Learning Relevance Restricted Boltzmann Machine for Unstructured Group Activity and Event Understanding

Abstract

Analyzing unstructured group activities and events in uncontrolled web videos is a challenging task due to (1) the semantic gap between class labels and low-level visual features, (2) the demanding computational cost given high-dimensional low-level feature vectors and (3) the lack of labeled training data. These difficulties can be overcome by learning a meaningful and compact mid-level video representation. To this end, in this paper a novel supervised probabilistic graphical model termed Relevance Restricted Boltzmann Machine (ReRBM) is developed to learn a low-dimensional latent semantic representation for complex activities and events. Our model is a variant of the Restricted Boltzmann Machine (RBM) with a number of critical extensions: (1) sparse Bayesian learning is incorporated into the RBM to learn features which are relevant to video classes, i.e., discriminative; (2) binary stochastic hidden units in the RBM are replaced by rectified linear units in order to better explain complex video contents and make variational inference tractable for the proposed model; and (3) an efficient variational EM algorithm is formulated for model parameter estimation and inference. We conduct extensive experiments on two recent challenging benchmarks: the Unstructured Social Activity Attribute dataset and the Event Video dataset. The experimental results demonstrate that the relevant features learned by our model provide better semantic and discriminative description for videos than a number of alternative supervised latent variable models, and achieves state of the art performance in terms of classification accuracy and retrieval precision, particularly when only a few labeled training samples are available.

Appendix: Parameters of Free-Form Variational Posterior \(\varvec{q(t_{mj}})\)

The expressions of parameters in $q(t_{mj})$ (28) are listed as follows:

$$\begin{aligned} {\omega _{pos}}= & {} \mathcal {N}(\alpha |\beta ,\gamma + 1 ), \ \sigma _{pos}^2 = {({\gamma ^{ - 1}} + 1)^{ - 1}}, \end{aligned}$$

(33)

$$\begin{aligned} {\mu _{pos}}= & {} \sigma _{pos}^2(\frac{\alpha }{\gamma } + \beta ), \end{aligned}$$

(34)

$$\begin{aligned} {\omega _{neg}}= & {} \mathcal {N}(\alpha |0,\gamma ), \ \sigma _{neg}^2 = 1 , \ {\mu _{neg}} = \beta , \end{aligned}$$

(35)

$$\begin{aligned} Z= & {} \frac{1}{2}{\omega _{pos}}\text {erfc}\left( \frac{ - {\mu _{pos}}}{\sqrt{2\sigma _{pos}^2} } \right) + \frac{1}{2}{\omega _{neg}}\text {erfc}\left( \frac{{\mu _{neg}}}{\sqrt{2\sigma _{neg}^2} } \right) ,\nonumber \\ \end{aligned}$$

(36)

where $\text {erfc}(\cdot )$ is the complementary error function and

$$\begin{aligned} \alpha= & {} {\left\langle {\frac{{{{\varvec{\upeta }}_{ \cdot j}}\left( {{{\mathbf {y}}_m} + {{\mathbf {s}}_m} - \sum \nolimits _{j' \ne j} {{{\varvec{\upeta }}_{ \cdot j'}}{\mathbf {A}}t_{mj'}^r} } \right) }}{{{{\varvec{\upeta }}_{ \cdot j}}{\mathbf {A}\varvec{\upeta }}_{ \cdot j}^T}}} \right\rangle _{q({\varvec{\upeta }})q({\mathbf {t}})}}, \end{aligned}$$

(37)

$$\begin{aligned} \gamma= & {} \left\langle {{{\varvec{\upeta }}_{ \cdot j}}{\mathbf {A}\varvec{\upeta } }_{ \cdot j}^T} \right\rangle _{q({\varvec{\upeta }})}^{ - 1}, \ \beta = \sum \limits _{i = 1}^N {{W_{ij}}{v_{mi}}} + K{b_j}. \end{aligned}$$

(38)

We can see that $q(t_{mj})$ depends on expectations over $\varvec{\upeta }$ and $\{ {t_{mj'}}\} _{j' \ne j}$, which is consistent with the graphical model representation of ReRBM in Fig. 3.