2.1 Mining Techniques

The most simple classification rule based on a set of instances is called 1R or 1-Rule. In this approach, the system selects one attribute of the collected sensor readings and makes a classification decision based on it. While this a very simple approach, it tends to work reasonably well for some applications [18]. The rule selection can be described as follows: For each possible attribute, the system can count how often each value of that attribute appears in any given class and make an attribute-class assignment based on the value appearing most often. It can calculate the error of all of the attributes based on the cross validation set and select the attribute with the least error. This algorithm faces two major issues: First, it may not be able to account for the values that are missing in the training set. Second, when an attribute has a large range of values, it is prone to over-fitting (or may detect trends specific to the training data that are not desired for detection and mining).

Statistical modeling is a potential solution to the problem. Instead of selecting only one attribute, the system can select all of the attributes, assuming that they are independent. Such an approach is known as Naive Bayes and can perform well when the assumptions hold [19]. The approach has two major problems. First, it assumes that each of the attributes is independent, which is likely not the case for many real problems. This problem has been extensively studied in [20,21], where the authors propose a semi-Bayes approach to modeling the actual data dependencies, correct data bias and manage attribute weights. The second problem is the assumption that the attributes have normal distribution, which may not hold in many practical applications.

Another way to address the issue of different attributes having diverse ranges is based on divide-and-conquer. Typically, this suggests creation of a tree-like structure, where each node corresponds to a specific attribute [22]. This way an attribute does not correspond to a whole level of the tree, meaning that at the same level different branches may use different attributes. This approach works in a top-down manner, where, at each level of the tree, it seeks the best attribute to split the remaining data. The difficulty of this approach lies in selecting proper attributes at levels in the tree. It often uses feature selection algorithms such as information gain [23], mutual information [24], and utility-based solutions such as Bayesian information criterion (BIC) [25]. Shortcomings of these approaches are defined by their respective assumptions. For example, information gain tends to work very well when attributes have very few possible values, suitable for binary attributes [26]. Information-gain performance decreases as the number of possible values increases due to the nature of the entropy calculations.

Previously described approaches work best with nominal attributes; however, the idea can be extended to the numerical attributes as well. The most simple and relatively effective approach is known as linear regression, where the idea is to represent class values as linear combinations of the attributes and their respective weights [27]. The idea is to calculate proper weights during the training process and apply the classifiers on the validation data. While this approach often works very well, there is a serious drawback: it assumes that the data can be modeled in a linear fashion, which may not be a valid assumption. This problem can be addressed with the help of logistic regression and then evaluated with log-likelihood maximization [28]. A major problem with this approach is probabilities not adding up to 1 when the logistic regression is applied to multiple classes.

In instance-based learning, the training trials themselves are used to evaluate unknown samples. It is done with the help of a distance function defined for the data of interest. For classification purposes, the system measures the distance from an unknown trial to the training sample and selects the one with the shortest distance. A simple example of this learning time is the 1-nearest-neighbor (1-NN) approach. However, this approach considers each attribute equally just like Naive Bayes. Additionally, a specific classification can be heavily affected by the outliers that do not represent the class well. These problems can be partially addressed by a k-NN approach, where instead of finding the nearest sample in the training data, the system looks for a consensus among k nearest neighbors [29]. However, k-NN approaches are very slow.

Clustering algorithms are applied when there is no predetermined class to be detected, but rather the observed instances are split into natural groups. During the clustering step, the instances are combined together, based on strong resemblance, to form groups that can act as classes during the detection process. There are many approaches for clustering implementation, but they mainly focus on bringing the similar instances together, while separating the dissimilar instances. One of the most commonly used clustering approaches is known as k-means [30]. It takes the training instances and the number of desirable clusters as an input and groups instances together based on their proximity. In the context of the Euclidean distance, the k-means approach iteratively minimizes the total squared distance from each instance to the cluster centers. It generally has two weaknesses. First, the best number of clusters is not always obvious, while a bad choice can result in improper grouping. Second, the iterative approach heavily depends on the initial selection of the cluster centers. Different random selections can result in significantly different clustering.

