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Driving Style Analysis Using Primitive Driving Patterns With Bayesian Nonparametric Approaches

Wenshuo Wang, Junqiang Xi, Ding Zhao

arXiv:1708.08986v1cs.CV

TL;DR

Driving-style analysis needs methods that capture dynamic behavioral semantics rather than only aggregate driving statistics. The paper learns semantically labeled primitive patterns with an HDP-HSMM without prespecifying their number, and reports that this approach produces expected-duration patterns for car-following behaviors.

  • Problem

    Existing statistical approaches capture static driving habits but do not describe the dynamic behavioral semantics or decision making involved in driving styles.

  • Method

    The paper combines a hierarchical Dirichlet process with a hidden semi-Markov model to learn primitive driving patterns without prior knowledge of their number, then labels them semantically.

  • Results

    The HDP-HSMM obtains the lowest proportion of primitive patterns shorter than 1.0 s: 0.0065, versus 0.0216 for HDP-HMM and 0.0441 for sticky HDP-HMM.

  • Takeaways & Limitations

    Primitive-pattern analysis can support semantic understanding of driver behaviors and driving styles in car-following scenarios.

Abstract

from arXiv · show

Analysis and recognition of driving styles are profoundly important to intelligent transportation and vehicle calibration. This paper presents a novel driving style analysis framework using the primitive driving patterns learned from naturalistic driving data. In order to achieve this, first, a Bayesian nonparametric learning method based on a hidden semi-Markov model (HSMM) is introduced to extract primitive driving patterns from time series driving data without prior knowledge of the number of these patterns. In the Bayesian nonparametric approach, we utilize a hierarchical Dirichlet process (HDP) instead of learning the unknown number of smooth dynamical modes of HSMM, thus generating the primitive driving patterns. Each primitive pattern is clustered and then labeled using behavioral semantics according to drivers' physical and psychological perception thresholds. For each driver, 75 primitive driving patterns in car-following scenarios are learned and semantically labeled. In order to show the HDP-HSMM's utility to learn primitive driving patterns, other two Bayesian nonparametric approaches, HDP-HMM and sticky HDP-HMM, are compared. The naturalistic driving data of 18 drivers were collected from the University of Michigan Safety Pilot Model Deployment (SPDM) database. The individual driving styles are discussed according to distribution characteristics of the learned primitive driving patterns and also the difference in driving styles among drivers are evaluated using the Kullback-Leibler divergence. The experiment results demonstrate that the proposed primitive pattern-based method can allow one to semantically understand driver behaviors and driving styles.

I. INTRODUCTION

The paper motivates a primitive-pattern framework because aggregate driving statistics capture static habits but not dynamic behavioral semantics or decision making. It therefore learns patterns from time-series data without prespecifying their number and labels them semantically for driving-style analysis.

  • Driving style affects eco-driving, road safety, and intelligent vehicles.
  • Statistical features such as means, standard deviations, and maxima classify driving habits but do not describe dynamic behavioral semantics or decision making.
  • Primitive driving patterns decompose complex behavior into smaller segments that reveal dynamic decision-making processes and driving styles.
  • Prior approaches define patterns through templates, metric changes, derived signals, or manually specified behavioral categories.
  • The proposed learning-based framework uses Bayesian nonparametric modeling to learn primitive patterns from time-series data without prior knowledge of their number, then semantically labels them.

II. BAYESIAN NONPARAMETRIC LEARNING APPROACHES BASED ON HMM

The framework models primitive driving patterns as latent states generating observed driving data, while Bayesian nonparametric extensions avoid fixing the number of patterns. Its HSMM formulation additionally represents variable state durations explicitly.

  • Bayesian nonparametric learning addresses driving-pattern modeling when the number of primitive patterns is unknown.
  • The graphical models compare three Bayesian nonparametric HMM-based approaches for univariate time series of length T.
  • 1) Hidden Markov Model: The HMM represents primitive driving patterns as hidden states that generate observed driving data through state-specific emissions and transitions.
  • 2) Hidden Semi-Markov Model: The HSMM extends the HMM by assigning each hidden state a variable duration drawn from a state-specific duration distribution.

3) Hierarchical Dirichlet Process:

The HDP supplies a nonparametric prior for HMM transition measures when the number of latent dynamic modes is unknown. Its hierarchical construction shares a global discrete measure across state-specific transition distributions.

  • Hierarchical Dirichlet Process: The HDP is used to model an unknown number of latent dynamic modes or primitive patterns in HMM and HSMM models.The number of modes is not specified in advance.
  • Hierarchical Dirichlet Process: A Dirichlet process places a distribution over discrete probability measures with infinitely many atoms on a parameter space.The base measure is H, and the weights are generated through stick breaking.
  • Hierarchical Dirichlet Process: The HDP defines a prior over HMM transition probability measures by relating state-specific measures to a shared global measure.Each Gj is modeled as a variation on G0, while G0 is drawn from a DP with base measure H.
  • Hierarchical Dirichlet Process: Table I reports the parameter values used for the models.

