IEEE TRANSACTIONS OF ROBOTICS, VOL. X, NO. Y, DATE

1

Improving Control of Dexterous Hand Prostheses
Using Adaptive Learning
Tatiana Tommasi, Francesco Orabona, Claudio Castellini and Barbara Caputo

Abstract—At the time of writing, the main means of control
for polyarticulated self-powered hand prostheses is surface electromyography (sEMG). In the clinical setting, data collected fromtwo electrodes are used to guide the hand movements selecting
among a finite number of postures. Machine learning has been
applied in the past to the sEMG signal (not in the clinical setting)with interesting results, which provide more insight on how
these data could be used to improve the prostheses functionality.
Researchers have mainly concentrated so far on increasing theaccuracy of sEMG classification and/or regression, but in general,a finer control implies a longer training period. A desirable
characteristic would be to shorten the time needed by a patient
for learning how to use the prosthesis.
To this aim, we propose here a general method to re-use pastexperience, in the form of models synthesized from previous
subjects, to boost the adaptivity of the prosthesis. Extensive tests
on databases recorded from healthy subjects in controlled andnon-controlled conditions reveal that the method significantly
improves the results over the baseline, non-adaptive case. This
promising approach might be employed to pre-train a prosthesis
before shipping it to a patient, leading to a shorter training phase.
Index Terms—learning and adaptive systems, prosthetics, electromyography, human-computer interfaces

I. I NTRODUCTIONI

N the prosthetics/rehabilitation robotics community it isgenerally understood nowadays [1], [2], [3] that advanced
hand prostheses are in dire need of accurate and reliable
control schemas to make them easy to use by the patient.
Together with excessive weight and low reliability, lack ofcontrol (inconsistency between the desired and performed
movements) is the main reason why 30% to 50% of upper-limb
amputees do not use their prosthesis regularly [4], although theexact factors leading to abandonment of a prosthesis seem todepend on the age and status of each subject, still remaining
to be thoroughly investigated [5].
The force-controlled and polyarticulated hand prosetheses
currently being used in the clinical setting are not yet comparable with non-prosthetic mechanical hands, but enjoy a highlevel of dexterity. They have five fingers and can potentiallyachieve an infinite number of configurations, e.g., the BeBionic
hand by RSL Steeper (www.bebionic.com), Vincent Systems’ Vincent hand (www.handprothese.de) and the i-LIMB
by Touch Bionics (www.touchbionics.com, see Figure 1).
T. Tommasi and B. Caputo are with the Idiap Research Institute, Martigny,
Switzerland, and the École Polytechnique Fédérale de Lausanne, Switzerland.
Email: tatiana.tommasi@idiap.ch, barbara.caputo@idiap.ch
Francesco Orabona, Toyota Technological Institute at Chicago, Illinois,
USA. Email: francesco@orabona.com
Claudio Castellini is with the Robotics and Mechatronics Center, German Aerospace Research Center, Oberpfaffenhofen, Germany. Email: claudio.castellini@dlr.de

Fig. 1.
Dexterous hand prostheses: (left to right) RSL Steeper’s
BeBionic (reproduced from www.bebionic.com), Vincent Systems’ Vincent hand (www.handprothese.de) and Touch Bionics’s i-LIMB Ultra(www.touchbionics.com).

However, control by the patient is poor, and it is still enforced
using two surface electromyography (sEMG) electrodes andcomplex sequences of muscle contraction impulses; this isessentially an old scheme enforced since the 1960s [6], [7],[8]. The patient must get acquainted and proficient with this“language” if (s)he wants to achieve a minimum degree ofcontrol over the prosthesis.
To overcome this drawback, a more “natural” form ofcontrol has been individuated and studied since two decades;
namely, sEMG has been revamped by the application of machine learning techniques. More electrodes (typically 5+) andcomplex statistical classification/regression techniques (e.g.,
support vector machines [9], linear discriminants [10], [11],neural networks [12]) allow, at least in principle, to more easily
detect what the patient wants to do. The word “natural” hereis still quite a misnomer, as it refers to the choice among
a finite number of predefined hand configurations; but thiskind of control is still much more natural than before, as eachposture is achieved by configuring one’s muscle remnants asthey would be if the missing limb were still there. Recent
results on amputees indicate that even long-term patients cangenerate rather precise residual activity, to the extent that
there is essentially no statistically significant difference inthe classification/regression accuracy attained by trans-radial
amputees and intact subjects [9], [13].
In this paper we concentrate upon a specific aspect ofhand prostheses control, namely, we try to reduce the training
time, i.e. the time required to perform the adaptation of theprosthesis itself to the patient. Anatomical similarity among
humans intuitively suggests that good statistical models built in
the past might be proficiently reused when training a prosthesis
for a new patient. This idea cannot be naı̈vely enforced
with standard learning techniques, as shown at least in [14],where cross-subject analysis (i.e., using a model trained onIEEE TRANSACTIONS OF ROBOTICS, VOL. X, NO. Y, DATEa subject to do prediction on a new subject) is performed
with poor results. We present here a more refined approachto the problem exploiting adaptive learning in order to boost
the training phase of a hand prosthesis by reusing previous
experience.
We build on our own previous work [15] which proposed a
principled method to choose one among multiple pre-trainedmodels on known subjects as source for adaptation, and toevaluate the right degree of closeness to the target task for a
new subject. This approach was based on an estimate of themodel generalization ability through the leave-one-out error
which was minimized solving a non convex optimization task.
Here we improve the original method in two key aspects:(1) we constrain the new model, to be close to a linear
combination of pre-trained models stored in the memory of
the prosthesis; (2) the learning process to define from whomand how much to adapt is now defined through a convex
optimization problem avoiding local minima issues. This leadto a bootstrapping in the control abilities of the new subject,
who can now acquire control of the device faster than what
would be achieved without adaptation.
We test our method on two databases. The first is the one
already described in [14], [15], consisting of sEMG, postureand force signals gathered from 10 intact subjects in various(controlled, non-controlled) laboratory situations. The second
is the NinaPro database [16], a publicly available databasewhich contains kinematic and sEMG data from the upper
limbs of 27 intact subjects while performing a total of 52 handpostures. The benefits are apparent and the perspective is thatof shipping a pre-trained prosthesis which would very quickly
adapt to the patient, with the effect of enabling him/her to ahigher comfort and aid during daily-life activities.
The paper is organized as follows: after reviewing related
work, in Sections II and III we present our method. Section
IV describes the databases used, while Section V shows anddiscusses the results. Lastly, Section VI contains conclusions
and ideas for future work.
A. Related work
1) Using sEMG for hand prostheses: Surface EMG detects
muscle unit activation potentials, which typically present aquasi linear relation with the force exerted by the muscle towhich the electrode is applied. In the more specific case ofhand prostheses, several electrodes are applied to the forearm(or stump) while the subject reaches specific hand configurations (postures) and/or grabs a force sensor. The raw sEMG
signal is then preprocessed (filtered, rectified, subsampled);features are subsequently extracted from it and fed, together
with force values and labels denoting the postures, to a(usually supervised) machine learning method. Hand postures
can be classified accordingly, and the force applied is predictedusing a regression scheme. The two processes can happen
simultaneously [17]. Up to 12 hand postures [13] have beenclassified with acceptable accuracy, and there are strong hints[18], [9], [13], [19], [20] that with data from trans-radial
amputees it may be possible to achieve similar performance.
Comprehensive surveys can be found in [21], [2], [3] andthe most recent results at the time of writing are probably