2.2 Structural Recognition in BSN

In the context of BSN data, the idea of structural data representation and recognition is explored in [31]. This approach has a major weakness. The comparison evaluation is based on the value of Levenstein distance (or edits distance) [32]. Edit distance calculation assigns the same weight to deletion, insertion, and substitution operations. It is not a problem when the compared strings have similar size. However, BSNs can observe the same movement at different speeds, which may mean that the speed of movement execution can dominate the edit distance value. It is possible to manually manage the weights of each one of the three edit distance operations; however, that would generate a heuristic approach [33]. Another way to deal with this issue is to normalize the length of each primitive in motion transcripts [34]. While this approach might work in some specific applications, in general it is very hard to predict how to scale parts of movements depending on the overall execution speed. A possible solution to this problem is to identify significant transitions in the motion transcripts and base the comparison on variations in these transitions. In the field of speech processing, a similar function is often performed by n-gram features. N-grams are substrings of length N. They were first introduced by Shannon [35] as a means of analyzing vulnerability of ciphers but since have been extensively used in the field of speech and text recognition.

N-grams [36] proved to be useful for structural parameter extraction when used for spoken language recognition [37]. N-grams can be used to capture phoneme, in the case of spoken language, and grammatical constructs, in the case of written language, to identify bodies of speech or text. Similarly, n-grams can be used to analyze text summaries [38] or translation quality [36] with respect to co-occurrence statistics. While good at recognizing major structural differences, n-grams can also be used in the case of fine grain spelling error correction [39]. In addition to maintaining structural information of the considered string, n-grams can significantly reduce the amount of information that needs to be stored and verified. Instead of storing a large body of text, the system can identify important transitions and improve both the memory usage and the execution speed of the search. These important n-grams can be better organized with a suffix tree [40], which would increase the speed of identifying language constructs [41]. In fact, suffix trees are often used to index large amounts of data in the natural language processing and other fields. For example, in the field of molecular biology, DNA sequences can be indexed with the help of suffix trees [42]. In [43] the authors discuss an efficient query algorithm on a large compressed body of text using suffix trees. The general effectiveness of the suffix trees is discussed in the work trying to identify local patterns in an event sequence database [44].

At first glance, the above examples have little in common with data collected from BSNs. Suffix tree approaches normally index a uni-dimensional data set, while BSNs normally have a set of multiple sensors with multiple dimensions of sensing. This problem can be resolved by combining all data readings and representing them with uni-dimensional primitives [31]. While this simple approach seems to resolve the issue, it fails to recognize that each one of the sensing dimensions (or individual orthogonal sensing axis of sensors such as accelerometer) can observe variations such as changing speed and amplitude of the signal. In a text data set, the variations are one dimensional, just like the data itself; this is not the case in multidimensional sensor readings of BSNs. Furthermore, it is not clear how variations occurring in multiple sensing dimensions should be handled in the context of a one-dimensional primitive. It is possible that different combinations of signal variations may hinder the structural consistency of the combined primitive representation. Classical mining techniques are not well suited for BSN data due to their inability to capture structural and relational properties of the signals and not providing a compressed data representation. Therefore, novel data-mining methodologies are required to address these shortcomings.

3.1 BSN System

The BSN system in this chapter consists of a set of wearable nodes placed on the human body to collect inertial activities from human movements and a computer that maintains the BSN repository and facilitates data organization and mining. The wearable nodes are connected to the computer via wireless radios. The system overview is shown in Figure 1 and the details on the operation of the system are described in the following sections and summarized in section 7.

3.2 Wearable Sensor Hardware

Each wearable sensor has a tri-axial accelerometer (providing x-, y-, and z-axis of acceleration) and a bi-axial gyroscope (providing x and y axis of angular velocity) that is sampled at 50 Hz. This sampling frequency is high enough to provide acceptable resolution of the movements, and has been previously suggested by several investigations on physical movement monitoring applications [45,46]. Furthermore, it satisfies the Nyquist criterion [47]. After collecting the data, each node sends its readings to the base-station, which forwards all of the received data to the PC via a USB connection for further processing.

3.3 Pilot Application

To illustrate data mining in a large BSN repository, the proposed approach is applied to a classification problem, where the classification is performed by mining a database of inertial sensor data. Furthermore, as the mining approach is designed for a large data set, the aim is to make it as fast as possible. The database in this case consists of data of ten movements from three subjects. The details of the experimental movements can be found in Table 1. Every subject repeated each movement ten times. Each subject was asked to wear nine sensor nodes positioned on both ankles, both thighs, both wrists and upper arms, and one on the belt (as shown in Figure 2).

