Rémi Flamary
email: remi.flamary@insa-rouen.fr

Alain Rakotomamonjy

Decoding finger movements from ECoG signals using switching linear models

One of the major challenges of ECoG-based Brain-Machine Interfaces is the movement prediction of a human subject. Several methods exist to predict an arm 2-D trajectory. The fourth BCI Competition gives a dataset in which the aim is to predict individual finger movements (5-D trajectory). The difficulty lies in the fact that there is no simple relation between ECoG signals and finger movement. We propose in this paper to decode finger flexions using switching models. This method permits to simplify the system as it is now described as an ensemble of linear models depending on an internal state. We show that an interesting accuracy prediction can be obtained by such a model.

Introduction

Some people who suffer some neurological diseases can be highly paralyzed because they do not have anymore control on their muscles. Therefore, their only way to communicate is by using their electroencephalogram signals. Brain-Computer interfaces (BCI) research aim at developing systems that help those disabled people communicating with machines. Non-invasive BCIs have recently received a lot of interest because of their easy protocol for sensors implantation on the scalp surface [START_REF] Wolpaw | Control of a two-dimensional movement signal by a noninvasive brain-computer interface in humans[END_REF][START_REF] Blankertz | The BCI competition 2003: progress and perspectives in detection and discrimination of EEG single trials[END_REF]. Furthermore, although the electroencephalogram signals have been recorded through the skull, those BCI have shown great performance capabilities, and can be used by real Amyotrophic Lateral Sclerosis (ALS) patients [START_REF] Sellers | A p300-based brain-computer interface: Initial tests by als patients[END_REF][START_REF] Nijboer | A braincomputer interface for people with amyotrophic lateral sclerosis[END_REF].

However, non-invasive recordings still show some drawbacks including poor signal to noise ratio and poor spatial resolution. Hence, in order to overcome these difficulties, invasive BCI may be used. For instance, Electrocorticographic recordings (ECoG) have recently received a great amount of interest owing to their semi-invasive nature as they are recorded from the cortical surface. Indeed, they offer higher spatial resolution and they are far less sensitive to artifact noise. Feasibility of invasive-based BCI have been proven by several recent papers [START_REF] Leuthardt | A brain-computer interface using electrocorticographic signals in humans[END_REF][START_REF] Hill | Classifying eeg and ecog signals without subject training for fast bci implementation: Comparison of non-paralysed and completely paralysed subjects[END_REF][START_REF] Hill | Classifying Event-Related Desynchronization in EEG, ECoG and MEG signals[END_REF][START_REF] Shenoy | Generalized features for electrocorticographic bci[END_REF]. In many of these papers, the BCI paradigm considered is motor imagery yielding thus to a binary decision BCI.

A recent breakthrough has been made by Schalk et al. [START_REF] Schalk | Decoding twodimensional movement trajectories using electrocorticographic signals in humans[END_REF] which has proven that ECoG recordings can lead to multiple-degree BCI control. Followed by Pistohl et al. [START_REF] Pistohl | Prediction of arm movement trajectories from ecog-recordings in humans[END_REF], these two works have considered the problem of predicting arm movements from ECoG signals. Both approaches are based on estimating a linear relation between features extracted from ECoG signals and the actual arm movement.

In this work, we investigate a finer degree of resolution in BCI control by addressing the problem of estimating finger flexions through ECoG signals. Indeed, we propose in this paper a method for decoding finger movements from ECoG data based on switching models. The underlying idea of switching models is the hypothesis that movements of each of the five fingers are triggered by an internal discrete state that can be estimated and that all finger movements depend on that internal state. While such an idea of switching models have already been successfully used for arm movement prediction on monkeys from micro-electrode array measures [START_REF] Darmanjian | Independently coupled hmm switching classifier for a bimodel brainmachine interface[END_REF], here, we develop a specific approach adapted to finger movements. The global method has been tested on the 4th Dataset of the BCI Competition IV [START_REF] Miller | Prediction of finger flexion: 4th brain-computer interface data competition[END_REF].

The paper is organized as follows : First, we present the dataset from the BCI Competition IV used in this paper, then we explain our decoding method used to obtain finger flexion from ECoG signals. Finally we present the results obtained with our method and we discuss several ways of improving them.

Dataset

For this work, the fourth dataset from the BCI Competition IV [START_REF] Miller | Prediction of finger flexion: 4th brain-computer interface data competition[END_REF] was used. The subjects were 3 epileptic patients who had platinium electrode grids placed on the surface of their brain. The number of electrodes vary between 48 to 64 depending on the subject and their position on the cortex was unknown.

