Mathematical Problems in Engineering

Volume 2015 (2015), Article ID 280140, 12 pages

http://dx.doi.org/10.1155/2015/280140

## Empirical Validation of Objective Functions in Feature Selection Based on Acceleration Motion Segmentation Data

^{1}KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 305-338, Republic of Korea^{2}Chungbuk National University, 1 Chungdae-ro, Seowon-gu, Cheongju, Chungbuk 362-763, Republic of Korea^{3}Systran International, 163 Yangjaecheon-ro, Gangnam-gu, Seoul 135-855, Republic of Korea

Received 5 March 2015; Accepted 14 April 2015

Academic Editor: Sanghyuk Lee

Copyright © 2015 Jong Gwan Lim et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Recent change in evaluation criteria from accuracy alone to trade-off with time delay has inspired multivariate energy-based approaches in motion segmentation using acceleration. The essence of multivariate approaches lies in the construction of highly dimensional energy and requires feature subset selection in machine learning. Due to fast process, filter methods are preferred; however, their poorer estimate is of the main concerns. This paper aims at empirical validation of three objective functions for filter approaches, Fisher discriminant ratio, multiple correlation (MC), and mutual information (MI), through two subsequent experiments. With respect to 63 possible subsets out of 6 variables for acceleration motion segmentation, three functions in addition to a theoretical measure are compared with two wrappers, *k*-nearest neighbor and Bayes classifiers in general statistics and strongly relevant variable identification by social network analysis. Then four kinds of new proposed multivariate energy are compared with a conventional univariate approach in terms of accuracy and time delay. Finally it appears that MC and MI are acceptable enough to match the estimate of two wrappers, and multivariate approaches are justified with our analytic procedures.

#### 1. Introduction

As one of the human computer interactions, Inertial Measurement Unit (IMU) applications have been prominently increasing in quantity [1]. Of the related technological issues, motion segmentation using accelerometers has long been a significant problem [2–6]. Motion segmentation implies the discrimination of motion-involved periods and is handled within various domains depending on the detection signal. In the IMU applications, which generally depend on accelerometers, the process can be understood as acceleration end point detection in terms of signal processing. Since linear acceleration and angular rates from IMUs are rarely used without integration, motion segmentation is inevitable because it indicates the initial and final points in the integration or the starting and ending points in the period of interest for processing [4, 7, 8].

Typical problems in motion segmentation using acceleration have been associated with how accurately both ends can be found; thereby several constraints have been reported. First, measured acceleration is corrupted with the gravitational acceleration which is intractable to separate from acceleration by body motion [2, 8, 9]. Since it is exposed to noise whose source is also body motion, such as unintentional trembles or minute motion, the estimated motion segmentation might consequently include teacher noise. Additionally, measured acceleration prevails in such low frequency bands (0–20 Hz) that spectral information is sparse. As a result, motion segmentation specialized for acceleration is temporally processed mainly [3–6, 9]. While calculating the acceleration energy in the time domain, another constraint emerges. Sample-wise linear separation between motion and nonmotion states is formidable without modifying a multivalley structure; plus, time delay produced by modifying the multivalley structure has proportional relation to accuracy [3].

The proportional tendency between accuracy and time delay in conventional approaches provokes a new requirement for rapid response time with the advent of smart devices [9, 10]. Motion segmentation obsessed with accuracy naturally leads to requiring an appropriate trade-off between accuracy and delay. For accomplishing maximum accuracy with minimum time delay, the employment of multivariate energy appended to hyper decision boundaries has been introduced as a promising alternative [9, 11]. This approach achieves the time delay reduction by skipping energy smoothing, which is the main cause of the time delay in the previous univariate approach. Instead of an explicit energy smoothing process, a shorter time delay is produced implicitly when multivariate energy vectors are generated. The loss of accuracy resulting from the reduced time delay in this approach is compensated by motion state decision making with a nonlinear hyper decision boundary in high-dimensional space.

Consequently, accuracy is dependent on the separability between data distributions of two states represented by multivariate energy in high-dimensional space, and it is required to predict the discriminality of each data distribution represented by variables or their multidimensional combinations for building optimal multivariate energy. Because the performance of classifiers implementing a hyper decision boundary may well have a limit, it is important to find and identify variables that can have discriminant distributions between two states in multivariate space. In addition, it is so fundamental to depend on statistical regularities represented by data in pattern recognition that state separability can be used to show how well data is distributed in high-dimensional space for a given task.

#### 2. Problem Description

The key cause of the given problem is the multivalley structure that commonly occurs in calculating temporal energy. Figure 1 shows the parsed acceleration signal from a simple arm motion and its basic energy . There, the red dotted line represents the motion period, where nonzero values stand for motion state. Acceleration from arm motion has a multipeaked structure that is a representative of all human arm motion [3]. The energy calculation transforms the multipeaked structure into the multivalley structure at the bottom of Figure 1, which is commonly observed in various energy types [3–6, 9–11]. In this structure, the multiple valleys prevent a linear threshold from simply discriminating motion and nonmotion states, and this phenomenon explains why energy smoothing is required. As smoothing means to extract the desired signal by removing multiple peaks and valleys in the original signal in terms of signal processing, it represents the process to fill the valleys to make the difference between two states clear in this case. The main difference among algorithms is techniques employed to smooth these valleys: low-pass filtering including moving average, axial information integration, inactivated interval setting, extra signal addition, and so forth [2–6, 12].