3.4 Desirable Solution Properties

A data-mining technique for the BSN data repositories should take raw sensor readings as an input and perform a computationally efficient search in the repository to identify signals similar to the input. Due to a potentially large size of the repository, the approach needs to be fast yet reliable. Sensor readings can be viewed as observations made by the system. Upon receiving an observation as the input, the search approach should be able to identify a movement class to which the observation belongs, so that it can be stored in the appropriate place in the repository. It should be able to compare signals of two movements and find possible similarities. Furthermore, it should be able to identify similar portions of the signals, which can be useful to identify abnormality in movements. Finally, it needs to identify movements that contain certain instances of the signal (e.g., identify all movements where the torso moves forward).

4.1 Primitive Construction

Before applying a clustering technique, it is necessary to decide what data set the clustering is applied to. One way to handle this issue is to combine all axes of sensory data to define primitives. This approach is not most suitable because, when the multidimensional data is merged into a uni-dimensional primitive, combining variations of each of the sensing axes could modify the structure of the combined primitives. An example of such an alternation can be a slight delay of the movement. This alternation does not modify the structure of the individual sensory axis signals, but, since alternations of all of the axes are independent of each other, aligning them with respect to time can significantly change the structure of the combined primitives. Figure 3 demonstrates two trials of the same movement where a slight variation in one of the axes, which does not alter the signal structure for that axis, introduces changes to final primitives. While the signals in the second trial have the same structure as the signals in the first trial, as demonstrated by the individual transcripts, their timing is inconsistent with the signals in the first trial. The bottom part of the figure demonstrates the combined transcript generated from two individual transcripts. Large vertical blocks correspond to the parts of the combined transcript of the second trial that do not have a corresponding counterpart in the first trial. This suggests, if the primitive transitions are not aligned in the original signals, the time aligned combination of these signals may not be consistent between both trials. Noise in the inertial data will introduce yet another source of error.

To avoid the issue with alignment, the reading of each sensing axis can be performed separately. Primitives are created for each one of the axes and each sensing axis is treated as a separate classifier. This approach has an additional benefit of increasing the flexibility of the system. The system does not require all of the sensing axis used in one experiment to be present in other experiments, which means that it does not dictate a particular hardware configuration.

4.1.1 Data Clustering

Clustering is a very effective method of grouping similar data points and distinguishing between different data points. When trying to cluster BSN data, a clustering approach is normally applied to feature vectors extracted from the original signals. There are a variety of features that can be extracted from inertial data. Different approaches rely on first and second derivatives, signal mean, amplitude, variance, standard deviation, peak detection, morphological features, and more. Ideally, a small and simple feature set should be identified that would produce good results. The resultant clusters should be able to identify enough transitions in the signal so that each movement of interest would be characterized with a unique subset of such transitions. A primitive generation experiment concluded that first and second derivatives are sufficient to describe the structure of this data set. To minimize the effect of the inter-subject differences in features, the system normalizes features with respect to each subject using a standard score (or z-score) [48]. In general, the proposed approach is independent of the feature selection and only requires that selected features would represent the structure of the input signal.

There is a wide array of clustering techniques that includes hierarchical, partitional, conceptual, and density-based approaches. For BSN data mining, two clustering approaches were considered. The first approach was k-Means clustering [49]. k-Means is a hierarchical approach that attempts to partition the data in a way that every point is assigned to a cluster with the closest mean, or cluster center. The second approach was expectation maximization in Gaussian mixture models (GMM) [50]. Both approaches try to identify the centers of natural clusters of the data instead of artificially selecting points in the training set as cluster centers. GMM clustering computes the probability that any given point is assigned to every individual cluster and makes an assignment that maximizes its likelihood of such assignment. Both clustering approaches are computationally simple and identify cluster centers of the data set without any prior knowledge of the data. Both approaches start with random cluster centers and re-evaluate them after each round of assignment. Once the cluster centers stay constant within a predefined threshold, both algorithms assume to have converged to the natural cluster centers of the data and return the result.

A parameter to determine during unsupervised clustering is the number of clusters k that produces the best results. To find the best solution, k was varied from 2 to the length of the shortest observation in the training set, while evaluating parameters of both k-Means and GMM. In the case of k-Means, the decision was made based on cluster silhouette [51]. Silhouette is calculated based on the tightness of each cluster and its separation from other clusters. For every point i, the silhouette is defined as

$s(i)=\frac{b(i)-a(i)}{\max (a(i),b(i))}$ (1)

(1)

where a(i) is the average distance of point i to all other points in its cluster, b_j(i) is the average distance of point i to all the points in cluster j, and b(i)=min(b_j(i)), ∀j.

