Computational Intelligence - February 2013 - 59

Table 1 Notation used in our method.

SYMbOl

DeSCriPTiON

number of Topics

number of documenTs

number of unique locaTions

number of unique direcTions

number of locaTions in documenT j

The mulTinomial disTribuTion of Topics specific To documenT j

The mulTinomial disTribuTion of locaTions specific To Topic z

The mulTinomial disTribuTion of direcTions specific To Topic z

zji

The Topic associaTed wiTh The ith locaTion in The documenT j

lji

The ith locaTion in documenT j

dji

The direcTion associaTed wiTh The ith locaTion in documenT j

nz,v

The co-occur Time of The zth Topic and The vth locaTion

nz,w

The co-occur Time of The zth Topic and The wth direcTion

nj,z

The co-occur Time of The jth documenT and The zth Topic

the motion vector will be quantized
into a high dimensional codebook.
Then the data will be handled by the
two principal parts of our approach:
graph model and rough sets classifier.
The graph model is used to convert the
video data into another representation,
i.e., the original motion frames can be
represented by low dimension feature
vectors, which will also represent the
atomic activities existing in each scene.
The rough sets classifier is used to classify the video behaviors, which are represented in the low dimension feature
vectors. Hence the topic model generates low dimension features that the
rough sets classifier recognizes. In the
next sections, we will describe the
topic model and rough sets classifier in
detail.
B. Graph Model

The bag-of-words assumption [35] is
important to the topic model, under
which all features are considered conditionally independent. The temporal
and spatial information will be discarded. However video data is a
sequence of inherent temporal and spatial information, without which the
behavior analysis will not be accurate.
Based on the original LDA model, the
follow-up improvements are focused
on offsetting the lost information. In
the text mining field, analysis of the
topic variation over time has become a
popular issue. The key to this issue is
how to introduce the time factor in the

i
z

d
i

}

j
Figure 4 The graph model of our method.

model [9], [36]-[38]. In the topic over
time model (TOT) [9], the time factor
was introduced as time-stamp for each
word, while in [36]-[38] models were
built under the Markov assumption. In
the TOT model, when a word was
sampled from a topic, a time-stamp was
also sampled.
Motivated by this, we propose
another way to use the model to generate a motion frame.
In most approaches, the codebook is
generated as follows:
❏ Divide the video into non-overlapping
video clips which are used as docu-

ments. If the video runs at 30fps, the
clip length is 1s, then each document
consists of 30 frames.
❏ Divide the frame into a grid to
extract features. If the resolution is
360#288, and each cell is 8#8, then
the grid is 45#36.
❏ Use optical flow to extract features. If
a motion is detected in a cell, then a
word representing the direction will
be generated. The number of direction is usually set to 4.
❏ We can obtain a codebook with
45#36#4 words. However, in our
model we generate the codebook with
45#36 words, i.e., we consider each
cell as the word, and the direction is
just a direction-stamp of the cell.This is

Training
Data
Calculate
Reducts
Calculate
Decision
Rules

Testing
Data
Decision
Rules

Select Matching
Rules

Calculate Strength of Matching
Rules for Decision Class

Select Decision Class with Maximal
Strength of Selected Rules
Decision Value
for Testing Data
Figure 5 The flow of classification using rough sets method.

February 2013 | Ieee ComputatIonal IntellIgenCe magazIne

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