Electrocorticographic (ECoG) signals of the subject were recorded at a 1KHz sampling using BCI2000 [START_REF] Schalk | Bci2000: a general-purpose brain-computer interface (bci) system[END_REF]. A band-pass filter from 0.15 to 200Hz was applied to the ECoG signals. The finger flexion of the subject was recorded at 25Hz and up-sampled to 1KHz. Due to the acquisition process, a delay appears between the finger movement and the measured ECoG signal. To correct this time-lag we apply the 37 ms delay proposed in the dataset description [START_REF] Miller | Prediction of finger flexion: 4th brain-computer interface data competition[END_REF] to the ECoG signals.

The BCI Competition dataset consists in a 10 minutes recording per subject. 6 minutes 40 seconds (400,000 samples) were given for the learning models and the remaining 3 minutes 20 seconds (200,000 samples) were used for testing. However, since the finger flexion signals have been up-sampled and thus are partly composed of artificial samples, we have down-sampled the number of points by a factor of 4 leading to a training set of size 100,000 and a testing set of size 50,000. The 100,000 samples provided for learning have been splitted in a training (75,000) and validation set (25,000). Then, all parameters of the approach have been optimized in order to maximize the performance on the validation set. Note that all results presented in the paper have been obtained using the testing set provided by the competition (after up-sampling then back by a factor of 4).

In this competition, method performance was measured through the crosscorrelation between the measured and the estimated finger flexion. The correlation were averaged across fingers and across subject to obtain the overall method performance. Note that the fourth finger was not used for evaluation in the competition since its movements were proven to be correlated with the other one movements [START_REF] Miller | Prediction of finger flexion: 4th brain-computer interface data competition[END_REF].

3 Finger flexion decoding using switching linear models This section presents the full methodology we have used for addressing the problem of estimating finger flexions from ECoG signals. In the first part, we propose an overview of the switching models. Then, we describe how we learn the function that estimates which finger is about to move. Afterwards, we detail the linear models associated to each moving finger. Finally, we briefly detail how the complete method works in the decoding stage.

Overview

In order to obtain an efficient prediction of finger flexions, we have made the hypothesis that for such movements the brain can be understood as a switching model. This translates into the assumption that the measured ECoG signals and the finger movements are intrinsically related by an internal state k. In our case, this state corresponds to each finger moving, k = 1 for the thumb to k = 5 for the baby finger or k = 6 for no finger movement. Here, we used mutually-exclusive states because the experimental set-up considered specifies that only one or no finger is moving. Figure 1 gives the picture of our finger movement decoding scheme. Basically, the idea is that based on some features extracted from the ECoG signals, the internal hidden state triggering the switching finger models can be estimated. Then, this state allows the system to select an appropriate model H k (x) for estimating all finger flexions, with x being a feature vector.

For the complete model, we need to estimate the function f (•) that maps the ECoG features to an internal state k ∈ {1, • • • , 6} and the functions H k (•) that relates the brain signals to all finger flexion amplitudes. The next paragraphs present how we have modeled these functions and how we have estimated them from the data.

Moving finger estimation

The methodology used for learning the f (•) function which estimates the moving finger is given in the sequel. Figure 2. For a single channel, the procedure is the following. The signal from that channel is divided in non-overlapping window of 300 samples. For each window, an auto-regressive model has been estimated. Thus, AR coefficients are obtained at every 300 samples (denoted by the vertical dashed line and the cross in Figure 2). In order to have a continuous AR coefficients value, a smoothing spline-based interpolation between two consecutive AR coefficients has been used. Note that instead of interpolating, we could have computed the AR coefficients at each time instant, however, the approach we propose here has the double advantage of being less-computationally demanding and of providing some smoothed (and thus more robust to noise) AR coefficients. Finally, only the two first AR coefficients are used as features. Signal dynamics have been taken into account by applying a similar procedure to shifted version of the signal at (+t s and -t s ). Hence, for measurements involving 48 channels, the feature vector at a time instant t is obtained by concatenating features extracted from all channels, leading to a resulting vector of size 48 × 3 × 2 = 240.

Channel Selection Actually, we do not consider in the model all the channels. Indeed, a channel selection algorithm has been run in order to reduce the number of channels. For this channel selection procedure, the feature vector x t at time t has been computed as described above, except that we have not considered the shifted signal versions and used only the first AR coefficient.

Then, for each finger, based on the training set, we estimated a linear regression y = x t c k where x ∈ R chan is a feature vector of number of channels dimension, y = {1, -1} stating if the considered finger is moving or not. Once, we have estimated the coefficient vector c k for each finger, we selected the K channels that present the largest values of :

6 k=1 |c k |
where the absolute value is considered as element-wise. This channel selection allows us to reduce substantially the number of channels so as to minimize the computational effort needed for estimating and evaluating the function f (•) and it yields better performance. K has been chosen so that the cross-correlation on the validation set is maximal.