2

those exposed in [22], [23], [24] and [25]. The use of sEMG
has been widely explored and a number of possible features
have been extracted and tested with many machine learning
methods.
2) Adaptive learning: One of the main assumptions ofmachine learning is that the training data on which any method
is learned and the test data on which it is verified are drawn
from the same distribution. However, in real problems this is
not always the case and adaptive learning is used to overcome
the distribution mismatch. In general the goal of transfer learning [26] and domain adaptation [27] is to reuse information
gathered on some source task when solving a new target
problem and they respectively address two aspects of thisproblem. Transfer learning focuses mostly on binary tasks andon the use of helpful information across different categories(classes with different labels). Domain adaptation considers
the possibility to exploit common information among slightly
different tasks when the set of labels is the same. By applying
domain adaptation, data collected in different domains can beused together (source + target) or it is possible to leverage on
pre-trained models built on rich training sets (source) whenfacing the same problem in a new domain with few available
samples (target).
In the last years, various techniques for domain adaptationand transfer learning have gathered attention in natural language processing [28], [29], computer vision [30], [31] andsentiment classification [32], [33]. Many adaptive methods
have been compared and benchmarked in [29], however mostof them are computationally inefficient because it is necessary
to retrain each time over old source and new target data. An
approach that does not use re-training, based on SVMs has
been proposed in [34], but the authors do not address thepossibility that the known source model may be too different
from the new target one because of high variability between
the two domains.
3) Adaptive learning on sEMG data: Adaptive learning canbe used to augment the prostheses control and in particular to
shorten the training time/aid the collection of training data.
One interesting attempt in this direction can be foundin [35], where two adaptive methods (one supervised, one
unsupervised) are shown to dramatically outperform a nonadaptive approach.
The solution of adapting from data collected on different
subjects is adopted in [36]: decoupling between subjectdependent and motion-dependent components is enforced on alimited dataset, and an improvement over the baseline method
is shown. In [37] samples from multiple source subjects are
combined to the target subject samples. When learning thefinal classifier on the whole set of data a weighting factor
is added to evaluate the real relevance of each source withrespect to the target task. The sensitivity of the method to thisparameter is evaluated empirically, but how to choose it is left
as an open problem.
In [15] we proposed an approach that exploited previously
trained models on known subjects as a starting point whenlearning on a new one. This method chooses automaticallythe best prior knowledge to use and how much to rely on
it, overcoming at the same time the problems present inIEEE TRANSACTIONS OF ROBOTICS, VOL. X, NO. Y, DATE

3[37] and [34]. Compared with [35] that performs adaptation
during the prediction task, our algorithm defines a way ofboosting the performance in training, i.e. before beginningthe prediction. We propose here to enlarge the approach in[15], even building over our [31] that shares the same basic
mathematical framework. Specifically we propose a novel
multiclass adaptive learning method able to rely over manyprior knowledge models at the same time, with the aim to
exploit at the best all the available information.
II. D EFINING THE A DAPTIVE M ODELIn this section we describe the mathematical framework at
the basis of our adaptive learning method. We first introduce
the basic notation (Section II-A), then we present our algorithm for online model adaptation from the best known subject(Section II-B) and how to enlarge it to exploit multiple known
subjects (Sections II-C). We end explaining how to extend thedescribed approach in the multiclass setting (Section II-D).
In the following we denote with small and capital bold
letters respectively column vectors and matrices, e.g. a =[a1 , a2 , . . . , aN ]T ∈ RN and A ∈ RG×N with Aji
corresponding to the (j, i) element. The subscripts indicate
specific rows and columns. When only one subscripted index
is present, it represents the column index: e.g. Ai is the i-th
column of the matrix A.
A. Background
Assume xi ∈ Rm is an input vector and yi ∈ R is
its associated output. Given a set {xi , yi }N
i=1 of samples
drawn from an unknown probability distribution, we wantto find a function f (x) such that it determines the best
corresponding y for any future sample x. This is a generalframework that includes both regression and classification. The
problem can be solved in various ways. Here we will use
kernel methods and in particular Least-Squares Support Vector
Machines (LS-SVM, [38]). In LS-SVM the function f (x) is
built as a linear model w · φ(x) + b, where φ(·) is a nonlinear function mapping input samples to a high-dimensional(possibly infinite-dimensional) Hilbert space called feature
space. Rather than being directly specified, the feature space isusually induced by a kernel function K(x, x0 ) which evaluates
the inner product of two samples in the feature space itself,
i.e. K(x, x0 ) = φ(x) · φ(x0 ). A common kernel function is
the Gaussian kernel:
K(x, x0 ) = exp(−γ||x − x0 ||2 )(1)that will be used in all our experiments.
The parameters of the linear model, w and b, are foundby minimizing a regularized least-squares loss function [38].
This approach is similar to the well-known formulation of
Support Vector Machines (SVMs), the difference being thatthe loss function is the square loss which does not induce
sparse solutions.
This formulation can be easily generalized to the multiclass classification, where we have g = 1, . . . , G different
classes. Consider one model for each class, wg and bg , that
discriminates one class against the others (one-vs-all). Hencemodel g is trained on the binary problem to distinguishclass g considered as positive, from all the others, considerednegative. The predicted class for sample i is then defined asargmaxg {wg · φ(xi ) + bg }.
A key concept that we will use is the one of leaveone-out predictions [39]. Denote by ỹi , i = 1, . . . , N , theprediction on sample i when it is removed from the training
set and by `(y, ỹ) a generic loss function that measuresthe lossPof predicting ỹ when the true label is y. We haveNthat N1 i=1 `(yi , ỹi ) is an almost unbiased estimator of theclassifier generalization error [40], measured using `.
LS-SVMs make it possible to write the leave-one-out
predictions in closed form and with a negligible additional
computational cost [39]. This property is useful to find thebest parameters for learning (e.g. γ in (1)) and it will be
used in our adaptation method. Note that we use the samegeneral formulation to solve both regression and classification
problems.

B. Model Adaptation from the Best Subject
Let us assume we have K pre-trained models stored inmemory, trained off-line on data acquired on K different
subjects. When the prosthetic hand starts to be used by subject
K + 1, the system begins to acquire new data. Given the
differences among the subjects’ arms and as well in theplacement of the electrodes, these new data will belong to
a new probability distribution, in general different from the K
previously modeled and stored. Still, as all subjects performthe same grasp types, it is reasonable to expect that the new
distribution will be close to at least one of those alreadymodeled; then, it should be possible to use one of the pretrained model as a starting point for training on the new data.
We expect that, by doing so, learning should be faster thanusing the new data alone. To solve this problem we generalize
the adaptation approach proposed in [34] for SVMs: the basic
idea is to slightly change the regularization term of the SVM
cost functional, so that the solution will be close to the pretrained one. The optimization problem is:
min
w,b

N
X
1
kw − ŵk2 + C
ξi
2
i=1

subject to ξi ≥ 0, yi (w · φ(xi ) + b) ≥ 1 − ξi(2)where ŵ is a pre-trained model and C is a parameter totrade-off the errors and the regularization. In order to tune
the closeness of w to ŵ, we introduce a scaling factor βweighing the pre-trained model; also, we use the square loss
and therefore resort to the LS-SVM formulation. In this way
the leave-one-out predictions can be evaluated in closed form,
enabling automatic tuning of β. The optimization problem
reads now like this [15]:
min
w,b

N
CX 2
1
kw − β ŵk2 +ξ2
2 i=1 isubject to yi = w · φ(xi ) + b + ξi

(3)IEEE TRANSACTIONS OF ROBOTICS, VOL. X, NO. Y, DATE

4

and the corresponding Lagrangian problem is:

The complexity of the algorithm is dominated by the evaluation of the matrix P , which must anyway occur while training;
thus, the computational complexity of evaluating the leaveone-out errors is negligible, if compared to the complexity of
training. As a last remark, we underline that the pre-trainedmodel ŵ can be obtained by any training algorithm, as far
as it can be expressed as a weighted sum of kernel functions.
The framework is therefore very general.

