# Classifying Human Leg Motions with Uniaxial Piezoelectric Gyroscopes

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Classified Leg Motions and Experimental Methodology

- M1: standing without moving the legs (Figure 1(a)),
- M2: moving only the lower part of right leg to the back (Figure 1(b)),
- M3: moving both the lower and the upper part of the right leg to the front while bending the knee (Figure 1(c)),
- M4: moving the right leg forward without bending the knee (Figure 1(d)),
- M5: moving the right leg backward without bending the knee (Figure 1(e)),
- M6: opening the right leg to the right side of the body without bending the knee (Figure 1(f)),
- M7: squatting, moving both the upper and the lower leg (Figure 1(g)),
- M8: moving only the lower part of the right leg upward while sitting on a stool (Figure 1(h)).

## 3. Feature Extraction and Reduction

_{s}elements that can be represented as an N

_{s}× 1 vector

**s**= [s

_{1}, s

_{2}, …, s

_{Ns}]

^{T}is obtained. For the 10-second time windows and the 116 Hz sampling rate, N

_{s}= 1, 160. We considered using features such as the minimum and maximum values, the mean value, variance, skewness, kurtosis, autocorrelation sequence, cross-correlation sequence, total energy, peaks of the discrete Fourier transform (DFT) with the corresponding frequencies, and the discrete cosine transform (DCT) coefficients of

**s**. DCT is a transformation technique widely used in image processing that transforms the data into the form of the sum of cosine functions [56]. The features used are calculated as follows, with an explanation below of why we chose our final set of features:

_{i}is the ith element of the discrete-time sequence s, E{.} denotes the expectation operator, μ

**and σ are the mean and the standard deviation of s, R**

_{s}_{ss}(Δ) is the unbiased autocorrelation sequence of

**s**, μ

**is the mean of**

_{u}**u**, R

**(Δ) is the unbiased cross-correlation sequence between**

_{su}**s**and

**u**, S

_{DFT}(k) and S

_{DCT}(k) are the kth elements of the 1-D N

_{s}-point DFT and N

_{s}-point DCT, respectively.

- 1
- mean value of gyro 1 signal
- 2
- mean value of gyro 2 signal
- 3
- kurtosis of gyro 1 signal
- 4
- kurtosis of gyro 2 signal
- 5
- skewness of gyro 1 signal
- 6
- skewness of gyro 2 signal
- 7
- minimum value of gyro 1 signal
- 8
- minimum value of gyro 2 signal
- 9
- maximum value of gyro 1 signal
- 10
- maximum value of gyro 2 signal
- 11
- minimum value of cross-correlation between gyro 1 and gyro 2 signals
- 12
- maximum value of cross-correlation between gyro 1 and gyro 2 signals
- 13-17
- maximum 5 peaks of DFT of gyro 1 signal
- 18-22
- maximum 5 peaks of DFT of gyro 2 signal
- 23-27
- the 5 frequencies corresponding to the maximum 5 peaks of DFT of gyro 1 signal
- 28-32
- the 5 frequencies corresponding to the maximum 5 peaks of DFT of gyro 2 signal
- 33-38
- 6 samples of the autocorrelation function of gyro 1 signal (sample at the midpoint and every 25th sample up to the 125th)
- 39-44
- 6 samples of the autocorrelation function of gyro 2 signal (sample at the midpoint and every 25th sample up to the 125th)
- 45
- minimum value of the autocorrelation function of gyro 1 signal
- 46
- minimum value of the autocorrelation function of gyro 2 signal
- 47-61
- 15 samples of the cross-correlation between gyro 1 and gyro 2 signals (every 20th sample)
- 63-81
- first 20 DCT coefficients of gyro 1
- 82-101
- first 20 DCT coefficients of gyro 2

- maximum value of gyro 1 signal
- maximum value of the cross-correlation between gyro 1 and gyro 2 signals
- minimum value of gyro 2 signal
- the 3rd maximum peak of DFT of gyro 2 signal
- minimum value of the cross-correlation between gyro 1 and gyro 2 signals
- the 3rd maximum peak of DFT of gyro 1 signal

**x**= [x

_{1}, …, x

_{N}]

^{T}.