Model estimation

The model for estimating which finger is moving is a more sophisticated version of the one used above for channel selection. At first, since the finger movements are mutually-exclusive, we have considered a winner-takesall strategy :

f (x) = argmax k=1,••• ,6 f k (x) (1)
Here again, f k (x) is a linear model that is trained by presenting couples of feature vector and a state y = {1, -1}. The main differences between the channel selection procedure and the one used for learning f k (•) are that : the features here take into account some dynamics of the ECoG signals and a finer feature selection has been performed by means of a simultaneous sparse approximation method.

Let us consider the training examples {x t , y t } ℓ t=1 where x t ∈ R d , y t,k = {1, -1}, being the k-th entry of vector y t , t denoting the time instant and k denoting all possible states (including no finger moving). y t,k tells us whether the finger k is moving at time t. Now, let us define the matrix Y, X and C as :

[Y] t,k = y t,k [X] t,j = x t,j [C] j,k = c j,k
where x t,j and c j,k are the j-th components of respectively x t and c k . The aim of simultaneous sparse approximation is to learn the coefficient matrix C while yielding the same sparsity profile in the different finger models. The task boils down to the following optimization problem:x where λ s is a trade-off parameter that has to be appropriately tuned and C i,• being the i-th row of C. Note that our penalty term is a mixed ℓ 1ℓ 2 norm similar to those used for group-lasso. Owing to the ℓ 1 penalty on the ℓ 2 row-norm, such a penalty tends to induce row-sparse matrix C. Problem (2) has been solved using the block-coordinate descent algorithm proposed by Rakotomamonjy [START_REF] Rakotomamonjy | Algorithms for multiple basis pursuit denoising[END_REF].

Ĉ = argmin C Y -XC 2 F + λ s i C i,• 2 (2)

Learning finger flexion models

Here, we discuss the model relating the ECoG data and finger movements for every possible values of k. In other words, supposing that a given finger, say the index, is going to move (as predicted by our finger moving estimation), we built an estimation of all finger movements. Hence, for each k, we are going to learn a linear model g k,j (x) = xT h (k) j with j = 1, • • • , 5, x a feature vector and h (k) j a weighting vector indexed by the moving finger k and the finger j which flexions are to estimate. We have chosen a linear model since they have been shown to provide good performances for decoding movements from ECoG [START_REF] Pistohl | Prediction of arm movement trajectories from ecog-recordings in humans[END_REF][START_REF] Schalk | Decoding twodimensional movement trajectories using electrocorticographic signals in humans[END_REF].

At a time t, the feature vector x t has been obtained by following the same line as Pistohl et al. [START_REF] Pistohl | Prediction of arm movement trajectories from ecog-recordings in humans[END_REF]. Indeed, we use filtered time-samples as features. x t has been built in the following way. All channels have been filtered with a Savitsky-Golay (third order, 0.4 s width) low-pass filter. Then, x t is composed of the concatenation of the time samples at t, tτ and t + τ all smoothed signals at all channels. Samples at tτ and t + τ have been used in order to to take into account some temporal delays between the brain activity and finger movements. Now, let us detail how, for a given moving finger k, the weight matrix

H k = [h (k) 1 • • • h (k)
5 ] has been learned. For a given finger k, we have used as a training set all samples x t where that finger is known to be moving. For this purpose, we have manually segmented the signals and extracted the appropriate signal segments, needed for building the target matrix Ỹk , which contains all finger positions, and for extracting the feature matrix Xk . This training samples extraction stage is illustrated on Figure 3. Then for learning the global linear model, we have solved the following multi-dimensional ridge regression problem. min

H k Ỹk -Xk H k 2 F + λ k H k 2 F (3)
with λ k being a regularization parameter that has to be tuned.

For this problem of finger movements estimation, we also noted that feature selection helps in improving performance. Again, we have used the estimated weighting matrix Ĥ coefficients for pruning the model. Indeed, we have kept in the model the M features which correspond to the M largest entries of vector

5 i=1 | ĥ(k) i |.
For possible k and subjects, M is chosen as to minimize a validation error. Note that such an approach for pruning model can be interpreted as a shrinkage of a least-square parameters.

Decoding finger movement

When all models have been learned, the decoding scheme is the one given in Figure 1. Given the two feature vectors x t and xt at a time t, the finger position estimation is obtained as:

ŷ = xT t Ĥk with k = argmax k x t t c k (4)
with ŷ being a row vector containing the estimated finger movement, k the finger that is supposed to move, xt the extracted feature at time t and Ĥk the estimated linear model for state k.

Results

In this section we present the performance of our switching model decoder. At first, we explain how all parameters of the models have been set. Then, we present some results which help us understanding the contribution of the different parts of our models, Finally, we evaluate our approach and compare ourselves to the BCI competition results.

Parameter selection

The parameters used in the moving finger estimation are selected by a validation method on the last part of the training set (75,000 for the training, 25,000 for validation). We suppose that the size of the set is important enough to avoid over-fitting. Using this method, we select the number of selected channels, the time-lag t s used in feature extraction and the regularization term λ s of Eq. [START_REF] Blankertz | The BCI competition 2003: progress and perspectives in detection and discrimination of EEG single trials[END_REF].