N
X

N
X

C
1
kw−β ŵk2 +ξ2 −ai {w·φ(xi )+b+ξi −yi } ,22 i=1 i i=1(4)where a ∈ RN is the vector of Lagrange multipliers. The
optimality conditions can be expressed as:
L=

N
X
∂L
= 0 =⇒ w = β ŵ +ai φ(xi ) ,
∂w
i=1

∂L
= 0 =⇒∂bNX

ai = 0 ,

(5)

(6)

i=1

∂L
= 0 =⇒ ai = Cξi ,
(7)
∂ξi
∂L
= 0 =⇒ w · φ(xi ) + b + ξi − yi = 0 . (8)∂aiFrom (5) it is clear that the adapted model is given by thesum of the pre-trained model ŵ (weighted by β) and a newmodel w obtained from the new samples. Note that when β
is 0 we recover the original LS-SVM formulation without any
adaptation to previous data. Using (5) and (7) to eliminate w
and ξ from (8) we find that:NX

aj φ(xj ) · φ(xi ) + b +j=1ai= yi − β ŵ · φ(xi ) .
C(9)Denoting with K the kernel matrix, i.e. K ji = K(xj , xi ) =φ(xj ) · φ(xi ), the obtained system of linear equations can be
written more concisely in matrix form as:


 

a
y − β ŷK + C1 I 1
=
,
(10)
b
0
1T
0
where y and ŷ are the vectors containing respectively the label
samples and the prediction of the previous model i.e. y =[y1 , . . . , yN ]T , ŷ = [ŵ · φ(x1 ), . . . , ŵ · φ(xN )]T . Thus themodel parameters can be calculated with:




a
y − β ŷ
=P
,
(11)
b
0
where P = M −1 and M is the first matrix on the left in(10).
We now show that for (3) it is possible to write theleave-one-out predictions in a closed formula (proof in the
Appendix). Let [a0T , b0 ]T = P [y T , 0]T and [a00T , b00 ]T =P [ŷ T , 0]T with a = a0 + βa00 , then
Proposition 1. The prediction ỹi , obtained on sample i when
it is removed from the training set, is equal toa00
a0i+β i .
(12)
Pii
Pii
Notice that in the above formula β is the only parameter,
hence, it is possible to set it optimally in order to minimize
the sum of the leave-one-out errors `(yi , ỹi ), while at thesame time choosing the best pre-trained model for adaptation.
Moreover, a depends linearly on β, thus it is straightforward
to define the learning model which is fixed once β has beenchosen.
yi −C. Model Adaptation from Multiple Subjects
The approach described in the previous Section has amain drawback: although many prior knowledge models areavailable, it uses only one of them, selected as the most usefulin term of minimal leave-one-out errors. Even if the pre-trainedmodels are not equally informative, relying on more than oneof them may be beneficial. To this goal it is possible to define a
new learning problem which considers the linear combinationof all the known models [31]:
2

K

X
1
w−
β k ŵk
min
w,b 2
k=1

N

+

CX 2
ξ
2 i=1 isubject to yi = w · φ(xi ) + b + ξi .

(13)

The original single coefficient β has been substituted with avector β containing as many elements as the number of priormodels, K. For this formulation the optimal solution is:
w=

K
X

k

k

β ŵ +NX

ai φ(xi ) .

(14)

i=1

k=1

Here w is expressed as a weighted sum of the pre-trainedmodels scaled by the parameters β k , plus the new model
built on the incoming training data [31]. The leave-one-out
prediction of each sample i can again be written in closed
form, similarly to Proposition 1, asKỹi = yi −X a00ka0i+
βk i ,
Pii
Pii

(15)

k=1

where [a00kT , b00k ]T = P [ŷ kT , 0]T and ŷ k is the vector
which contains the predictions of the k-th previous model[ŵk · φ(x1 ), . . . , ŵk · φ(xN )]. As before, the leave-one-out
errors can be calculated and minimized to evaluate the best
weights β k .
D. Multiclass Extensions
In case of classification problems, the methods discussed tillhere are suitable for binary tasks but can be extended to thecase of G classes using the one-vs-all formulation described in
Section II-A. We define the matrix Y ∈ RG×N composed by
the columns Y i , where for each sample i the vector Y i has all
the components equal to −1 except for the yi -th that is equal
to 1. In the same way, define the matrix Ŷ , composed by thecolumns Ŷ i that contain the predictions generated by a known
multiclass model on the sample i. For each sample i we also
obtain a vector of G leave-one-out predictions, we indicate itwith Ỹ i , and it is easy to show that it can be calculated asỸ i = Y i −A0i
A00+β i ,
Pii
Pii

(16)

IEEE TRANSACTIONS OF ROBOTICS, VOL. X, NO. Y, DATE

51) Best Prior Model: A first solution could be to consider:

where
0

0

[A , b ] = [Y , 0]P

T

,

(17)

[A00 , b00 ] = [Ŷ , 0]P T .

(18)

Here A0 , A00 ∈ RG×N and b, 0 ∈ RG . In case of multiple
prior models, we use the superscript k to indicate each ofthem and, considering their linear combination, we get
KỸ i = Y i −A0i X k A00k
i
+
,
β
Pii
Pii

(19)

k=1

with
k

[A00k , b00k ] = [Ŷ , 0]P T .

(20)`(Y i , Ỹ i ) =1,
1 + exp(−10(maxg6=yi {Ỹgi } − Ỹyi i ))and to evaluate it separately for each of the k ∈ {1, . . . , K}
pre-trained models on the basis of (16), varying β with small
steps in [0, 1] (this is the approach used in [15]). The minimal
result identifies both the best known subject for adaptation and,at the same time, the corresponding β. Still, this approach,as (21), is non-convex thus reaching the global optimum is
not computationally efficient. This solution is schematically
depicted in Figure 2 (left).
2) Multiple Prior Models: To consider multiple priorknowledge models we propose to use (19) in the convex
multiclass loss [41]:`(Y i , Ỹ i ) = max{1 − Ỹyi i + max{Ỹgi }, 0}.
g6=yiIII. L EARNING H OW M UCH TO A DAPTThe adaptive learning methods described above look for themodel parameters (w,b) once the value of the weight β, orthe corresponding vector β, has been chosen. Searching the
optimal β defines a separate learning problem which depends
on the choice of the loss function `. As a result we havean indication of how much each of the pre-trained models isreliable for adaptation. In the following we define how to face
this issue in the classification and regression cases, a generalscheme of the proposed solutions is in Figure 2.

A. Classification
For a binary classification problem, and in case of a single
pre-trained model, we can follow the approach proposed in[39] and find β by minimizing leave-out-out errors using thelogistic loss function:`(yi , ỹi ) =1.
1 + exp(−10(ỹi − yi ))(21)

Note that the resulting objective function would be non-convex
w.r.t. β. When moving to the choice of multiple weights
for all the pre-trained models we can also overcome thenon-convexity issue described above, by minimizing the loss
function proposed in [31]:`(yi , ỹi ) = max(1 − yi ỹi , 0),(22)this is a convex upper-bound to the misclassification loss andit also has a smoothing effect, similar to the logistic functionin (21).
However in our application we have multiple pre-trainedmodels and G classes, corresponding to the different grasp
types. Hence it is necessary to define a loss function overvectors, that compose all these values to define a single
estimate of the multiclass error.

(23)

(24)

This loss is zero if the confidence value for the correct label
is larger by at least one than the confidences assigned to therest of the labels. Otherwise, we suffer a loss which is linearly
proportional to the difference between the confidence of thecorrect label and the maximum among the confidences of theother labels. The final objective function is:
min
β

N
X

`(Y i , Ỹ i ) subject tokβk2 ≤ 1,

βk ≥ 0 . (25)i=1

The condition of having β in the intersection of the unitaryball and the positive semi-plane can be seen as a form of
regularization and it is a natural generalization of the original
constraint β ∈ [0, 1] used in [15]. This constraint is necessary
to avoid overfitting problems which can happen when thenumber of known models is large compared to the numberof training samples [31].
We implemented the optimization process using a simple
projected sub-gradient descendent algorithm, where at each
iteration β is first projected onto the l2 -sphere, kβk2 ≤ 1
and then onto the positive semi-plane. The pseudo-code isin Algorithm 1, where in line 8 1{·} denotes the indicatorfunction. Figure 2 (center) describes this solution.
3) Different Weights for Different Classes: Until now we
considered techniques which assign a unique weight to each
known subject. This means that, the whole set of one-vsall pre-trained models for a subject are equally weighted.
However, for example, when learning the model for the firstclass, it may be useful to give more weight in adaptation to
the first subject than to the second, while it could be theopposite when learning the model for the second class, andso on. Hence, to have one more degree of freedom and decide
the adaptation specifically for each class, we enlarge the set ofweight parameters introducing the matrix B ∈ RK×G where
each row k ∈ {1, . . . , K} contains the vector β Tk with G
elements, one for each class. This approach is described in
Figure 2 (right).
The optimization problem is analogous to the one describedin (25), with a change in the constraints. Each class problem is
now considered separately, so we have G conditions, one forIEEE TRANSACTIONS OF ROBOTICS, VOL. X, NO. Y, DATE

6

Fig. 2. This figure shows the three methods adopted to leverage information from multiple known subjects when learning on a new one. For all the known
subjects many sEMG signal samples are available, while few sEMG signals are recorded from the new subject. Left: choose only the best known subject anduse its reweighted model as a starting point for learning. Center: consider a linear combination of the known subjects with equal weight for all the grasp
models of each subject. Right: consider again a linear combination of all the known models but assign a different weight to each grasp model for each subject.