## 4. Classification Techniques

_{i}with each motion type (i = 1, …, c). An unknown motion is assigned to class ω

_{i}if its feature vector

**x**= [x

_{1}, …, x

_{N}]

^{T}falls in the region Ω

_{i}A rule that partitions the decision space into regions Ω

_{i}, i = 1, …, c is called a decision rule. In our work, each one of these regions corresponds to a different motion type. Boundaries between these regions are called decision surfaces. The training set contains a total of I = I

_{1}+ I

_{2}+ … + I

_{c}sample feature vectors where I

_{i}sample feature vectors belong to class ω

_{i}, and i = 1, …, c. The test set is then used to evaluate the performance of the decision rule.

#### 4.1. Bayesian Decision Making (BDM)

_{i}) be the a priori probability of the motion belonging to class ω

_{i}. To classify a motion with feature vector

**x**, a posteriori probabilities p(ω

_{i}∣

**x**) are compared and the motion is classified into class ω

_{j}that has the maximum a posteriori probability such that p(ω

_{j}∣

**x**) > p(ω

_{i}∣

**x**) ∀i ≠ j. This is known as Bayes' minimum error rule and can be equivalently expressed as:

**x**) denotes the label for feature vector

**x**. However, because these a posteriori probabilities are rarely known, they need to be estimated. A more convenient formulation of this rule can be obtained by using Bayes' theorem:

**x**∣ω

_{i}) are the class-conditional probability density functions (CCPDFs) which are also unknown and need to be estimated in their turn based on the training set. In Equation (3), $p(\text{x})={\sum}_{i=1}^{c}p(\text{x}\mid {\omega}_{i})p({\omega}_{i})$ is a constant and is equal to the same value for all classes. Then, the decision rule becomes: if p(

**x**∣ω

_{j})p(ω

_{j}) > p(

**x**∣ω

_{i})p(ω

_{i}) ∀i ≠ j ⇒

**x**∈ Ω

_{j}.

_{i}) are assumed to be equal for each class, the a posteriori probability becomes directly proportional to the likelihood value p(

**x**∣ω

_{i}). Under this assumption, the decision rule simplifies to:

_{j}(

**x**) > q

_{i}(

**x**) ∀i ≠ j ⇒

**x**∈ Ω

_{j}, where the function q

_{i}is called a discriminant function.

**x**

_{i}

_{1}, …,

**x**

_{iIi}}. Then the ML estimates for the mean vector and the covariance matrix are

**x**, the decision rule in Equation (4) is used for classification.

#### 4.2. Rule-Based Algorithm (RBA)

_{i}≤ τ

_{i}?,” where τ is the threshold value for a given feature and i = 1, 2, …, T, with T being the total number of features used [60]. Selecting and calculating features before using them in the RBA is an important necessary issue to make the algorithm independent of the calculation cost of different features. These rules are determined by examining the training vectors of all classes. More discriminative features are used at the nodes higher in the tree hierarchy. Decision-tree algorithms start from the top of the tree and branch out at each node into two descendant nodes based on checking conditions similar to above. This process continues until one of the leaves is reached or until a branch is terminated.