Silhouette s(i) describes how well the point i is mixed with the similar data points and is separated from the different data points. As a result, the quality of a clustering model with k clusters and d training points can be evaluated as

$Quality(k)=\frac{{\sum }_{i:1}^{d}s(i)}{d}$ (2)

(2)

The larger the average silhouette value, the better is the model. Therefore, the best value of k can be selected by finding the largest Quality(k) [51].

Expectation maximization (EM) was used [52] to find the best mixing parameters for the GMM. The mixing parameters such as the mean and covariance matrices depend on the number of clusters k. Once the GMM parameters are selected, there are multiple ways to evaluate the quality of clustering that include log likelihood, Akaike’s information criterion (AIC) [53], and Bayesian information criterion (BIC) [54]. Table 2 demonstrates the difference between quality estimation models for a GMM with k clusters, maximum likelihood of the estimated model L, and n points in the training set.

Table 2

Quality Estimation of GMM-Based Clustering Using EM

Log Likelihood	AIC	BIC
ln(L)	−ln(L)+2 * k	−ln(L)+k * ln(n)

Log likelihood reports the likelihood of the model, and AIC and BIC attempt to penalize the system for increasing the number of clusters. For the collected inertial dataset the penalty of the BIC was harsh and led to an extremely small number of clusters. As a result AIC was selected as the GMM evaluation tool.

4.2 Motion Transcripts

Each movement can be described as a series of primitives. When an unlabeled movement needs to be classified, the system can extract features from each of its data points, and based on the clustering technique, assign motion primitives to them. Motion transcripts are sequences of primitives over a certain alphabet assigned to movement trials. Since the data from different wireless nodes in a BSN are not comparable, the system has to make sure to differentiate between individual nodes by using a unique alphabet for each one. Figure 4 demonstrates a sample transcript generated by the ankle node for a “Lie to Sit” movement. Each one of the sensing axes uses a separate alphabet, so while they are displayed with the same color, the primitives of different transcripts are not related.

5.1 N-gram Selection

The objective of this operation is to identify a small number of n-grams that can uniquely characterize the movement of interest and provide means of distinguishing the movement from others in the repository. There are a variety of ways to select proper n-grams, once all n-grams are extracted from the training data. Information gain (IG) has proven to be effective in the field of natural language processing [55]. Information gain becomes complicated to compute and less effective when each evaluated feature can have a larger range of values. However, in our experiments, each n-gram has two possible values. A specific n-gram can be present in a motion trial and the value of “1” is assigned to it, or the n-gram can be absent with a value of “0” assigned. While IG proved effective on the described data set, the proposed approach is not dependent on this particular n-gram selection technique and can be modified based on the specific user demands.

IG can assess the effectiveness of a feature by tracking changes in the entropy after consideration of that feature. IG of a feature f on the collection of movements m is defined as

$Gain(m,f)=H(m)-H(m|f)$ (3)

(3)

where H (m) defines entropy of the movement set and H (m|f) defines conditional entropy of the movement set with respect to feature f. A slightly modified approach is used here, because when the system is looking for a target movement all other movements can be treated the same way. It is possible that a feature might be good at identifying one movement while being unable to differentiate between the rest of the movements. That feature would have a bad general information gain, but if the information gain is computed with respect to each movement, suitable features can be identified for each movement. Practically, this means that while computing information gain of a feature with respect to a particular movement m_i, the movement set is split into subsets of {m_i} and {‘not’ m_i} or {m−m_i}. In this case, H (m_i|f) can be different for each m_i and need to be calculated individually. This means that the information can be redefined as

$Gain(m_i,f)=H(m_i)-H(m_i|f)$ (4)

(4)

where H (m_i) represents the amount of expected information that set m carries itself with respect to movement m_i. Conditional entropy H (m_i|f) defines the expected amount of information the set m carries with respect to feature f and movement m_i.

