lacks sturdy, naturally separable patterns — particularly if meal instances and calorie distributions are too uniform.
• Some clusters overlap considerably, notably Cluster 0 and Cluster 1, making it more durable to tell apart between really completely different behaviors.
• With out labeled information or anticipated floor fact, evaluating cluster high quality is troublesome. A possible enchancment can be to inject recognized patterns into the dataset to check whether or not the clustering algorithm can reliably get well them.

Regardless of these limitations, this work exhibits how a nuanced distance metric — designed for irregular, real-life patterns — can floor insights conventional instruments might overlook. The methodology may be prolonged to personalised well being monitoring, or any area the place when issues occur issues simply as a lot as what occurs.

I’d love to listen to your ideas on this venture — whether or not it’s suggestions, questions, or concepts for the place MDTW may very well be utilized subsequent. That is very a lot a piece in progress, and I’m all the time excited to study from others.

In case you discovered this convenient, have concepts for enhancements, or wish to collaborate, be at liberty to open a difficulty or ship a Pull Request on GitHub. Contributions are greater than welcome!

Thanks a lot for studying all the way in which to the tip — it actually means loads.

Code on GitHub : https://github.com/YagmurGULEC/mdtw-time-series-clustering

REFERENCES

[1] Khanna, Nitin, et al. “Modified dynamic time warping (MDTW) for estimating temporal dietary patterns.” 2017 IEEE World Convention on Sign and Info Processing (GlobalSIP). IEEE, 2017.