- Is the variance of gyro 2 signal < 0.1?
- Is the variance of gyro 1 signal < 0.1?
- Is the min value of gyro 1 signal > 0.6?
- Is $\frac{\text{max value of gyro}\phantom{\rule{0.2em}{0ex}}1\phantom{\rule{0.2em}{0ex}}\text{signal}}{\text{min value of gyro}\phantom{\rule{0.2em}{0ex}}1\phantom{\rule{0.2em}{0ex}}\text{signal}}<0.1$?
- Is $\frac{\text{variance of gyro}\phantom{\rule{0.2em}{0ex}}2\phantom{\rule{0.2em}{0ex}}\text{signal}}{\text{min value of autocorrelation function of gyro}\phantom{\rule{0.2em}{0ex}}2}>1.04$?
- Is max value of cross-correlation function < 0.4?
- Is $\frac{\text{max value of gyro}\phantom{\rule{0.2em}{0ex}}2\phantom{\rule{0.2em}{0ex}}\text{signal}}{\text{min value of gyro}\phantom{\rule{0.2em}{0ex}}2\phantom{\rule{0.2em}{0ex}}\text{signal}}<1.4$?

#### 4.3. Least-Squares Method (LSM)

**x**= [x

_{1}, x

_{2}, …, x

_{N}]

^{T}represents a test feature vector,

**r**= [r

_{i}

_{1}, r

_{i}

_{2}, …, r

_{iN}]

^{T}represents the average of the reference feature vectors for each distinct class, and ${\mathcal{D}}_{i}^{2}$ is the square of the distance between these two vectors.

#### 4.4. k-Nearest Neighbor (k-NN) Algorithm

**x**in a given set of many feature vectors. The neighbors are taken from a set of feature vectors (the training set) for which the correct classification is known. The occurrence number of each class is counted among these neighbor vectors and suppose that k

_{i}of these k vectors come from class ω

_{i}. Then, a k-NN estimator for class ω

_{i}can be defined as $\widehat{p}({\omega}_{i}\mid \text{x})=\frac{{k}_{i}}{k}$, and p̂(

**x**∣ω

_{i}) can be obtained from p̂(

**x**∣ω

_{i})p̂(ω

_{i}) = p̂(ω

_{i}∣

**x**)p̂(

**x**). This results in a classification rule such that

**x**is classified into class ω

_{j}if k

_{j}= max

_{i}(k

_{i}), where i = 1, …, c. In other words, the k nearest neighbors of the vector

**x**in the training set are considered and the vector

**x**is classified into the same class as the majority of its k nearest neighbors [61]. It is common to use the Euclidean distance measure, although other distance measures such as the Manhattan distance could in principle be used instead. The k-NN algorithm is sensitive to the local structure of the data.

#### 4.5. Dynamic Time Warping (DTW)

**x**and

**y**with lengths N and M:

**d**is constructed by using all the elements of the feature vectors

**x**and

**y**. The (n, m)th element of this matrix, d(n, m), is the distance between the nth element of

**x**and the mth element of

**y**and is given by $d(n,m)=\sqrt{{({x}_{n}-{y}_{m})}^{2}}=\phantom{\rule{0.2em}{0ex}}|{x}_{n}-{y}_{m}|$ [64].

**W**is a contiguous set of matrix elements that defines a mapping between

**x**and

**y**. Assuming that the lth element of the warping path is w

_{l}= (n

_{l}, m

_{l}), the warping path

**W**with length L is given as:

- (monotonicity) Warping function should be monotonic, meaning that the warping function cannot go “south” or “west”:n
_{l}≥ n_{l}_{−1}and m_{l}≥ m_{l}_{−1} - (boundary condition) The two vectors/sequences that are compared should be matched at the beginning and the end points of the warping path:w
_{1}= (1, 1) and w_{L}= (N, M) - (continuity condition) Warping function should not bypass any points:n
_{l}− n_{l}_{−1}≤ 1 and m_{l}− m_{l}_{−1}≤ 1 - Maximum amount of warp is controlled by a global limit:|n
_{l}− m_{l}| <GThis global constraint G is called a window width and is used to speed up DTW and prevent pathological warpings [64]. A good path is unlikely to wander very far from the diagonal.