Algorithm 1

Projected Sub-gradient Descent Algorithm

1: β = [β1 . . . βK ] ← 0
2: t ← 1
0

3: calculate A
4: calculate A

according to (17)00kaccording to (20)

5: repeat
A0

PK

00k

k Ai
Pii

∀i = 1, . . . , N

6:Ỹ i ← Y i − Piii +7:gi∗ ← argmaxg6=yi {Ỹgi } , ∀i = 1, . . . , N

8:di ← 1{1 − Ỹyi i + Ỹgi∗ i > 0} , ∀i = 1, . . . , N

9:β k ← β k − √1t

10:

if kβk2 > 1 then11:β ← β/kβk2

PN

k=1 β

i=1 di00k(A00k
g ∗ i −Ay i )
i

i

Pii

12:

end if13:

β k ← max(β k , 0), ∀k = 1, . . . , K

14:

t←t+1

, ∀k = 1, . . . , K

15: until convergence

Similarly to what we showed before, it is possible to learn
the regression model relying on information from the closest
known subject, or on the combination of multiple pre-trainedmodels.
1) Best Prior Model: We can use the leave-one-out prediction in (12) to evaluate the square loss (Mean Square Error
MSE):
 0
2
a00
ai
`(yi , ỹi ) = (yi − ỹi )2 =
+β i
.
Pii
Pii
The choice of the square loss gives us, summing over i, aquadratic function in β and the minimum is obtained using:PN a0i a00i
β=P

i=1 Pii Pii
 00 2
ai
Pii

.

(26)

N
i=1

We use the constraint β ≥ 0, just imposing β = 0 every time
it results negative. Hence, differently from the classificationcase, here we do not need any optimization procedure, theoptimal β is given by a closed formula. Once calculated theminimum value of the summed square loss values for eachk ∈ {1, 2, . . . K}, comparing all of them, we can identify thebest known subject to use for adaptation when learning theregression model on a new subject.

B. Regression2) Multiple Prior Models: To take advantage from all theavailable pre-trained models we can combine them linearlyand search for a vector of weights as in classification. Hencethe loss function ` can now be defined as
!2
K
00k
X
a0i
a
+
.
(27)
`(yi , ỹi ) =
βk i
Pii
Pii

Our goal in using regression is the prediction of the force
applied by one subject in grasping, independently of thespecific kind of grasp performed. Thus now the output yi foreach corresponding input xi is a continuous real value, rather
than a discrete one as in classification.

Adding also the condition kβk2 ≤ 1, we can find the best
β vector which minimizes the loss with a Quadratically Constrained Quadratic Program (QCQP) solver. In our experiments
we used CVX [42], a package for specifying and solving
convex programs in MATLAB.

Output: βeach of the columns Bg of the B matrix, we impose kBg k2 ≤1 and Bji ≥ 0.

k=1

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7

(a)

(b)

(c)

Fig. 3. The three different grasp type recorded in the hand posture and force signal dataset [14]: (a) index precision grip; (b) other fingers precision grip;(c) power grasp. Reproduced from [14].

(a)

(b)

(c)

(d)

(e)

(f )

Fig. 4. The six different grasp types extracted from the Ninapro dataset [16]: (a) tip pinch grasp; (b) prismatic four fingers grasp; (c) power grasp; (d)parallel extension grasp; (e) lateral grasp; (f ) open a bottle with a tripod grasp. Reproduced from [16].

IV. E XPERIMENTAL DATA
To test the effectiveness of our model adaption techniques
we use two datasets.
a) Hand posture and force signals [14]: This database ofsEMG / hand posture / force signals has been already presented
in [14], and used in [14], [15]. (The following description of
the database is very concise; the interested reader should referto the above cited paper(s) for more details.) The signals arecollected from 10 intact subjects (2 women, 8 men) using 7
sEMG electrodes (Aurion ZeroWire wireless) placed on thedominant forearm according to the medical literature [43]. A
FUTEK LMD500 force sensor [44] is used to measure theforce applied by the subject’s hand during the recording. Data
are originally sampled at 2kHz. Each subject starts from a rest
condition (sEMG baseline activity) then repeatedly grasps theforce sensor using, in turn, three different grips, visible in
Figure 3. The subject either remains seated and relaxed while
performing the grasps, or is free to move (walk around, sit
down stand up, etc.). These phases are referred to as Still-Arm(SA) and Free-Arm (FA) respectively. Each grasping action isrepeated along 100 seconds of activity. The whole procedure
is repeated twice. The root mean square of the signals along
1s (for classification) and 0.2s (for regression) is evaluated;subsampling at 25Hz follows. Samples for which the applied
force is lower than 20% of the mean force value obtainedfor each subject are labeled as “rest” class. After this preprocessing we got around 15000 samples per subject, eachsample consists of a 7 elements sEMG signal vector and one
force value.
b) Ninapro [16]: This database has been presented in[16] and already used in [45]. It contains kinematic and sEMG

data from the upper limbs of 27 intact subjects (7 women,
20 men) while performing 12 finger, 9 wrist, 23 grasping
and functional movements, plus 8 isometric, isotonic handconfigurations. Data are collected using 10 surface sEMG
electrodes (double-differential OttoBock MyoBock 13E200),
8 placed just beneath the elbow at fixed distance from theradio-humeral joint, while 2 are on the flextor and extensor
muscles. Each subject sits comfortably on an adjustable chairin front of a table and is instructed to perform ten repetitionsof each movement by imitating a video, alternated with a rest
phase. The sEMG electrodes are connected to a standard DAQ
card sampling the signals at 100 Hz and provide an RMS
rectified version of the raw sEMG signal. (For a more detailed
description of the dataset the interested reader should referto [16],[45]). We focused only on the grasp and functional
movements extracting 6 actions: tip pinch, prismatic four
fingers, power, parallel extension, lateral and open a bottlewith a tripod grasp (see Figure 4). Each of them belongs to adifferent branch of a hierarchy containing all the dataset handpostures and the first three grasps are the most similar to theones considered in [14]. We randomly extracted two sets of 10
and 20 subjects from the dataset and performed classification
experiments on the described 7 class (6 grasps plus rest)
problem considering the Mean Absolute Value (MAV) of thesEMG signal as time domain features [45]. We repeated thepreprocessing and data split procedure described in [45] withan extra subsampling of the “rest” data to get a class-balanced
setting.

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8

V. E XPERIMENTAL R ESULTS

excluded form the dataset and the parameters are chosen over
the remaining set K = {1, . . . , K\k ∗ } looking for the values
that produce on average the best recognition rate or correlation
coefficient by learning on each subject k in K and testing on{K\k ∗ , k}.