Similarly, all parameters(τ , the number of selected channels and λ k ) needed for estimating H k have been set so that they optimize the model performance of on the validation sets. For this model selection part, the size of training and validation sets vary according to k and they are summarized in Table 1 for subject 1.

Evaluating of the linear models H k

Models H k correspond to the linear regressions between the ECoG features and the finger flexions when the k-th finger is moving. The signals used for evaluating these models are extracted in the same manner as the learning sets y k and Xk (see Figure 4) but by assuming that the true segmentation of finger movements are known. To evaluate these models, we measure the cross-correlation between the true y k and estimated finger flexion Xk ĥk k only when the finger k is moving. The correlations can be seen on Table 2.

We observe that by using a linear regression between the ECoG signals and the finger flexions, we achieve a correlation of 0.46 (averaged across fingers and subjects). This results correspond to those obtained for the arm trajectory prediction (Schalk [START_REF] Schalk | Decoding twodimensional movement trajectories using electrocorticographic signals in humans[END_REF] obtained 0.5 and Pistohl [START_REF] Pistohl | Prediction of arm movement trajectories from ecog-recordings in humans[END_REF] obtained 0.43). Fig. 4: Signal extraction for linear model estimation: (upper plot) full signal with segmented signal, corresponding to moving finger, bracketed by the vertical lines and (lower plot) the extracted signal corresponding to the concatenation of the samples when finger 1 is moving.

Evaluating the switching decoder method

In order to evaluate the efficiency of the switching model decoder and each block of the decoder contribution. We report three different results: first, for a given finger, we compute the estimated finger flexion using a linear model learned on all samples (including those where the considered finger is not moving), then we decode finger flexions with our switching decoder while assuming that the exact sequence of hidden states is known 1 and finally we use our switching decoder with the estimated hidden states.

For a sake of baseline comparison with our switching models decoder, we have estimated the finger flexions by means of a single linear model which has been trained using all the time samples. The obtained correlation are given in Table 3a and the regression result can be seen on the upper plots of Figure 5. We can see that the correlation obtained are rather low due the fact that without switching models the amplitude of the flexion signals remains small.

The switching model decoder is a two-part process as it requires to have the linear models H k and the sequence of hidden states. First we apply the decoder using the true sequence obtained thanks to the actual finger flexion. Suppose that we have the exact sequence k and we apply the switching decoder with this sequence. We know that these results may never be attained as it supposes the sequence labeling method to be perfect but it gives a interesting idea of the maximal performance that our method can provide for given linear models H k . Results can be seen in the middle plots of Figure 5 and correlations are in Table 3b. We obtain a high accuracy accross all subjects with an average correlation of 0.61 when using an exact sequence. This proves that the switching model can be efficiently used for decoding ECoG signals. Note that by using switching linear models, we include a switching mean that induce a high accuracy of correlation.

1 This is possible since the finger movements on the test set are now available Finally, we use our global method for obtaining the finger movement estimation. In other words, we used the switching models H k to decode the signals with Equation ( 4) and the estimated sequence k. The finger movement estimation can be seen on the lower plot of Figure 5b and the correlation measures are in Table 3c. As expected, the accuracy is lower than the one obtained with the true segmentation. However, we obtained an average correlation of 0.42 which is far better than when using a global regression approach. These predictions of the finger flexions were presented in the BCI Competition and achieved the second place. Note that the last 3 fingers have the lowest correlation. Those one are highly physically correlated and they are much more difficult to discriminate than the two first ones. The first finger is by far the best estimated one as we obtained a correlation averaged accross subject of 0.56 .

Discussion and future works

The results presented in the previous section corresponds to the method used for the BCI Competition.

We first note that the best performance obtained by Liang et al. [START_REF] Liang | Decoding finger flexion using amplitude modulation from band-specific ecog[END_REF] gives a correlation of about 0.46. Their method considers an amplitude modulation along time to cope with the abrupt change in the finger flexions amplitude along time. Such an approach is somewhat similar to ours since they try to distinguish situations where fingers are moving or not.

Then, we believe that our approach can be improved in several ways. Indeed, we choose to use linear models depending on the internal states, but [START_REF] Pistohl | Prediction of arm movement trajectories from ecog-recordings in humans[END_REF] proposed to use a kalman filter for the decoding of movement. This 3: Correlation between measured and estimated movement for a global linear regression (a), switching decoder with exact sequence (b) and switching decoder with an estimated sequence (c) approach may be extended to using switching kalman filters in the switching model decoder.