**D**is constructed starting at (n, m) = (1, 1). D(n, m) represents the cost of the least-cost path that can be obtained until reaching point (n, m). As stated above, the warp path must either be incremented by one or stay the same along the n and m axes. Therefore, the distances of the optimal warp paths one data point smaller than lengths n and m are contained in the matrix elements D(n − 1, m − 1),D(n − 1, m), and D(n, m − 1). Therefore, D(n, m) is calculated by:

**W**is shown in Figure 10. Part of the DTW path in this figure is given by:

#### 4.6. Support Vector Machines (SVMs)

**x**

_{i}that are vectors in some space X ⊆ $\mathcal{R}$

^{N}and their labels ℓ

_{i}∈ {−1,1} where ℓ

_{i}= ℓ(

**x**

_{i}) and i = 1, …, I. Here, ℓ

_{i}is used to label the class of the feature vectors as before. If the feature vector is a class 1 vector, then ℓ

_{i}= +1; if it is a class 2 vector ℓ

_{i}= −1. The goal in training a SVM is to find the separating hyperplane with the largest margin so that the generalization of the classifier is better. All vectors lying on one side of the hyperplane are labeled as +1, and all vectors lying on the other side are labeled as −1. The support vectors are the (transformed) training patterns that lie closest to the hyperplane and are at equal distance from it. They correspond to the training samples that define the optimal separating hyperplane and are the most difficult patterns to classify, yet the most informative for the classification task.

**x**) ≥ 0, we label

**x**as +1, otherwise as −1. When K satisfies Mercer's condition, K(

**u, v**) = ϕ(

**u**) · ϕ(

**v**) where ϕ(.) : X → $\mathcal{F}$ is a nonlinear mapping and “·” denotes the inner or dot product. We can then rewrite f(

**x**) in the transformed space as f(

**x**) = a · ϕ(

**x**). The linear discriminant function f(

**x**) is based on the hyperplane a · ϕ(

**x**) = 0 where $\text{a}={\sum}_{i=1}^{I}{\beta}_{i}\mathit{\varphi}({\text{x}}_{i})$ is a weight vector. Thus, by using K, the training data is projected into a new feature space $\mathcal{F}$ which is often higher dimensional. The SVM then computes the β

_{i}'s that correspond to the maximal margin hyperplane in $\mathcal{F}$. By choosing different kernel functions, we can project the training data from X into spaces $\mathcal{F}$ for which hyperplanes in $\mathcal{F}$ correspond to more complex decision boundaries in the original space X. Hence, by nonlinear mapping of the original training patterns into other spaces, decision functions can be found using a linear algorithm in the transformed space by only computing the kernel K(

**x, x**

_{i}).

_{i}= +1) symbolize the first class (class 1) and circles (ℓ

_{i}= −1) symbolize the second class (class 2). These two types of training vectors can be separated with infinitely many different hyperplanes, three of which are shown in Figure 12(a). For each of these hyperplanes, correct classification rates may be different when test vectors are presented to the system. To have the smallest classification error at the test stage, the hyperplane should be placed between the support vectors of two classes with maximum and equal margin for both classes [79]. For a SVM, the optimal hyperplane classifier is unique [60]. The equation of a hyperplane that may be used to classify these two classes is given by:

**a**and the transformed feature vector ϕ(

**x**

_{i}) have been augmented by one dimension to include a bias weight so that the hyperplanes need not pass through the origin. For this hyperplane to have maximum margins, dotted and dashed margin lines in Figure 12(b) are given by the following two equations, respectively:

**n**, a

_{0}] where

**n**is the normal vector of the hyperplane, it can be shown that the distance between the two margin lines is 2/‖

**n**‖. Therefore, to maximize the separation between these margin lines, ‖

**n**‖ should be minimized. Since a

_{0}is a constant, this is equivalent to minimizing ‖

**a**‖.

**a**‖

^{2}subject to the constraint given by Equation (17) [80]. Using the method of Lagrange multipliers, we construct the functional