4) Sticky HDP-HMM and HDP-HSMM:

The paper compares HDP-HMM, sticky HDP-HMM, and HDP-HSMM as Bayesian nonparametric extensions of HMM and HSMM models. Stickiness increases self-transition probability, while HSMM additionally models explicit state durations.

  • Model Variants: Applying an HDP prior to HMM and HSMM yields HDP-HMM, sticky HDP-HMM, and HDP-HSMM models.
  • Sticky HDP-HMM: The sticky HDP-HMM adds κ > 0 to bias the process toward self-transition and increase expected self-transition probability.
  • Sticky HDP-HMM: When κ = 0, the sticky HDP-HMM reduces to the original HDP-HMM.
  • HDP-HSMM: The HDP-HSMM specifies state-specific transition distributions and jointly samples state parameters and duration parameters.
  • HDP-HSMM: The normalized transition expression is used to estimate self-transition in the state sequence.

B. Observation (or Emission) Model

The observation model assumes Gaussian emissions to make Bayesian nonparametric inference tractable. The experimental analysis applies these models to car-following driving styles using naturalistic data.

  • Observation Model: The observation model can use Gaussian emissions or switch linear dynamic models, including vector autoregressive models.
  • Observation Model: The paper assumes Gaussian observations so that the nonparametric inference algorithm remains tractable.Under this assumption, θ_i contains the mean and covariance parameters.
  • Implementation: The implementation uses pyhsmm and related code, with hyperparameters determined according to stated rules.
  • Prior Specification: Gamma priors are placed on γ, α, and κ, while inverse-Wishart priors provide conjugate priors for Gaussian parameters.
  • Application: The developed models are applied to analyze driving styles in car-following behavior.

A. Equipment and Participants

The study uses naturalistic car-following data from 18 drivers, collected with vehicle, Mobileye, and data-acquisition systems. Events are represented by relative distance, relative speed, and acceleration, normalized before Bayesian nonparametric segmentation.

  • Equipment and Participants: 18 equipped vehicles and drivers were selected from the SPMD database for on-road experiments.The database contains naturalistic driving records from 2,842 equipment vehicles in Ann Arbor over more than two years.
  • Equipment and Participants: Mobileye recorded road and surrounding-vehicle information, while CAN-bus signals supplied subject-vehicle variables at 10 Hz.
  • Equipment and Participants: Drivers completed unrestricted daily trips for several months, with recording equipment hidden to avoid influencing behavior.
  • Data Extraction and Preprocessing: Car-following events were extracted using subject acceleration, relative range, and relative range rate.Relative range is Δd = x2 − x1, and relative range rate is Δv = v2 − v1.
  • Data Extraction and Preprocessing: Events required a same-lane lead vehicle, lead distance below 120 m, speed above 18 km/h, no unresolved cut-in, and duration above 50 s.
  • Data Extraction and Preprocessing: Each event variable was normalized to reduce scale effects before Bayesian nonparametric segmentation into primitive-pattern regimes.The observation vector was x = [Δd, Δv, a_x]^⊤, and the analysis included M = 18 drivers.

C. Variable Segmentation and Threshold Selection

The framework segments range, range rate, and acceleration into perceptually motivated levels, combining them into 75 semantically labelable primitive patterns. Distribution fitting and percentile thresholds determine these variable categories.

  • Distribution fitting: Four distributions—Normal, Beta, Student-t, and Gamma—are fitted to relative range, relative range rate, and acceleration.Student-t fits range rate and acceleration better, while Gamma and Beta fit range better.
  • Threshold selection: Relative range is divided into long, normal, and close distance using thresholds of 27.32 m and 57.33 m.These correspond to the 30th and 85th percentile values and align with median and free-flow distinctions.
  • Threshold selection: Relative range rate is divided into five semantic segments: rapidly closing in, closing in, keeping, falling behind, and rapidly falling behind.The thresholds use percentile values informed by reported velocity-difference perception limits.
  • Threshold selection: Acceleration is divided into aggressive acceleration, gentle acceleration, no acceleration, gentle deceleration, and aggressive deceleration.Thresholds of -0.24, -0.07, 0.06, and 0.23 m/s^2 quantitatively match kinesthetic perception and comfort thresholds.
  • Pattern construction: 75 primitive car-following patterns result from combining 3 range levels with 5 range-rate and 5 acceleration levels.These combinations support semantic analysis of driving styles and dynamic modes.

IV. MODEL EVALUATION AND RESULT ANALYSIS

HDP-HSMM provides the strongest likelihood-based segmentation among the compared methods and produces more plausible primitive-pattern durations and switching behavior. Its learned patterns are therefore used for subsequent driving-style analysis.