Furthermore, our approach for estimating the sequence of hidden states can be highly improved. Liang [START_REF] Liang | Decoding finger flexion using amplitude modulation from band-specific ecog[END_REF] proposed to use Power Spectral Densities of the ECoG channel as features and we believe that these features may be added and used in the sequence labeling. In our method the features are low-pass filtered in order to increase recognition performance, but other sequence labeling methods like HMM [START_REF] Darmanjian | Independently coupled hmm switching classifier for a bimodel brainmachine interface[END_REF] have been used in BCI. Other sequence labeling methods like Conditional Random Fields [START_REF] Lafferty | Conditional random fields: Probabilistic models for segmenting and labeling sequence data[END_REF] known to outperform HMM in some case or Sequence SVM [START_REF] Bordes | Sequence labelling svms trained in one pass[END_REF] may be used to get a better sequence of hidden states.

Another interesting approach that may be investigated is the mixture of sources approach. Indeed, one may considered that each moving finger is associated to a source of ECoG signals. Then, the problem of identifying which finger is moving may boil down to a source separation problem.

Conclusions

In this paper, we present a method for the decoding finger flexions from ECoG signals. The decoder is based on switching linear models. Our approach has been tested on a the BCI Competition IV Dataset 4 and achieved the second place in the competition. Results show that the switching model approach produce better result than using a unique model. Furthermore an accurate finger flexion estimation may be achieved when using an exact sequence of hidden states showing the interest of the switching models.

In future works, we plan to improve the result of the switching models decoder by two different approaches. On the one hand, we can use more general models than linear ones for the movement prediction (switching kalman filters, nonlinear regression). On the other hand we can improve the sequence labeling along time with new approach and by using new features extracted from the ECoG signals.

Feature extractionFig. 1 :

 1 Fig.1: Diagram of our switching models decoder. We see that from the ECoG signals, we estimate two models. (bottom flow) one which outputs a state k predicting which finger is moving and (top flow) another one that, given the predicted moving finger, estimates the flexion of all fingers.

Fig. 2 :

 2 Fig. 2: Diagram of the feature extraction procedure for the moving finger decoding. Here, we have outlined the processing of a single channel signal.

Fig. 3 :

 3 Fig. 3: Workflow of the learning sets extraction (X k and Y k ) and estimation of the linear models H k .

  models and estimated sequence corr=0.70 (subject 1, finger 1) models and estimated sequence corr=0.61 (subject 1, finger 2) Measured Estimated (b) Subject 1, Finger 2

Fig. 5 :

 5 Fig. 5: True and estimated finger flexion for (upper plots) a global linear regression, (middle plots) switching decoder with true moving finger segmentation and (lower plots) with the switching decoder with an estimated moving finger segmentation.

Table 1 :

 1 Number of samples used in the validation step for subject 1

		Finger Learning Validation
		1	8355	3848
		2	9750	2965
		3	13794	3287
		4	6179	2915
		5	10729	5362
		6	26074	6623
	Finger Sub. 1 Sub. 2 Sub. 3 Average
	1	0.4191 0.5554 0.7128 0.5625
	2	0.4321 0.4644 0.6541 0.5169
	3	0.6162 0.3723 0.2492 0.4126
	4	0.4091 0.5668 0.0781 0.3513
	5	0.4215 0.5165 0.5116 0.4832
	Avg. 0.4596 0.4951 0.4411 0.4653

Table 2 :

 2 Correlation coefficient obtained by the linear models h

	(k)

k .

Table


Emilie Niaf

Rémi Flamary

Carole Lartizien

Stéphane Canu

Émilie Niaf

Handling uncertainties in SVM classification

Keywords: support vector machines, maximal margin algorithm, uncertain labels

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

In the mainstream supervised classification scheme, an expert is required for labelling a set of data used then as inputs for training the classifier. However, even for an expert, this labeling task is likely to be difficult in many applications. In the end the training data set may contain inaccurate classes for some examples, which leads to non robust classifiers [START_REF] Stempfel | Learning SVMs from Sloppily Labeled Data[END_REF]. For instance, this is often the case in medical imaging where radiologists have to outline what they think are malignant tissues over medical images without access to the reference histopatologic information. We propose to deal with these uncertainties by introducing probabilistic labels in the learning stage so as to: 1. stick to the real life annotation problem, 2. avoid discarding uncertain data, 3. balance the influence of uncertain data in the classification process. Our study focuses on the widely used Support Vector Machines (SVM) two-class classification problem [START_REF] Schölkopf | Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond[END_REF]. This method aims a finding the separating hyperplane maximizing the margin between the examples of both classes. Several mappings from SVM scores to class membership probabilities have been proposed in the literature [START_REF] Platt | Probabilistic outputs for support vector machines and comparisons to regularized likelihood methods[END_REF][START_REF] Sollich | Probabilistic methods for support vector machines[END_REF]. In our approach, we propose to use both labels and probabilities as input thus learning simultaneously a classifier and a probabilistic output. Note that the output of our classifier may be transformed to probability estimations without using any mapping algorithm. In section 2 we define our new SVM problem formulation (referred to as P-SVM) to deal with certain and probabilistic labels simultaneously. Section 3 describes the whole framework of P-SVM and presents the associated quadratic problem. Finally, in section 5 we compare its performances to the classical SVM formulation (C-SVM) over different data sets to demonstrate its potential.