**a**, while maximizing with respect to the undetermined Lagrange multipliers λ

_{i}≥ 0. This can be done by solving the constrained optimization problem by quadratic programming [81] or by other techniques. The solution of the weight vector is ${\text{a}}^{\ast}={\sum}_{i=1}^{I}{\ell}_{i}{\mathrm{\lambda}}_{i}\mathit{\varphi}({\text{x}}_{i})$, corresponding to β

_{i}= ℓ

_{i}λ

_{i}. Then, the decision function is given by:

#### 4.7. Artificial Neural Networks (ANN)

**x**∈ ℝ

^{N}, the target output is 1 for the class that the vector belongs to, and 0 for all other output neurons. The sigmoid function used as the activation function in the hidden and output layers is given by:

**w**is the weight vector, t

_{ik}and o

_{ik}are the desired and actual output values for the ith training pattern and the kth output neuron, and I is the total number of training patterns. When the entire training set is covered, an epoch is completed. The error between the desired and actual outputs is computed at the end of each iteration and these errors are averaged at the end of each epoch (Equation (22)). The training process is terminated when a certain precision goal on the average error is reached or if the specified maximum number of epochs (5,000) is exceeded, whichever occurs earlier. The latter case occurs very rarely. The acceptable average error level is set to a value of 0.06. The weights are initialized randomly with a uniform distribution in the interval [0,1], and the learning rate is chosen as 0.3.

## 5. Experimental Results

#### 5.1. Computational Cost of the Classification Techniques

#### 5.2. Discussion

## 6. Potential Application Areas

## 7. Conclusions and Future Work

## A Principal Component Analysis (Karhunen-Loéve Transformation)

- Mean of each feature vector is calculated and subtracted.
- Covariance matrix of training feature vectors is calculated.
- Eigenvalues and eigenvectors of the covariance matrix are calculated.
- Transformation matrix is obtained by arranging the eigenvectors in descending order of their eigenvalues.
- Features are transformed to a new space where they become uncorrelated.

## Acknowledgments

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**Figure 3.**Position of the two gyroscopes on the human leg (body figure adopted from http://www.answers.com/body breadths).

**Figure 8.**An example of the selection of the parameter k in the k-NN algorithm. The inner circle corresponds to k = 4 and the outer circle corresponds to k = 12, producing different classification results for the test vector.

**Figure 11.**In (a), (c), and (e), the upper curves show reference vectors and the lower curves represent test vectors of size 32 × 1. Parts (b), (d), and (f) illustrate the least-cost warp paths between the two feature vectors, respectively. In (a), reference and test vectors are from different classes. In (c) and (e), both the reference and the test vectors are from the same class.

**Figure 12.**(a) Three different hyperplanes separating two classes; (b) SVM hyperplane (solid line), its margins (dotted and dashed lines), and the support vectors (circled solid squares and dots).

**Figure 13.**Correct classification rates of the k-NN algorithm for (a) k = 1, …, 28 (RRSS) and (b) k = 1, …, 55 (LOO).

**Table 1.**Features selected by inspection (left) and the features selected by using the covariance matrix (right).

features selected by inspection: | features selected from the covariance matrix: |
---|---|

1: min value of cross-correlation | 1: min value of gyro 2 |

2: max value of cross-correlation | 2: min value of gyro 1 |

3: variance of gyro 2 | 3–8: 6 samples of the autocorrelation |

4: min value of gyro 1 | function of gyro 2 |

5: max value of gyro 1 | 9: 1st max peak of DFT of gyro 2 |

6: skewness of gyro 1 | 10: max value of gyro 2 |

7: skewness of gyro 2 | 11: min value of autocorrelation of gyro 2 |

8: mean of gyro 2 | 12: 3rd max peak of DFT of gyro 2 |

9: min value of gyro 2 | 13: max value of gyro 1 |

10–14: maximum 5 peaks of DFT of gyro 2 | 14: min value of cross-correlation |

**Table 2.**Sample SFFS results where average correct classification rates over all classification techniques are given for two different runs.