Once all n-grams have an IG assigned to them for each movement, the list of IGs can be sorted to select t n-grams that have the best IG. This is a very simple approach because it does not consider correlation between features, meaning that some of the features can be redundant. However, even this simple approach can generate good results [56]. Information gain performance can also suffer from movement or subject-specific signal variations. For example, if a subject has a consistent way of performing a movement, which differs from other subjects, the information gain may select the subject-specific transitions as characteristic for the whole movement. In reality these transitions will not be observed from any other subject and represent an over-fitting. The over-fitting problem can be addressed by disqualifying n-grams that do not appear in enough training trials before the information gain is applied. This step makes selecting a clustering technique that creates a sufficient number of clusters even more important. If the number of primitives is low, selecting only the most frequent n-grams, before the information gain is applied, is likely to result in almost identical n-gram subsets selected for every movement.

7.1 Training

During the training phase of the execution, the system acquires parameters that can be used during the query processing. The training starts with selecting a portion of the available data trials for training. First and second derivatives are then extracted from each one of the trials for every sensing axis. Features are then normalized with respect to each subject using a standard score (or z-score) [48] in order to remove intersubject variations of the same movements. Then normalized features are used to define data clusters as described in section 4.1. Once the data clusters are defined, primitives are extracted for the data points in each training trial and then combined to define motion transcripts as described in section 4.2. The next step is to extract n-grams from each one of the transcripts generated for the training samples. Since the number of n-grams is very large, the system then selects a small number of t n-grams using the information gain as described in section 5.1. Finally, the system constructs a Patricia tree with selected n-grams on the edges and movement classes on the leafs as described in section 6. The overall process is demonstrated in Figure 6. The parameters defined during the training are data clusters for each sensing axis, n-grams selected with respect to the IG criteria, and the Patricia trees for classification. Clusters are represented by the cluster center coordinates, while important features selected for each sensing axis of each mote are then combined and stored.

7.2 Query Processing

When the system needs to search for a query or a movement, it receives input in the form of the sensor readings. First and second derivatives are extracted from the sensor readings of each of the sensing axes. Based on these features and clusters, defined during the training of the system, each data point of the trial is labeled with a primitive. Primitives are combined with respect to timing alignment into motion transcripts. The system then traverses the transcript of the trial and verifies if it contains important n-grams selected during the training. Using this information, the system traverses the Patricia tree defined for this sensing axis during the training and returns the set of movements assigned to the leaf where the traversal terminated. If the traversal terminated at node p that is not a leaf, the algorithm returns all the movements assigned to the leafs of the subtree rooted at node p. This allows the system to avoid introducing bias for the axis that observes the same signal for two different movements. Since all these operations are defined in terms of the individual sensing axis, an approach is required to combine the local decisions. A simple voting scheme is used, which performs well in the context of this dataset. However, this method can be improved by treating each sensory axis as an individual classifier. To determine the final decision, the individual classifiers can be combined in an intelligent way such as AdaBoost [58]. The flow of the query processing is demonstrated in Figure 7.

Because the system initially processes each sensing axis individually, it is possible to query only for a subset of axes available in the system. This can be useful when a specific sensor is not available to all users. For example, one user can use a three-dimensional gyroscope, while another may use only a two-dimensional gyroscope. Additionally, since the system uses a voting scheme, it is possible to make classification decisions based on the local view of only a subset of nodes.

8.1 k-Means or GMM?

The movement transcript generated based on the k-Means and GMM clustering was used to compare two clustering approaches for a 3-gram with the number of selected n-grams varying from 1 to 6 per sensing axis as shown in Table 3, and with {1..6}-gram with only 1 n-gram selected from each sensing axis as shown in Table 4. Both tables indicate that an increase in t or n would increase the precision and recall for both approaches until the over-fitting point is reached. It is also clear that the GMM approach outperforms the k-Means approach with respect to varying both n and k, and therefore is a better candidate for the example application.

8.2 Classification Accuracy

To evaluate classification accuracy, the precision and recall of movement classification were evaluated using the n-gram size of n=3 and number of features t={1, 2…5} with the GMM clustering model. Half of the dataset was used to train the system, while the other half was used to test it. The results of the classification are demonstrated in Table 5. The table contains the F-score defined as (2×P×R)/(P+R), where P is the classification precision and R is the classification recall. This table confirms that adding more n-grams would improve both average precision and average recall until an over-fitting point is reached. Note that individual values for movements sometimes decrease when an additional feature is selected. This is due to the fact that the data set has a considerable amount of noise, and while an n-gram improves the overall classification accuracy, it may cause confusion in classification of some trials where it appears as noise and not an important transition. Table 5 displays the number of n-grams extracted from each sensing axis, so the total number of the n-grams extracted by a sensor node should be multiplied by 5. However, even after that, the classification accuracy is fairly high for the number of features considered.