PROBLEM FORMULATION

We present below a new formulation for the two-class classification problem dealing with uncertain labels. Let X be a feature space. We define (x i , l i ) i=1...m the learning dataset of input vectors (x i ) i=1...m ∈ X along with their corresponding labels (l i ) i=1...m , the latter of which being

• class labels:

l i = y i ∈ {-1, +1} for i = 1 . . . n (in classification), • real values: l i = p i ∈ [0, 1] for i = n + 1 . . .

m (in regression)

. p i , associated to point x i allows to consider uncertainties about point x i 's class. We define it as the posterior probability for class 1.

p i = p(x i ) = P(Y i = 1 | X i = x i ).
We define the associated pattern recognition problem as min

w 1 2 w 2 (1)
subject to

y i (w ⊤ x i + b) ≥ 1, i = 1...n z - i ≤ w ⊤ x i + b ≤ z + i , i = n + 1...m
Where boundaries z - i , z + i directly depend on p i . This formulation consists in minimizing the complexity of the model while forcing good classification and good probability estimation (close to p i ). Obviously, if n = m, we are brought back to the classical SVM problem formulation.

Following the idea of soft margin introduced in regular SVM to deal with the case of inseparable data, we introduce slack variables ξ i . This measure the degree of misclassification of the datum x i thus relaxing hard constraints of the initial optimization problem which becomes

min w,ξ,ξ -,ξ + 1 2 w 2 + C n i=1 ξ i + C m i=n+1 (ξ - i + ξ + i ) (2) subject to          y i (w ⊤ x i + b) ≥ 1 -ξ i , i = 1...n z - i -ξ - i ≤ w ⊤ x i + b ≤ z + i + ξ + i , i = n + 1...m 0 ≤ ξ i , i = 1...n 0 ≤ ξ - i and 0 ≤ ξ + i , i = n + 1...m
Parameters C and C are predefined positive real numbers controlling the relative weighting of classification and regression performances.

Let ε be the labelling precision and δ the confidence we have in the labelling. Let's define η = ε + δ. Then, the regression problem consists in finding optimal parameters w and b such that

| 1 1 + e -a(w ⊤ xi+b) -p i |< η ,
Thus constraining the probability prediction for point x i to remain around to

1 1+e -a(w ⊤ x i +b) within distance η [5, 6, 7]. The boundaries (where w ⊤ x i + b = ±1), define parameter a as: a = ln( 1 η -1)
Finally:

max(0, p i -η) ≤ 1 1 + e -a(w ⊤ xi+b) < min(p i + η, 1), ⇐⇒ z - i ≤ w ⊤ x i + b < z + i ,
where

z - i = -1 a ln( 1 pi-η -1) and z + i = -1 a ln( 1 pi+η -1).

DUAL FORMULATION

We can rewrite the problem in its dual form, introducing Lagrange multipliers. We are looking for a stationary point for the Lagrange function L defined as

L(w, b, ξ, ξ -, ξ + , α, β, µ + , µ -, γ + , γ -) = 1 2 w 2 + C n i=1 ξ i + C m i=n+1 (ξ - i + ξ + i ) - n i=1 α i (y i (w ⊤ x i + b) -(1 -ξ i )) - n i=1 β i ξ i - m i=n+1 µ - i ((w ⊤ x i + b) -(z - i -ξ - i )) - m i=n+1 γ - i ξ - i - m i=n+1 µ + i ((z + i + ξ + i ) -(w ⊤ x i + b)) - m i=n+1 γ + i ξ + i with α ≥ 0, β ≥ 0, µ + ≥ 0, µ -≥ 0,γ + ≥ 0 and γ -≥ 0
Computing the derivatives of L with respect to w, b, ξ, ξ -and ξ + leads to the following optimality conditions:

                     0 ≤ α i ≤ C, i = 1...n 0 ≤ µ + i ≤ C, i = n + 1...m 0 ≤ µ - i ≤ C, i = n + 1...m w = n i=1 α i y i x i - m i=n+1 (µ + i -µ - i )x i y ⊤ α = m i=n+1 (µ + i -µ - i )
where

e 1 = [1 . . . 1 n times 0 . . . 0 (m-n) times
] ⊤ and e 2 = [0 . . . 0 n times

1 . . . 1 (m-n) times ] ⊤ .
Calculations simplifications then lead to

L(w, b, ξ, ξ -, ξ + , α, β, µ, γ + , γ -) = -1 2 w ⊤ w + n i=1 α i + m i=n+1 µ - i z - i - m i=n+1 µ + i z + i Finally, let Γ = [α 1 . . . α n µ + n+1 . . . µ + m µ - n+1 . . . µ - m ] ⊤ be a vector of dimension 2m -n. Then w ⊤ w = Γ ⊤ G Γ where G =   K 1 -K 2 K 2 -K ⊤ 2 K 3 -K 3 K ⊤ 2 -K 3 K 3   with K 1 = (y i y j x ⊤ i x j ) i,j=1...n , K 2 = (x ⊤ i x j y i ) i=1...n,j=n+1...m , K 3 = (x ⊤ i x j ) i,j=n+1...m ,
The dual formulation becomes