features selected (1st run): | % | features selected (2nd run): | % |
---|---|---|---|

max value of gyro 1 | 56.7 | max value of gyro 1 | 56.8 |

max value of cross-correlation | 86.2 | max value of cross-correlation | 86.9 |

3rd max peak of DFT of gyro 2 | 93.8 | min value of gyro 2 | 93.8 |

variance of gyro 2 | 95.0 | 3rd max peak of DFT of gyro 2 | 95.8 |

min value of cross-correlation | 95.9 | min value of cross-correlation | 96.3 |

min value of gyro 2 | 96.1 | skewness of gyro 1 | 97.2 |

skewness of gyro 1 | 96.8 | 2nd DCT coefficient of gyro 2 | 97.4 |

5th max peak of DFT of gyro 2 | 97.0 | ||

6th DCT coefficient of gyro 2 | 97.2 |

**Table 3.**Correct differentiation rates for different feature reduction methods and RRSS cross validation.

method: | correct differentiation rate (%) | ||||
---|---|---|---|---|---|

by inspection (14 features) | PCA to 14 features (6 features) | covariance matrix (14 features) | PCA to 101 features (8 features) | SFFS (6 features) | |

BDM | 97.5 | 97.7 | 96.2 | 98.0 | 97.3 |

LSM | 97.0 | 96.9 | 91.8 | 88.5 | 94.6 |

k-NN (k = 1) | 96.9 | 96.9 | 95.3 | 94.9 | 96.4 |

DTW-1 | 92.1 | 92.2 | 87.9 | 82.6 | 95.4 |

DTW-2 | 96.9 | 96.3 | 95.1 | 93.6 | 95.7 |

SVM | 99.2 | 99.1 | 94.6 | 94.6 | 97.2 |

ANN | 88.6 | 90.2 | 87.7 | 88.8 | 87.8 |

**Table 4.**Correct differentiation rates for different feature reduction methods and P-fold cross validation.

method: | correct differentiation rate (%) | ||||
---|---|---|---|---|---|

by inspection (14 features) | PCA to 14 features (6 features) | covariance matrix (14 features) | PCA to 101 features (8 features) | SFFS (6 features) | |

BDM | 98.9 | 98.5 | 98.1 | 99.1 | 98.1 |

LSM | 97.3 | 97.5 | 92.1 | 89.5 | 94.6 |

k-NN (k = 1) | 97.1 | 98.1 | 94.8 | 95.4 | 97.4 |

DTW-1 | 91.8 | 92.8 | 87.7 | 83.8 | 95.7 |

DTW-2 | 98.0 | 96.9 | 96.1 | 95.2 | 97.0 |

SVM | 99.7 | 99.4 | 95.3 | 96.7 | 97.9 |

ANN | 86.4 | 88.8 | 85.0 | 83.2 | 84.4 |

**Table 5.**Correct differentiation rates for different feature reduction methods and LOO cross validation.

method: | correct differentiation rate (%) | ||||
---|---|---|---|---|---|

by inspection (14 features) | PCA to 14 features (6 features) | covariance matrix (14 features) | PCA to 101 features (8 features) | SFFS (6 features) | |