8.3 Parameter Trade-offs

The classification accuracy in the proposed data-mining approach depends on two parameters: the length of the substring n and the number of n-grams t selected for classification. As t is increasing, so does the accuracy until the over-fitting point is reached. After the over-fitting point is reached, the accuracy of the approach will no longer improve with additional features. It is clear that a large n inherently is able to capture more structural information. However, since a moving window is used for n-gram extraction, a single erroneous primitive affects more n-grams for larger values of n, which is equivalent to experiencing the over-fitting sooner. The algorithm is expected to converge to the best accuracy faster for large values of n, but it also means that the over-fitting point will happen faster. Table 6 demonstrates the F-score of accuracy vs. the number of n-grams t for different values of n.

From the tables, it is clear that higher values of n are desirable before over-fitting, which means that n should be determined based on the expected amount of noise in the original signal. For a lower amount of noise, a higher value of n would work better, while when the amount of noise is larger, lower values of n will provide a safer solution with less risk of over-fitting. In this example, the precision is improving from n=3 to n=5, it is fairly stationary from n=5 to n=7, and finally, at n=9 has decreasing performance. The fact that larger n-grams take more time to locate in the training trials should also be considered. The system can evaluate multiple possibilities during the training and generate the curves to identify the best operational point from the perspective of accuracy and speed trade-offs.

8.4 Movement Template Evaluation

Based on the parameters selected in section 8.3, T_i is defined as the combination sets of 3-grams selected for each sensing axis during the training process for movement M_i. Here the entire data set is used to train the templates. Once the training is complete and the templates are generated, the average quality measure is evaluated for each T_i. It is done by checking how often the n-grams of each T_i appear in movement trials of every movement. Intuitively, n-grams of T_i should appear more often in M_i than any other movement in order for the template to be effective. Table 7 demonstrates the results of this evaluation normalized with respect to the size of each template, meaning that on average, 51% of T₁ appear in trials of M₁, while only 36% of T₁ appear in trials of M₂.

Two observations can be made based on the results in Table 7. First, it is clear that n-grams of T_i appear most often in the M_i itself. This observation is in line with the expectation for a good template. While n-grams of the T_i , on average, appear 10% more often in the respective M_i , they also appear in trials of other movements with a sizable number of occurrences. These results suggest that a closer look on a per-trial basis is required to evaluate the template quality. The intuitive approach to this problem is to search for trials that have the entire template present. However, in a realistic system with noisy trials, this solution is not practical, since it’s unlikely that many trials will be perfect. Table 7 confirms this: the highest average values for each T_i are close to 50% and not 100%. This problem is solved by introducing a variable α, which defines the proportion of the number of n-grams from a T_i that need to be present in a trial for it to be classified as M_i. If the α value is too low, it is likely that some trials will be erroneously identified as M_i, increasing the number of false positives and decreasing the precision of the template. However, if the α value is too high, some trials of M_i will not be identified, increasing the amount of false negative errors and decreasing the recall of the template. Additionally, lower values of α can speed up the computation, which is desirable in our problem due to a potentially large number of movements in the repository. To achieve a balance between the precision and recall, as well as to promote faster data mining, the value of α=.5 is selected. The value of 50% is also suggested by Table 7, where the average presence of more than 50% n-grams from a template T_i identifies the movement M_i associated with that template. Table 8 demonstrates the normalized number of trials of each movement identified as M_i by each of the templates T_i, meaning, for example, that template T₁ selects 78% of trials belonging to M₁.

With α=.5, each T_i correctly identifies substantially more trials of its own movement than any other movement. This low value of α also defines a search speed increase of up to 50% since only 50% of the trials in templates need to be located. However, higher false negative and false positive errors are observed for certain templates, which suggests that a static value of α is inappropriate. Templates T₁ and T₂ do well at identifying only trials of their respective movements. However, less than half of the appropriate trials are identified. This suggests that the value of α=.5 is too high for these templates. At the same time, T₆ and T₇ have a much better rate of recognizing trials of their respective movements, but they also falsely identify trials of other movements. This suggests that the value of α=.5 is too low for these templates. Defining a movement-specific value of α_i, based on the training set for each template can decrease the amount of errors in the system.