As already mentioned in Section II-B, our working assumption is to have K pre-trained models stored in memory; newdata comes from subject K + 1 and the system starts training,to build the K +1’th model. The performance is then evaluatedusing unseen data from subject K+1. To simulate this scenario
and to have a reliable estimation of the performance, we use aleave-one-out approach: out of the 10(20) subjects for which
we have data recordings, we train 9(19) models off-line. These
correspond to the K stored models in memory, while data fromthe remaining subject are used for the adaptive learning of theK+1’th model. This procedure is repeated 10(20) times, using
in turn all the recorded subjects for the adaptive learning of
the model.
We name the proposed adaption methods respectively:
Best-Adapt: adaptive learning starting from the best priorknowledge model (method originally presented in [15] andrevised here in Section III-A1);• Multi-Adapt: adaptive learning starting from a linear combination of the known models (Section III-A2);• Multi-perclass-Adapt: adaptive learning (for classification)
starting from a linear combination of the known models
with a different weight for each class (Section III-A3).
•

To assess the performance of all these methods we comparethem to three baseline approaches:
No-Adapt: is plain LS-SVM using only the new data fortraining, as it would be in the standard scenario without
adaption.
• Prior Average: consists in using only the pre-trained models without updating them with the new training data. We
consider their average performance.
• Prior Start: this corresponds to the performance of the bestmodel chosen by Best-Adapt at the first training step.
• Prior Test: this is the result that can be obtained a posteriori comparing all the prior knowledge models on the test
set and choosing the best one.
•

As a measure of performance, for classification we use thestandard classification rate; for regression, the performanceindex is the correlation coefficient evaluated between the predicted force signal and the real one. Although we minimized
the MSE in the regression learning process, the choice ofthe correlation coefficient is suggested by a practical consideration: when driving a prosthesis, or even a non-prosthetic
mechanical hand, we are not interested in the absolute force
values desired by the subject: mechanical hands usually cannot
apply as much force as human hands do, for obvious safety
reasons, or e.g., in teleoperation scenarios, they could be able
to apply much more force than a human hand can. As alreadydone, e.g. in [17], [9], [14], we are rather concerned withgetting a signal which is strongly correlated with the subject’s
will. The significance of the comparisons between the methods
is evaluated through the sign test [46].
To build the pre-trained models we used the standard SVM
algorithm. All the parameters to be set during training (C andγ of the Gaussian kernel) were chosen by cross-validation.
Specifically when the subject k ∗ is the new problem, this is

A. Hand posture and force signals [14]For the experiments running on the dataset described in[14], the training sequences are random subsets from theentire dataset of the new subject, i.e. they are taken without considering the order in which they were acquired. We
considered 24 successive learning steps, for each of them thenumber of available training samples increases by 30 elements
reaching a maximum of 720 samples. The test runs over all theremaining samples. We conducted three sets of experiments
considering different prior knowledge-new problem couples:
SA-SA, FA-FA and SA-FA. In the first two cases we haveconsistent recording conditions among the source and the newtarget problem. The last case reproduces the more realistic
scenario where the prior knowledge is built on data recordedon subjects in laboratory controlled conditions while the new
subject moves freely. We both classify the grasp type andpredict the force measured by the force sensor.
Figure 5 (left) reports the obtained classification rate ateach step when using SA-SA data. The plot shows that Multiperclass-Adapt outperforms both the baselines No-Adapt, Priors, and all the other adaptive learning methods. The difference
between Multi-perclass-Adapt and Best-Adapt shows an average advantage in recognition rate of around 2% (p < 0.03).
The gain obtained by Multi-perclass-Adapt with respect to NoAdapt (p < 0.003) stabilizes around 5% for 500-720 training
samples.
Analogous results are obtained when considering FA-FA
data: Figure 5 (center) reports the classification rate resultsin this setting. Multi-perclass-Adapt shows again the best
performance, but now the advantage with respect to BestAdapt is significant (p < 0.03) only for less than 100
training samples. Multi-perclass-Adapt outperforms No-Adapt(p < 0.03) with a gain of 4% in recognition rate for 500-720
samples.
Finally, Figure 5 (right) shows the SA-FA results. Herethe statistical comparison among Multi-perclass-Adapt, BestAdapt and No-Adapt is the same as in the FA-FA case.
Analyzing Figure 5 as a whole, we can state that all the
proposed adaptive methods outperform learning from scratchwith the best results obtained when exploiting a linear combination of pre-trained models with a different weight foreach known subject and each class (Multi-perclass-Adapt).
Moreover, we notice that learning with adaption with 30
training samples performs almost as No-Adapt with around
300 samples. Considering the acquisition time, this means thatthe adaptive methods are almost ten time faster than learningfrom scratch. Using the prior knowledge by itself appears asa good choice if only very few training samples are available
but loses its advantage when the dimension of the training set
increases. Passing from SA-SA and FA-FA to SA-FA we canalso notice that the results for Prior Average show a small

IEEE TRANSACTIONS OF ROBOTICS, VOL. X, NO. Y, DATE

9Classification, FA−FA, 10 subjects 3 postures

Classification, SA−FA, 10 subjects 3 postures
75

70

70

70

65
60
55
50
Multi−perclass−Adapt
Multi−Adapt
Best−Adapt [15]No−Adapt
Prior Test
Prior Average
Prior Start

45
40
35
30
0

100

200

300

400

500

600

700

65
60
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50
Multi−perclass−Adapt
Multi−Adapt
Best−Adapt [15]No−Adapt
Prior Test
Prior Average
Prior Start

45
40
35
30
0

800

Classification Rate (%)

75

Classification Rate (%)

Classification Rate (%)

Classification, SA−SA, 10 subjects 3 postures
75

100

200

Number of Samples

300

400

500

600

700

65
60
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50
Multi−perclass−Adapt
Multi−Adapt
Best−Adapt [15]No−Adapt
Prior Test
Prior Average
Prior Start

45
40
35
30
0

800

100

200

Number of Samples

300

400

500

600

700

800

Number of Samples

Fig. 5. Hand posture and force signals dataset [14]. Classification rate obtained averaging over all the subjects as a function of the number of samples
in the training set. The title of each figure specifies if the data used as source and target are registered in Still-Arm (SA) or Free-Arm (FA) setting.

Regression, SA−SA, 10 subjects 3 postures

Regression, FA−FA, 10 subjects 3 postures

0.86

0.84

0.82

Multi−Adapt
Best−Adapt [15]No−Adapt
Prior Test
Prior Average
Prior Start

0.8

0.78
0

100

200

300

400

500

600

700

0.88

0.86

0.84

0.82

Multi−Adapt
Best−Adapt [15]No−Adapt
Prior Test
Prior Average
Prior Start

0.8

0.78
0

800

Correlation Coefficient

0.88

Correlation Coefficient

Correlation Coefficient

0.88

Regression, SA−FA, 10 subjects 3 postures

100

200

Number of Samples

300

400

500

600

700

0.86

0.84

0.82

Multi−Adapt
Best−Adapt [15]No−Adapt
Prior Test
Prior Average
Prior Start

0.8

0.78
0

800

100

200

Number of Samples

300

400

500

600

700

800

Number of Samples

Fig. 6. Hand posture and force signals dataset [14]. Correlation coefficient obtained averaging over all the subjects as a function of the number of samples
in the training set. The title of each figure specifies if the data used as source and target are registered in Still-Arm (SA) or Free-Arm (FA) setting.

Worst Subject, Classification, SA−SA
80

60
55
50
Multi−perclass−Adapt
Multi−Adapt
Best−Adapt [15]No−Adapt
Prior Test
Prior Average
Prior Start

45
40
35
30
0

100

200

300

400

500

600

700

75
70
65
Multi−perclass−Adapt
Multi−Adapt
Best−Adapt [15]No−Adapt
Prior Test
Prior Average
Prior Start

60
55
50
45
0

800

Worst Subject, Regression, SA−SA

100

200

Number of Samples

300

400

500

600

700

0.805
0.8

0.9

0.89

0.88

0.87

Multi−Adapt
Best−Adapt [15]No−Adapt
Prior Test
Prior Average
Prior Start

0.86

0.85
0

800

Correlation Coefficient

65

Best Subject, Regression, SA−SA
0.91

Correlation Coefficient85

Classification Rate (%)

Classification Rate (%)

Best Subject, Classification, SA−SA
70

100

200

Number of Samples

300

400

500

600

700

0.795
0.79
0.785
Multi−Adapt
Best−Adapt [15]No−Adapt
Prior Test
Prior Average
Prior Start

0.78
0.775
0.77
0

800

100

200

Number of Samples

300

400

500

600

700

800

Number of Samples

Fig. 7. Hand posture and force signals dataset [14]. Classification and Regression in the SA-SA setting for the best and worst subjects. With best andworst we mean the subjects for which the difference in performance between learning with adaption and learning from scratch is respectively maximum andminimum.
Best−Adapt

Multi−Adapt

Multi−perclass−Adapt

1

1

1

1

0.8

0.9

0.5

2

2

2
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0.8

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New subject

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10

1

2

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10

Prior knowledge subject

Fig. 8. Hand posture and force signals dataset [14]. Maps of the beta values for the three adaptive methods in classification, SA-SA, obtained for 300
training samples. The title of each figure indicates the adaptive method that produced the corresponding beta weights, in particular for Multi-perclass-Adapt
we are showing the average values over the four classes (3 grasp postures plus rest). The rows 1 and 9 in all the matrices correspond respectively to the best
and worst subject in classification considered in Figure 7, first and second plots from the left.