BDM | 99.1 | 99.3 | 98.2 | 99.1 | 98.2 |

LSM | 97.1 | 97.3 | 92.0 | 90.4 | 94.2 |

k-NN (k = 1) | 97.1 | 98.2 | 94.6 | 95.1 | 97.6 |

DTW-1 | 91.7 | 93.8 | 88.0 | 83.7 | 96.0 |

DTW-2 | 98.2 | 97.8 | 95.2 | 95.1 | 97.3 |

SVM | 98.9 | 98.4 | 96.4 | 98.4 | 98.2 |

ANN | 85.1 | 88.8 | 84.8 | 83.3 | 80.1 |

classified | |||||||||
---|---|---|---|---|---|---|---|---|---|

M1 | M2 | M3 | M4 | M5 | M6 | M7 | M8 | ||

true | M1 | 56 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

M2 | 0 | 55 | 0 | 0 | 0 | 0 | 0 | 1 | |

M3 | 0 | 0 | 56 | 0 | 0 | 0 | 0 | 0 | |

M4 | 0 | 0 | 0 | 54 | 2 | 0 | 0 | 0 | |

M5 | 0 | 0 | 0 | 3 | 53 | 0 | 0 | 0 | |

M6 | 0 | 0 | 0 | 0 | 0 | 56 | 0 | 0 | |

M7 | 0 | 0 | 0 | 0 | 0 | 0 | 56 | 0 | |

M8 | 0 | 2 | 0 | 0 | 0 | 0 | 0 | 54 |

classified | |||||||||
---|---|---|---|---|---|---|---|---|---|

M1 | M2 | M3 | M4 | M5 | M6 | M7 | M8 | ||

true | M1 | 56 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

M2 | 0 | 56 | 0 | 0 | 0 | 0 | 0 | 0 | |

M3 | 0 | 0 | 49 | 0 | 0 | 0 | 7 | 0 | |

M4 | 0 | 0 | 0 | 46 | 10 | 0 | 0 | 0 | |

M5 | 0 | 0 | 0 | 4 | 52 | 0 | 0 | 0 | |

M6 | 0 | 0 | 0 | 0 | 0 | 56 | 0 | 0 | |

M7 | 0 | 0 | 1 | 0 | 0 | 0 | 55 | 0 | |

M8 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 56 |

classified | |||||||||
---|---|---|---|---|---|---|---|---|---|

M1 | M2 | M3 | M4 | M5 | M6 | M7 | M8 | ||

true | M1 | 56 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

M2 | 0 | 46 | 0 | 0 | 0 | 0 | 0 | 10 | |

M3 | 0 | 0 | 54 | 2 | 0 | 0 | 0 | 0 | |

M4 | 0 | 0 | 0 | 50 | 6 | 0 | 0 | 0 | |

M5 | 0 | 0 | 0 | 3 | 53 | 0 | 0 | 0 | |

M6 | 0 | 0 | 0 | 0 | 0 | 56 | 0 | 0 | |

M7 | 0 | 0 | 0 | 0 | 0 | 0 | 56 | 0 | |

M8 | 0 | 5 | 0 | 0 | 0 | 0 | 0 | 51 |

classified | |||||||||
---|---|---|---|---|---|---|---|---|---|

M1 | M2 | M3 | M4 | M5 | M6 | M7 | M8 | ||

true | M1 | 56 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

M2 | 0 | 52 | 0 | 0 | 0 | 0 | 0 | 4 | |

M3 | 0 | 0 | 56 | 0 | 0 | 0 | 0 | 0 | |

M4 | 0 | 0 | 0 | 52 | 4 | 0 | 0 | 0 | |

M5 | 0 | 0 | 0 | 2 | 54 | 0 | 0 | 0 | |

M6 | 0 | 0 | 0 | 0 | 0 | 56 | 0 | 0 | |

M7 | 0 | 0 | 0 | 0 | 0 | 0 | 56 | 0 | |

M8 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 55 |

classified | |||||||||
---|---|---|---|---|---|---|---|---|---|

M1 | M2 | M3 | M4 | M5 | M6 | M7 | M8 | ||

true | M1 | 56 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

M2 | 0 | 49 | 0 | 0 | 0 | 2 | 0 | 5 | |

M3 | 0 | 0 | 56 | 0 | 0 | 0 | 0 | 0 | |

M4 | 0 | 0 | 0 | 52 | 4 | 0 | 0 | 0 | |

M5 | 0 | 0 | 1 | 3 | 52 | 0 | 0 | 0 | |

M6 | 0 | 0 | 0 | 0 | 0 | 56 | 0 | 0 | |

M7 | 0 | 0 | 2 | 0 | 0 | 0 | 54 | 0 | |

M8 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 55 |

classified | |||||||||
---|---|---|---|---|---|---|---|---|---|

M1 | M2 | M3 | M4 | M5 | M6 | M7 | M8 | ||