                           min Γ 1 2 Γ ⊤ GΓ -ẽ⊤ Γ, f ⊤ Γ = 0 with ẽ = [ 1 . . . 1 n times -z + n+1 • • • -z + m n-m times z - n+1 . . . z - m n-m times ] with f ⊤ = [y ⊤ , -1 • • • -1 n-m times , 1 . . . 1 n-m times ] and 0 ≤ Γ ≤ [C . . . C n times C . . . C n-m times C . . . C n-m times ] ⊤ (3)

KERNELIZATION

Formulations (2) and ( 3) can be easily generalized by introducing kernel functions. Let k be a positive kernel satisfying Mercer's condition and H the associated Reproducing Kernel Hilbert Space (RKHS). Within this framework equation ( 2) becomes

min f,b,ξ,ξ -,ξ + 1 2 f 2 H + C n i=1 ξ i + C m i=n+1 (ξ - i + ξ + i ) (4) subject to          y i (f (x i ) + b) ≥ 1 -ξ i , i = 1...n z - i -ξ - i ≤ f (x i ) + b ≤ z + i + ξ + i , i = n + 1...m 0 ≤ ξ i , i = 1...n 0 ≤ ξ - i and 0 ≤ ξ + i i = n + 1...m Formulation (3) remains identical, with K 1 = (y i y j k(x i , x j )) i,j=1...n , K 2 = (k(x i , x j )y i ) i=1...n,j=n+1...m , K 3 = (k(x i , x j )) i,j=n+1...m ,

EXAMPLES

In order to experimentally evaluate the proposed method for handling uncertain labels in SVM classification, we have simulated different data sets described below. In these numerical examples, a RBF kernel k(u, v) = e -u-v 2 /2σ 2 is used and C = C = 100. We implemented our method using the SVM-KM Toolbox [START_REF] Canu | Svm and kernel methods matlab toolbox[END_REF]. We compare the classification performances and probabilistic predictions of the C-SVM and P-SVM approaches. In the first case, probabilities are estimated by using Platt's scaling algorithm [START_REF] Platt | Probabilistic outputs for support vector machines and comparisons to regularized likelihood methods[END_REF] while in the second case, probabilities are directly estimated via the formula defined in (2):

P (y = 1|x) =
P (y i = 1|x i ) log( P (y i = 1|x i ) Q(y i = 1|x i ) )
for probability distributions P and Q (for evaluating probability estimation).

Probability estimation

We generate two unidimensional datasets, labelled '+1' and '-1', from normal distributions of variances σ 2 -1 = σ 2 1 =0.3 and means µ -1 =-0.5 and µ 1 =+0.5. Let's (x l i ) i=1...n l denote the learning data set (n l =200) and (x t i ) i=1...n t the test set (n t =1000). We compute, for each point x i , its true probability P (y i = +1|x i ) to belong to class '+1'. From here on, learning data are labelled in two ways, as follows a) For i = 1 . . . n l , we get the regular SVM dataset by simply using a probability of 0.5 as the threshold for assigning class labels y i associated to point x i . This is what would be done in practical cases when the data contains class membership probabilities and a SVM classifier is used.

if P (y l i = 1|x l i ) > 0.5, then y l i = 1, if P (y l i = 1|x l i ) ≤ 0.5, then y l i = -1 (5)
This dataset (x l i , y l i ) i=1...n l is used to train the C-SVM classifier. b) We define another data set (x l i , ŷl i ) i=1...n l such that, for i = 1 . . . n,

if P (y l i = 1|x l i ) > 1 -η, then ŷl i = 1, if P (y l i = 1|x l i ) < η, then ŷl i = -1, ŷl i = P (y l i = 1|x l i ) otherwise. (6)
If the probability values are sufficiently close to 0 or 1 (closeness being defined by the precision and confidence), we admit that they belong respectively to class -1 or 1. This probabilistic dataset (x l i , ŷl i ) i=1...n l is used to train the P-SVM algorithm. We compare our two approaches using the test set (x t i ) i=1...n t . As we know the true probabilities (P (y t i = 1|x t i )) i=1...n t , we can estimate the probability prediction error (KL). Figure 1 shows the probability predictions performances improvement shown by the P-SVM: the true probabilities (black) and P-SVM estimations (red) are quasi-superimposed (KL=0.2) whereas Platt's estimations are less accurate (KL=11.3).