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10Classification, 20 subjects 6 postures
65

60

60

55

55

50
45
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35

Multi−perclass−Adapt
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Best−Adapt [15]No−Adapt
Prior Test
Prior Average
Prior Start

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25
20
15
0

200

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800

1000

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Classification Rate (%)

Classification, 10 subjects 6 postures
65

50
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35

Multi−perclass−Adapt
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Best−Adapt [15]No−Adapt
Prior Test
Prior Average
Prior Start

30
25
20
15
0

200

Number of Samples

400

600

800

1000

Number of Samples

Fig. 9. Ninapro dataset [16]. Classification rate obtained averaging over all the subjects as a function of the number of samples in the training set. The
title of each figure indicates the the number of subjects and hand postures considered.

drop (46.3%, 45.5%, 44.3%) related to the change in domain
between the data used for pre-trained model and the one used
for the new subject. The increasing difficulty of the task can
be also evaluated by the progressive decrease in performanceof Multi-perclass-Adapt at the very first step in the three cases:
SA-SA 63.6%, FA-FA 62.7%, SA-FA 60.0%.
The corresponding regression results are reported in Figure
6. From the plot on the left we can notice that, in the SASA case, both the adaptive learning methods outperform NoAdapt (p < 0.03). However here Multi-Adapt and Best-Adapt
performs almost equally (no statistical significant difference).
Figure 6 (center) shows that Best-Adapt is slightly worse
than Multi-Adapt when passing to the FA-FA setting. Still
the two methods are statistically equivalent and they show asignificant gain with respect to No-Adapt only for more than
200 training samples (p < 0.03).
The problem becomes even harder in the SA-FA case
(Figure 6 right), here Multi-Adapt outperforms No-Adapt only
for more than 500 training samples (p < 0.03).
Globally the increasing difficulty of the three regression task
passing from left to right in Figure 6 is demonstrated by thegeneral drop in performance. Although we decided to show thecorrelation coefficient results, the corresponding MSE would
lead to the same conclusions.
B. Ninapro [16]We shuffled randomly the samples of the Ninapro dataset
and we considered 36 learning steps adding each time 30
training samples till a maximum of 1080 data.
Figure 9 (left) reports the obtained classification rate at eachstep when considering 10 subjects for the 6 grasp postures plus
rest. The plot shows that all the adaptive methods performs
almost as No-Adapt, in particular for less than 200 samples
there is no statistical difference among learning from scratch,learning with adaption or using directly the prior knowledge(the fair comparison is with Prior Average and Prior Start).
It is important to remark that the “few sample” range grows
together with the number of considered classes: the samples
are selected randomly and a minimum amount of data perclass is needed to get meaningful classification results. Only
Multi-perclass-Adapt outperforms No-Adapt (p < 0.05) withan average advantage of 2.5% in recognition rate for morethan 200 samples.
Figure 9 (right) shows the corresponding results in case of
20 subjects. On average No-Adapt and Prior Average perform
almost equally to the previous case (with 10 subjects), showingthat the average learning capability per subject is almost stable
in a fixed range. On the other hand Prior Test and Prior Start
present an increase in performance: the higher is the numberof available prior models, the higher is the probability to finduseful information for the new problem. Moreover, here Multiperclass-Adapt outperforms both Best-Adapt and No-Adapt(p < 0.001) with an average gain of 6% with respect tolearning from scratch.
C. Discussion
As a general remark we can state that the three proposed adaptive methods (Multi-perclass-adapt, Multi-Adapt
and Best-Adapt), improve the learning performance to different extents if prior-knowledge contains useful information for
the new task, and never harm if any good match between thedata of the new subject and the old source subjects is found. To
further support this statement, Figure 7 shows the classification
and regression results on SA-SA data respectively for the
subject that have the maximum (best) and the minimum(worst) difference in recognition and regression performancewith adaptation compared to No-Adapt. The worst-case subject
represents the paradigmatic case of no previous models matching the current distribution; as a consequence the parameterβ (β) is set automatically to a small value (to a vector ofsmall norm). In this case there is essentially no transfer ofprior knowledge. More insight on this point is given by Figure
8. Here we are mapping the beta values for each adaptivemodel in a specific learning step (300 training samples) of theclassification SA-SA experiment. Best-Adapt chooses only one
prior model as reference, while Multi-Adapt can rely on morethan one known subject. For Multi-perclass-Adapt we show theaverage beta values over the four classes (3 grasps plus rest).

IEEE TRANSACTIONS OF ROBOTICS, VOL. X, NO. Y, DATEThe results are consistent to each other: e.g. for subject 1 (1strow in the matrices), all the adaptive methods choose subject
2 as very relevant, Multi-Adapt gives credit also to subject
8 and the same happens for Multi-perclass-Adapt which has
more freedom in weighting each class and finds also subject 9
a bit useful. Subject 1 corresponds to the best subject, with thecorresponding classification performance reported in Figure 7(first from the left). Subject 9 is instead the worst one (Figure
7 second from the left), and the 9th row of all the matrices of
Figure 8 actually indicates that all the beta values are small.
It is reasonable to claim that the overall performance of
the adaptive methods would increase along with the numberof stored models, since this would mean a larger probabilityof finding matching pre-trained models. This is confirmed by
the results on the Ninapro dataset. In the long run, a large
database of sEMG signals and force measures, with subjects
possibly categorized (per age, sex, body characteristics, etc.)
would definitely help getting uniformly better performance.
We point out here that the direct use of prior knowledge
on a new problem is only partially helpful without an appropriate way to (a) choose the best prior knowledge modeland (b) weigh and combine it with the new information. In
fact, Prior Test shows that possibly tuning on the test, oneprior-knowledge model useful for the new problem could befound, but its usefulness declines with the number of available
training samples. On the other hand, the Prior Average line
corresponds to an attempt to use directly a flat combinationof all the pre-trained models on a new subject: the obtained
performance shows that this is not a good solution.
Let us also briefly discuss the choice of the learningparameter C. Here we followed the standard approach inthe community, and kept the the parameter C fixed using
the best value obtained from cross validation on the known
subjects. Still, one might argue that the best way to define it
is to optimize it by using the available training samples of
the target subject, separately for each learning approach. For
the proposed adaptive methods, this would imply defining C
together with β, leading to a non-convex problem and a great
increase in computational complexity.
VI. C ONCLUSION
The results presented in this paper clearly show thatmachine-learning-based classification and regression applied
to surface EMG can be improved by means of re-using
previous knowledge. In particular, we start from SVM models
previously built by training on a pool of human subjects, todecrease the training time of a LS-SVM to new subjects.
All the proposed adaptive methods show a significant gain inrecognition rate for grasp type classification and in correlation
coefficient for regression when predicting the applied force,with respect to learning from scratch on the new subject. We
note that the classification error/regression accuracy values
obtained in our experiments are in many cases below the best
results shown in competing literature (an almost comprehensive table appears in [3], page 725); but the point here is toperform the comparison with non-adaptive baselines.
A comprehensive analysis of the practical applicability of
our methods on real patients is out of scope here; hopefully