  • Model comparison: HDP-HSMM achieves the largest training-data and predictive test-data log-likelihoods among the three methods.The comparison uses leave-one-out cross-validation; its advantage over sticky HDP-HMM is slight, with lower standard deviations.
  • Segmentation results: HDP-HMM merges distinct closing-in and falling-behind behaviors into one primitive pattern in the illustrated 0–20 s interval.The example contains both positive and negative range-rate and acceleration values, but the method does not separate them as expected.
  • Segmentation results: Sticky HDP-HMM identifies different patterns but frequently produces subsecond segments, including durations from 0.1 s to 0.8 s in the example.The paper characterizes this as sensitivity to data fluctuation and inconsistent with expected human driving-state durations.
  • Duration analysis: 0.0065 of HDP-HSMM primitive patterns last less than 1.0 s, versus 0.0216 for HDP-HMM and 0.0441 for sticky HDP-HMM.HDP-HSMM produces a similar number of patterns to sticky HDP-HMM while better maintaining expected durations.
  • Duration analysis: 5.47 s is the average primitive-pattern duration for HDP-HSMM, compared with 5.87 s for sticky HDP-HMM and 7.94 s for HDP-HMM.Most HDP-HSMM durations fall approximately between 3.93 s and 7.81 s.
  • Segmentation results: HDP-HSMM segments time series into reasonable patterns with lower switching frequency than HDP-HMM and sticky HDP-HMM.The comparison is based on the illustrated segment results for one event and driver #0.

C. Labeling Behavioral Semantics

The paper converts learned primitive segments into behavioral semantics by combining categorical levels of range rate, acceleration, and distance. K-means clustering helps group segments whose semantic labels are not immediately clear.

  • Semantic interpretation: Each primitive segment is interpreted through semantic levels for relative range rate, acceleration, and relative distance.The representation uses the ordered elements [S∆v, Sax, S∆d].
  • Semantic interpretation: A segment with rapid falling behind, normal distance, and gentle acceleration or deceleration is labeled behaviorally using its three feature levels.The example corresponds to ∆v > 1.0 m/s, ∆d in [47, 57] m, and acceleration magnitudes mostly in [0.05, 0.24].
  • Pattern labeling: K-means clusters each segment’s driving data into a representative point to make primitive patterns easier to label and compare.The method is applied because prior work has used it to label driving patterns.

V. DRIVING STYLE ANALYSIS BASED ON PRIMITIVE DRIVING PATTERNS

The paper analyzes driving styles through normalized frequencies of semantically labeled primitive patterns rather than only aggregate statistics. Across distance conditions, drivers show distinct preferred combinations of acceleration and range-rate behavior.

  • Frequency-based analysis: Normalized frequency distributions characterize how often each driver uses semantically labeled primitive patterns.The distributions are provided separately for close, normal, and long following distances.
  • Frequency-based analysis: The four-driver distributions use dark red for higher pattern probability and dark blue for lower probability.The displayed labels include range-rate and acceleration behaviors such as closing in, keeping, falling behind, and aggressive deceleration.
  • Pattern indexing: The framework uses pattern indices whose absolute magnitude represents driving-style aggressiveness, with larger magnitudes indicating more aggressive behavior.Acceleration and range-rate levels are mapped to integer values from -2 to 2.
  • Driver preferences: For close following distances, most drivers prefer falling behind or closing in with aggressive acceleration or deceleration, while driver #11 prefers no acceleration or deceleration.Drivers #4, #6, and #17 prefer rapidly falling behind while accelerating aggressively.
  • Driver preferences: For normal following distances, most drivers prefer falling behind or closing in with gentle deceleration, whereas drivers #1, #4, and #17 prefer rapidly closing in with aggressive acceleration.The paper reports these preferences using pattern indices for acceleration/deceleration and range rate.
  • Driver preferences: For long following distances, most drivers prefer closing in with no acceleration or deceleration, with several drivers showing different preferred patterns.Driver #12 is given as an example of preferring falling behind through aggressive deceleration.

B. Interdriver Differences in Driving Style

The paper uses normalized primitive-pattern distributions to describe individual driving styles and KL divergence to compare drivers. The resulting comparisons reveal condition-specific similarities and differences in car-following behavior.

  • Fig. 15 visualizes pairwise KL divergence, using dark red for large differences and dark blue for strong similarity.
  • Normalized primitive-pattern distributions provide an indicator for describing and analyzing individual driving styles.
  • KL divergence measures similarity or divergence between drivers’ primitive-pattern distributions, with larger values indicating greater differences.Self-comparison yields KL divergence equal to 0.
  • When following a lead vehicle closely, driver #8 differs from others, especially driver #12.
  • At longer following distances, drivers #6, #11, and #15 strongly differ from others.
  • The framework uses Bayesian nonparametric primitive-pattern learning and semantic labeling before comparing driver distributions with KL divergence.
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