true | M1 | 56 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

M2 | 0 | 54 | 0 | 0 | 0 | 0 | 0 | 2 | |

M3 | 0 | 0 | 56 | 0 | 0 | 0 | 0 | 0 | |

M4 | 0 | 0 | 0 | 53 | 3 | 0 | 0 | 0 | |

M5 | 0 | 0 | 0 | 5 | 51 | 0 | 0 | 0 | |

M6 | 0 | 0 | 0 | 0 | 0 | 56 | 0 | 0 | |

M7 | 0 | 0 | 1 | 0 | 0 | 0 | 55 | 0 | |

M8 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 55 |

**Table 12.**(a) Number of correctly and incorrectly classified feature vectors out of 56 for SVMs (LOO cross validation, 98.2%); (b) same for ANN (LOO cross validation, 80.1%).

(a) | |||
---|---|---|---|

classified | |||

correct | incorrect | ||

true | M1 | 56 | 0 |

M2 | 54 | 2 | |

M3 | 56 | 0 | |

M4 | 53 | 3 | |

M5 | 53 | 3 | |

M6 | 56 | 0 | |

M7 | 56 | 0 | |

M8 | 56 | 0 |

(b) | |||
---|---|---|---|

classified | |||

correct | incorrect | ||

true | M1 | 56 | 0 |

M2 | 20 | 36 | |

M3 | 52 | 4 | |

M4 | 21 | 35 | |

M5 | 43 | 13 | |

M6 | 56 | 0 | |

M7 | 56 | 0 | |

M8 | 55 | 1 |

**Table 13.**Pre-processing and training times and the storage requirements of the classification methods.

method: | pre-processing/training time (msec) | storage requirements | ||
---|---|---|---|---|

RRSS | P-fold | LOO | ||

BDM | 2.144 | 1.441 | 1.706 | mean, covariance, CCPDF |

RBA | – | – | – | rules |

LSM | 0.098 | 0.554 | 105.141 | average of training vectors for each class |

k-NN (k = 1) | – | – | – | all training vectors |

DTW-1 | 0.098 | 0.554 | 105.141 | average of training vectors for each class |

DTW-2 | – | – | – | all training vectors |

SVM | 72.933 | 1880.233 | 5843.133 | SVM models |

ANN | 151940 | 145680 | 189100 | network structure and connection weights |

method: | classification time (msec) | ||
---|---|---|---|

RRSS | P-fold | LOO | |

BDM | 2.588 | 1.220 | 8.188 |

RBA | 0.003 | 0.003 | 0.003 |

LSM | 0.070 | 0.074 | 0.063 |

k-NN (k = 1) | 0.095 | 0.452 | 24.033 |

DTW-1 | 1.775 | 1.937 | 2.000 |

DTW-2 | 49.640 | 94.014 | 107.400 |

SVM | 0.009 | 0.016 | 0.132 |

ANN | 0.882 | 2.547 | 1.391 |

© 2009 by the authors; licensee Molecular Diversity Preservation International, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

## Share and Cite

**MDPI and ACS Style**

Tunçel, O.; Altun, K.; Barshan, B. Classifying Human Leg Motions with Uniaxial Piezoelectric Gyroscopes. *Sensors* **2009**, *9*, 8508-8546.
https://doi.org/10.3390/s91108508

**AMA Style**

Tunçel O, Altun K, Barshan B. Classifying Human Leg Motions with Uniaxial Piezoelectric Gyroscopes. *Sensors*. 2009; 9(11):8508-8546.
https://doi.org/10.3390/s91108508

**Chicago/Turabian Style**

Tunçel, Orkun, Kerem Altun, and Billur Barshan. 2009. "Classifying Human Leg Motions with Uniaxial Piezoelectric Gyroscopes" *Sensors* 9, no. 11: 8508-8546.
https://doi.org/10.3390/s91108508