11

however, our results show that the presented method can beused in any (sEMG classification/regression) scenario.
The overall idea is that a prosthesis could be embedded withadditional, pre-existing knowledge before being shipped out toa new patient. This needs to be done once and for all and, most
likely, for a large pool of healthy subjects and/or amputees ofdiverse condition, age and type of operation, and degree ofmuscle remnant fitness. The fact that the free-arm condition
consistently benefits as well from the proposed technique —essentially to the same extent as the controlled one — is avery promising result, hinting that one could potentially pretrain a prosthesis in a laboratory and then ship it outside, andstill give a significant benefit to the patient with respect to thelearning-from-scratch case.
The databases we used consists of intact subjects only, but
it is believed that trans-radial amputees can generate similarly
accurate signals ([19] is the most recent result on this topic),
so this seems not to be a major objection to the applicability ofthe method. The project NinaPro (http://www.idiap.ch/project/ninapro/) is currently concerned with collecting such a large
database of mixed subjects. If confirmed on data acquired
from amputees, the current result could pave the way toa significantly higher acceptance of myoprostheses in theclinical setting. As future work it would be also interesting
to enlarge the presented approaches to more specific ongoinglearning conditions on the new subject, covering the hypothesisof an increased number of hand postures.
ACKNOWLEDGMENTS
This work is partially supported by the Swiss National
Science Foundation Sinergia project Ninapro (Non-Invasive
Adaptive Prosthetics). T. T. was supported by the EMMA
Hasler Project. We are thankful to Arjan Gijsberts for his help
in cleaning the code for the experiments and on the details
about the hand posture hierarchy over the Ninapro dataset.
The database presented in [14] and used in this work has
been collected and refined in 2009 at the Robotics, Brain
and Cognitive Sciences Department of the Italian Instituteof Technology, Genova, Italy, mainly by Angelo Emanuele
Fiorilla. We would like to thank him and Giulio Sandini ofthe same Institute for making the database available to us.
A PPENDIXC LOSED FORMULA FOR THE LEAVE - ONE - OUT PREDICTION
We show here that, following the same steps presented in[39], it is possible to demonstrate the Proposition 1 obtaining
the closed formula for the leave-one-out prediction in (12).
We start from

 

a
y − β ŷ
M
=
.
(28)
b
0
and we decompose M into block representation isolating thefirst row and column as follows:
 


m11
mT1
K + C1 I 1
=
.
(29)
M=
m1 M(−1)
1T
0
Let a(−i) and b(−i) represent the parameters of LS-SVM
during the i-th iteration of the leave-one-out cross validation

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12

procedure. In the first iteration, where the first training sample
is excluded we have


a(−1)
= P(−1) (y (−1) − β ŷ (−1) ) ,
(30)
b(−1)
T
where P(−1) = M−1
and(−1) , y (−1) = [y2 , . . . , yN , 0]00Tŷ (−1) = [w · φ(x2 ), . . . , w · φ(xN ), 0] . The leave-oneout prediction for the first training sample is then given by

ỹ1 =

mT1



a(−1)
b(−1)



+ βw0 · φ(x1 )(31)= mT1 P(−1) (y (−1) − β ŷ (−1) ) + βw0 · φ(x1 ) .

(32)

Considering the last N equations in the system in (28), it isclear that [m1 M(−1) ][aT , b]T = (y (−1) − β ŷ (−1) ) , and soỹ1 = mT1 P(−1) [m1 M(−1) ][a1 , . . . , aN , b]T + βw0 · φ(x1 )= mT1 P(−1) m1 a1 + mT1 [a2 , . . . , aN , b]T + βw0 · φ(x1 ) .
(33)
Noting from the first equation in the system in (28) that y1 −βw0 · φ(x1 ) = m11 a1 + mT1 [a2 , . . . , aN , b]T , we haveỹ1 = y1 − a1 (m11 − mT1 P(−1) m1 ) .

(34)

Finally, using P = M−1 and applying the block matrix
inversion lemma we get,

P=

µ−1
−1
P(−1) + µ P(−1) mT1 m1 P(−1)−µ−1 m1 P(−1)−µ−1 P(−1) mT1



where µ = m11 − mT1 P(−1) m1 and noting that the systemof linear equations (28) is insensitive to permutations of theordering of the equations and of the unknowns, we have
ai
.
(35)
ỹi = yi −Pii
Let a = a0 + βa00 , [a0T , b0 ]T = P [y T , 0]T and [a00T , b00 ]T =P [ŷ T , 0]T , from the equation above we get :ỹi = yi −a00
a0i
+β i .
Pii
Pii

(36)

R EFERENCES[1] M. Zecca, S. Micera, M. C. Carrozza, and P. Dario, “Control ofmultifunctional prosthetic hands by processing the electromyographic
signal,” Critical Reviews in Biomedical Engineering, vol. 30, no. 4–6,
pp. 459–485, 2002.
[2] S. Micera, J. Carpaneto, and S. Raspopovic, “Control of hand prostheses
using peripheral information,” IEEE Reviews in Biomedical Engineering,
vol. 3, pp. 48–68, Oct. 2010.
[3] B. Peerdeman, D. Boere, H. Witteveen, R. Huis in ‘t Veld, H. Hermens,
S. Stramigioli, H. Rietman, P. Veltink, and S. Misra, “Myoelectricforearm prostheses: State of the art from a user-centered perspective,” J
Rehabil Res Dev., vol. 48, no. 6, pp. 719–738, 2011.
[4] D. J. Atkins, D. C. Y. Heard, and W. H. Donovan, “Epidemiologic
overview of individuals with upper-limb loss and their reported research
priorities,” Journal Of Prosthetics And Orthotics, vol. 8, no. 1, pp. 2–11,
1996.
[5] E. A. Biddiss and T. T. Chau, “Upper limb prosthesis use and abandonment: a survey of the last 25 years,” Prosthetics and Orthotics
International, vol. 31, no. 3, pp. 236–257, 2007.

,[6] A. H. Bottomley, “Myoelectric control of powered prostheses,” J Bone
Joint Surg Br, vol. 47-B, no. 3, pp. 411—415, 1965.
[7] D. S. Childress, “A myoelectric three-state controller using rate sensitivity,” in Proceedings 8th ICMBE, Chicago, IL, 1969, pp. 4—5.
[8] L. Philipson, D. S. Childress, and J. Strysik, “Digital approaches tomyoelectric state control of prostheses,” Bulletin of Prosthetics Research,
vol. 18, no. 2, pp. 3—11, 1981.
[9] C. Castellini, E. Gruppioni, A. Davalli, and G. Sandini, “Fine detectionof grasp force and posture by amputees via surface electromyography,”
Journal of Physiology (Paris), vol. 103, no. 3-5, pp. 255–262, 2009.
[10] F. R. Finley and R. W. Wirta, “Myocoder computer study of electromyographic patterns,” Arch.Phys.Med., vol. 48, pp. 20–24, 1967.
[11] R. W. Wirta, D. R. Taylor, and F. R. Finley, “Pattern-recognition arm
prosthesis: A historical perspective - a final report,” Bull.Prosthet.Res.,
vol. Fall, pp. 8–35, 1978.
[12] C. Huang and B. Li, “A neural network-based surface electromyography
motion pattern classifier for the control of prostheses,” in International
Conference of Engineering in Medicine and Biology Society, 1997.
[13] F. V. Tenore, A. Ramos, A. Fahmy, S. Acharya, R. Etienne-Cummings,
and N. V. Thakor, “Decoding of individuated finger movements using
surface electromyography,” IEEE Trans. Biomed. Eng., vol. 56, no. 5,
pp. 1427—1434, 2009.
[14] C. Castellini, A. E. Fiorilla, and G. Sandini, “Multi-subject / dailylife activity EMG-based control of mechanical hands,” Journal of
Neuroengineering and Rehabilitation, vol. 6, no. 41, 2009.
[15] F. Orabona, C. Castellini, B. Caputo, E. Fiorilla, and G. Sandini, “Model
adaptation with least-squares SVM for hand prosthetics,” in Proceedingsof ICRA - International Conference on Robotics and Automation, 2009,
pp. 2897–2903.
[16] M. Atzori, A. Gijsberts, S. Heynen, A.-G. M. Hager, O. Deriaz, P. V.
der Smagt, C. Castellini, B. Caputo, and H. Mller, “Building theninapro database: a resource for the biorobotics community,” in IEEE
International Conference on Biomedical Robotics and Biomechatronics(BioRob), 2012.
[17] C. Castellini and P. van der Smagt, “Surface EMG in advanced handprosthetics,” Biological Cybernetics, vol. 100, no. 1, pp. 35–47, 2009.
[18] F. C. P. Sebelius, B. N. Rosén, and G. N. Lundborg, “Refined myoelectric control in below-elbow amputees using artificial neural networks anda data glove,” Journal of Hand Surgery, vol. 30A, no. 4, pp. 780—789,
2005.
[19] C. Cipriani, C. Antfolk, M. Controzzi, G. Lundborg, B. Rosen, M. Carrozza, and F. Sebelius, “Online myoelectric control of a dexterous handprosthesis by transradial amputees,” Neural Systems and Rehabilitation
Engineering, IEEE Transactions on, vol. 19, no. 3, pp. 260–270, june
2011.
[20] E. Scheme and K. Englehart, “Electromyogram pattern recognition forcontrol of powered upper-limb prostheses: State of the art and challenges
for clinical use,” Journal of Rehabilitation Research and Development,
vol. 48, no. 6, pp. 643–660, 2011.
[21] P. Parker, K. Englehart, and B. Hudgins, “Myoelectric signal processing
for control of powered limb prostheses,” Journal of Electromyography
and Kinesiology, vol. 16, pp. 541–548, 2006.
[22] R. Merletti, M. Aventaggiato, A. Botter, A. Holobar, H. Marateb, andT. Vieira, “Advances in surface EMG: Recent progress in detection
and processing techniques,” Critical reviews in biomedical engineering,
vol. 38, no. 4, pp. 305—345, 2011.
[23] R. Merletti, A. Botter, C. Cescon, M. Minetto, and T. Vieira, “Advancesin surface EMG: Recent progress in clinical research applications,”
Critical reviews in biomedical engineering, vol. 38, no. 4, pp. 347—
379, 2011.
[24] R. Merletti, A. Botter, A. Troiano, E. Merlo, and M. Minetto, “Technology and instrumentation for detection and conditioning of the surface
electromyographic signal: State of the art,” Clinical Biomechanics,
vol. 24, pp. 122—134, 2009.
[25] T. Lorrain, N. Jiang, and D. Farina, “Influence of the training set on
the accuracy of surface EMG classification in dynamic contractions forthe control of multifunction prostheses,” J Neuroeng Rehabil, vol. 8:25,
2011.
[26] S. J. Pan and Q. Yang, “A survey on transfer learning,” IEEE Transactions on Knowledge and Data Engineering, vol. 22, no. 10, pp. 1345–
1359, October 2010.
[27] H. Daumé III and D. Marcu, “Domain adaptation for statistical classifiers,” Journal of Artificial Intelligence Research (JAIR), vol. 26, pp.
101–126, 2006.
[28] S. B. David, J. Blitzer, K. Crammer, A. Kulesza, F. Pereira, and J. W.
Vaughan, “A theory of learning from different domains,” Machine
Learning, vol. 79, no. 1, pp. 151–175, May 2010.

