sify subsets of the full temporal record. This reduces the time needed to obtain a classi cation result { an obvious bene t to real-time identi cation applications, ...
A Dynamic Feedforward Neural Network for Subset Classi cation of Myoelectric Signal Patterns K. Englehart, B. Hudgins, M. Stevenson and P.A. Parker The University of New Brunswick, P.O. Box 4400, Fredericton, N.B., Canada E3B 5A3
Abstract Many biological signals are transient in nature, and the myoelectric signal (MES) is no exception. This is problematic for pattern classi ers that fail to incorporate the structure present in the temporal dimension of these signals. Standard feedforward neural network classi ers have diculty processing temporal signals { time cannot be implicitly represented by the network architecture. A dynamic feedforward neural network architecture is described here that more e ectively integrates the temporal information in transient signals. The internal representation of time also allows the dynamic network to classify subsets of the full temporal record. This reduces the time needed to obtain a classi cation result { an obvious bene t to real-time identi cation applications, such as the control of prosthetic devices1. Keywords { Neural Networks, Myoelectric Signal, Prosthetic Control
Introduction There are two stages to the classi cation of temporal signals: signal representation and pattern classi cation. The signal representation stage must describe the dynamic evolution of the temporal waveform. This preprocessing should subtend a series of feature sets extracted from each of a series of short time windows { or frames { of the data. If a standard feedforward neural network is to be used as a pattern classi er, the series of feature sets must be concatenated to yield a single feature set that must be applied all at once to the network input. A standard network is static in the sense that the network output depends only on the present set of inputs. In this case, time is represented explicitly in the form of additional spatial dimensions at the network input. As an example of this type of analysis, Hudgins [1] observed apparent structure in the myoelectric signal (MES) acquired from the biceps and triceps upon the
onset of upper-limb motion. This motivated the development of a control scheme for powered arm prostheses by identifying limb function intent from these MES burst patterns. Hudgins proposed representing the raw MES by a set of simple time-domain features2 extracted from each of six 40ms frames segmenting a 240ms burst pattern. A standard feedforward neural network was trained { with encouraging success { to classify four distinct types of arm movement3. Some problems, however, accompany this approach to \parallelizing time": (i) an external bu er must \parallelize" the data, (ii) a rigid limitation is imposed on the duration of the patterns, (iii) all of the data representing a single pattern must be collected before presentation to the network, and (iv) patterns that are temporally proximal may be spatially distant [2]. A network more suitable to temporal pattern recognition would allow time to be represented implicitly rather than explicitly.
Methods
Dynamic neural network structures incorporate memory; the output depends upon both past and present inputs. A straightforward means of implementing a dynamic structure is to replace each synaptic scalar weight with a nite impulse response (FIR) lter. The resulting architecture has been referred to as both a FIR neural network (FIRNN) [3] and a timedelay network (TDNN) [4]. The neural network no longer performs a simple static mapping from input to output: internal memory has now been added. Since there are no feedback loops, the network as a whole is still FIR. The coecients for the synaptic lter connecting neuron j to neuron m in layer l are speci ed by the vector l = [wl (0); wl (0); : : :wl (M (l) )]T ; (1) wjm jm jm jm
2 Mean absolute value, di erential mean absolute value, This work was supported by Natural Sciences and Engi- waveform length, and zero crossings. 3 Flexion and extension of the elbow, medial rotation and neering Research Council grants, the Department of National Defense, Hugh Steeper Ltd., and the Whitaker Foundation. lateral rotation of the forearm. 1
Classification Rate (%)
where M (l) is the order of the lters in layer l. The 100 number of nodes in layer l is denoted by N (l) . The problem of pattern recognition imposes ad80 ditional constraints upon the network architecture. Consider the task of classifying a pattern { of length 60 T frames with an n-dimensional feature set extracted from each frame { as belonging to one of m classes. The number of network inputs is equal to the spatial 40 s.d.=7.5 dimension of the input signal pattern (N (0) = n), s.d.=5.0 s.d.=3.0 and the number of network outputs is equal to the 20 s.d.=1.5 (L) impulse number of possible pattern classes (N = m). The sum of FIR orders in each layer is chosen to match 0 0 5 10 15 20 25 30 the pattern length [5]: M (1) + M (2) + : : : + M (L) = Classification Frame T ; 1. During each pattern presentation, each of Figure 1 { Subset classi cation of the FIRNN. T n-dimensional input vectors is clocked into and through the network for k = 1; 2; : : :; K iterations4 . The weights of the network are updated so as to min- upon the maximum network output) was obtained at imize the following cost function: every frame. Figure 1 shows the classi cation rate achieved by P K NL 2 (p) (p) the FIRNN using Gaussian error scaling functions (w) = (k)(dm (k) ; ym (k)) (2) N (; ) of various widths. The horizontal axis indip=1 k=1 m=1 cates the number of frames presented to the FIRNN where P is the number of patterns in the training set, before classi cation was performed. As expected, the ym(p) (k) is the value of the mth node at the network network classi es best at frame T . The de nition output at iteration k, and d(mp)(k) is the corresponding of (k) a ects how the network classi es at frames desired response. The squared error is weighted by an other than T. Here, (k) = N (15; ) for =7.5, 5.0, error scaling function, (k). The choice of (k) and 3.0 and 1.5 frames; the response of the network is shown for impulsive error scaling. It is apparent d(mp) (k) speci es the error de nition and the desired also that increasing preserves classi cation performance response that the network will attempt to emulate at frames other than T, at the expense of reducing during training. the peak classi cation rate at frame T. Choosing an impulsive error scaling function The goal is to maintain an acceptable classi cation (k) = (T) amounts to using only the error at it- performance at frames preceding T. The standard deeration k = T , when the pattern completely lls the viation of the error scaling function the tradeo network. This is the error de nition of an equivalent evident in Figure 1. The Gaussianyields shape chostatic network. Of interest here is to enable the net- sen heuristically { other forms are possible. was A richer work to recognize patterns before frame T. To this feature set would translate all curves upward, possiend, (k) can be speci ed to allow errors from other bly allowing a broader error window and thus, robust frames to in uence (w). A Gaussian error window classi cation upon fewer frames. (centered at frame T) will weight errors near frame T most heavily, and those at the extremes the least. References 1. Hudgins, B., P.A. Parker, and R.N. Scott, \A new
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Results
The FIRNN was trained to classify MES patterns of duration T = 15 frames as belonging to one of the four classes described by Hudgins. A Gaussian error scaling function was used to weight the output errors. Once trained, the network was used to classify patterns from a set of test data. To clock an entire pattern through the network, 2T ; 1 = 29 iterations are required. A classi cation result (based 4 To fully clock the T -frame pattern in and out of the network, K = 2T ; 1.
strategy for multifunction myoelectric control", IEEE Trans. Biomed. Eng., vol. 40. No. 1, Jan., 1993. 2. Elman, J.L., \Finding structure in time," Cognitive Science, vol. 14, pp. 179{211, 1990. 3. Wan, E., \Finite Impulse Response Neural Networks with Applications in Time-Series Prediction," Ph.D. Dissertation, Stanford University, Stanford CA, Nov., 1993. 4. Waibel, A., et al., \Phoneme Recognition using timedelay neural networks," IEEE Trans. ASSP, pp. 328339, Vol. 37, No. 3, March, 1989. 5. Englehart, K.B., Hudgins, B., Stevenson, M. and P.A. Parker, \Myoelectric signal classi cation using a nite impulse response neural network," 16th Ann. Int. Conf. IEEE EMBS, pp. 1093-1094, Nov., 1994.