IEEE TRANSACTIONS OF ROBOTICS, VOL. X, NO. Y, DATE

[29] H. Daumé III, “Frustratingly easy domain adaptation,” in Conferenceof the Association for Computational Linguistics (ACL), Prague, Czech
Republic, 2007.
[30] K. Saenko, B. Kulis, M. Fritz, and T. Darrell, “Adapting visual categorymodels to new domains,” in European Conference on Computer Vision(ECCV), 2010, pp. 213–226.
[31] T. Tommasi, F. Orabona, and B. Caputo, “Safety in numbers: Learning
categories from few examples with multi model knowledge transfer,” inIEEE Computer Vision and Pattern Recognition (CVPR), 2010.
[32] B. Cao, S. J. Pan, Y. Zhang, D.-Y. Yeung, and Q. Yang, “Adaptive
transfer learning,” in Proceedings of AAAI-10 - Twenty-Fourth AAAI
Conference on Artificial Intelligence, 2010, pp. 407–412.
[33] J. Blitzer, M. Dredze, and F. Pereira, “Biographies, bollywood, boomboxes and blenders: Domain adaptation for sentiment classification,”in Conference of the Association for Computational Linguistics (ACL),
2007, pp. 187–205.
[34] J. Yang, R. Yan, and A. G. Hauptmann, “Adapting SVM classifiers todata with shifted distributions,” in ICDMW ’07: Proceedings of theSeventh IEEE International Conference on Data Mining Workshops.
Washington, DC, USA: IEEE Computer Society, 2007, pp. 69–76.
[35] J. W. Sensinger, B. A. Lock, and T. A. Kuiken, “Adaptive patternrecognition of myoelectric signals: Exploration of conceptual framework
and practical algorithms,” IEEE Trans Neural Syst Rehabil Eng, vol. 17,
no. 3, pp. 270–278, 2009.
[36] T. Matsubara, S. Hyon, and J. Morimoto, “Learning and adaptation of astylistic myoelectric interface: Emg-based robotic control with individualuser differences,” in Proceedings of ROBIO, IEEE International Conference on Robotics and Biomimetics, Phuket Island, Thailand, 2011, pp.
390–395.
[37] Q. Sun, R. Chattopadhyay, S. Panchanathan, and J. Ye, “A two-stage
weighting framework for multi-source domain adaptation,” in Advancesin Neural Information Processing Systems (NIPS), 2011.
[38] N. Cristianini and J. Shawe-Taylor, An Introduction to Support Vector
Machines (and Other Kernel-Based Learning Methods). Cambridge
University Press, 2000.
[39] G. C. Cawley and N. L. C. Talbot, “Preventing over-fitting during model
selection via bayesian regularisation of the hyper-parameters,” J. Mach.
Learn. Res., vol. 8, pp. 841–861, May 2007.
[40] A. Luntz and V. Brailovsky, “On estimation of characters obtainedin statistical procedure of recognition (in russian),” Technicheskaya
Kibernetica, vol. 3, 1969.
[41] K. Crammer and Y. Singer, “On the algorithmic implementation ofmulticlass kernel-based vector machines,” J. Mach. Learn. Res., vol. 2,
pp. 265–292, March 2002.
[42] M. Grant and S. Boyd, “CVX: Matlab software for disciplined convex
programming, version 1.21,” http://cvxr.com/cvx, Apr. 2011.
[43] F. P. Kendall, E. K. McCreary, P. G. Provance, M. M. Rodgers, and
W. Romani, Muscles: Testing and Function, with Posture and Pain. 530
Walnut St.Philadelphia, PA 19106-3621: Lippincott Williams & Wilkins,
2005.
[44] “Futek LMD500 medical load cell (hand).” [Online]. Available:
http://www.futek.com/product.aspx?stock=FSH00125[45] I. Kuzborskij, A. Gijsberts, and B. Caputo, “On the challenge ofclassifying 52 hand movements from surface electromyography,” inInternational Conference of the IEEE Engineering in Medicine andBiology Society (EMBC), 2012.
[46] J. D. Gibbons and S. Chakraborti, Nonparametric Statistical Inference(Statistics: a Series of Textbooks and Monographs). Chapman andHall/CRC, 2003.

13

Tatiana Tommasi received the M.Sc. degree in physics and the Dipl. degree
in medical physics specialization from the University of Rome, La Sapienza,
Italy, in 2004 and 2008, respectively. She is currently a Ph.D. student inelectrical engineering at the École Polytechnique Fédérale de Lausanne, andResearch Assistant at the Idiap Research Institute, Martigny, Switzerland.
Her research interests include machine learning and computer vision witha particular focus on knowledge transfer and object categorization using
multimodal information.

Francesco Orabona is a Research Assistant Professor at the Toyota Technological Institute at Chicago. His research interests are in the area oftheoretically motivated and efficient learning algorithms, with emphasis on
online learning, kernel methods, and computer vision. He received the MS
degree in Electronic Engineering at the University of Naples ”Federico II”
in 2003 and the PhD degree in Bioengineering and Bioelectronics at the
University of Genoa, in 2007. He is (co)author of more than 30 peer-reviewed
papers.

Claudio Castellini, Ph.D. received a Laurea in Biomedical Engineeringsin 1998 from the University of Genova, Italy and a doctorate in Artificial
Intelligence in 2005 from the University of Edinburgh, Scotland. He then spent
4.5 years as a postdoctoral researcher in the Advanced Robotics Laboratoryof the University of Genova, Italy, working on machine learning applied tohuman sensorimotor data. Since 2009 he is a researcher at the DLR (German
Aerospace Center) in the Bionics group. He is (co)author of more than 35
peer-reviewed papers.

Barbara Caputo is a senior research scientist at the Idiap Research Institutesince 2006, where she leads the Cognitive visual Systems group. She received
her PhD in Computer Science from the Royal Institute of Technology (KTH)in Stockholm, Sweden, in 2004. Her main research interests are in computer
vision, machine learning and robotics, where Dr. Caputo has been active since1999. As a result of her activities, Dr. Caputo has edited 4 books, and she is(co)author of more than 70 peer-reviewed papers.