Noise robustness

We generate two 2D datasets, labelled '+1' and '-1', from normal distributions of variances σ 2 -1 =σ 2 1 =0.7 and means µ -1 = (-0.3, -0.5) and µ 1 =(+0.3, +0.5). As in the previous experiment, we compute class '1' membership probability for each point x l of the learning data set. We simulate classification error by artificially adding a centered uniform noise (δ of amplitude 0.1), to the probabilities, such that for i = 1 . . . n, P (y i = 1|x i ) = P (y i = 1|x i ) + δ i .

We then label learning data following the same scheme as described in ( 5) and [START_REF] Grandvalet | A probabilistic interpretation of SVMs with an application to unbalanced classification[END_REF]. Figure 2 shows the margin location and probabilities estimations using the two methods over a grid of values. Far from learning data points, both probability estimations are less accurate, this being directly linked to the choice of a gaussian kernel. However, P-SVM classification and probability estimations obtained for 1000 test points, are clearly more alike the ground truth (Acc P-SVM = 99% , KL P-SVM = 3.6) than C-SVM (Acc C-SVM = 95%, KL C-SVM = 95). Contrary to P-SVM which, by combining both classification and regression, predicts good probabilities, C-SVM is sensitive to classification noise and is no more converging to the Bayes rule as seen in [START_REF] Stempfel | Learning SVMs from Sloppily Labeled Data[END_REF]. Figure 3 shows the impact of noise amplitude on classifiers performances (values are averaged over 30 random simulations). Even if noise increases, classifications and probability predictions performances of the P-SVM remain significantly higher than those of C-SVM.

CONCLUSION

This paper has presented a new way to take into account both qualitative and quantitative target data by shrewdly combin- ing both SVM classification and regression loss. Experimental results show that our formulation can perform very well on simulated data for discrimination as well as posterior probability estimation. This approach will soon be applied on clinical data thus allowing to assess its usefulness in computer assisted diagnosis for prostate cancer. Note that this framework initially designed for probabilistic labels can also be generalized to other dataset involving quantitative data as it can be used for instance to estimate a conditional cumulative distribution function.

1 1+e

 1 -a(w ⊤ x+b) . Performances are evaluated by computing • Accuracy (Acc) Proportion of well predicted examples in the test set (for evaluating classification). • Kullback Leibler distance (KL) D KL (P ||Q) = n i=1

Fig. 1 :

 1 Fig. 1: Probability estimations comparison. Top plot shows the true posterior probabilities with C-SVM and P-SVM estimations overlaying. Lower plot shows the distance between true probabilities and estimations.

Fig. 2 :

 2 Fig. 2: Probability estimations of C-SVM and P-SVM over a grid using noisy learning data (uniform noise, amplitude 0.1). Noisy learning data are plotted in blue (class '-1') and red (class '1') stars.

Fig. 3 :

 3 Fig. 3: Noise impact on P-SVM and C-SVM classification performances


Rémi Flamary

Benjamin Labbé

Alain Rakotomamonjy

LARGE MARGIN FILTERING FOR SIGNAL SEQUENCE LABELING

Keywords: Filtering, SVM, BCI, Sequence Labeling

Signal Sequence Labeling consists in predicting a sequence of labels given an observed sequence of samples. A naive way is to filter the signal in order to reduce the noise and to apply a classification algorithm on the filtered samples. We propose in this paper to jointly learn the filter with the classifier leading to a large margin filtering for classification. This method allows to learn the optimal cutoff frequency and phase of the filter that may be different from zero. Two methods are proposed and tested on a toy dataset and on a real life BCI dataset from BCI Competition III.

INTRODUCTION

The aim of signal sequence labeling is to assign a label to each sample of a multichannel signal while taking into account the sequentiality of the samples. This problem typically arises in speech signal segmentation or in Brain Computer Interfaces (BCI). Indeed, in real-time BCI applications, each sample of an electro-encephalography signal has to be interpreted as a specific command for a virtual keyboard or a robot hence the need for sample labeling [START_REF] Blankertz | The BCI competition 2003: progress and perspectives in detection and discrimination of EEG single trials[END_REF][START_REF] Del R Millán | On the need for on-line learning in braincomputer interfaces[END_REF].

Many methods and algorithms have already been proposed for signal sequence labeling. For instance, Hidden Markov Models (HMM) [START_REF] Cappé | Inference in Hidden Markov Models[END_REF] are statistical models that are able to learn a joint probability distribution of samples in a sequence and their labels. In some cases, Conditional Random Fields (CRF) [START_REF] Lafferty | Conditional random fields: Probabilistic models for segmenting and labeling sequence data[END_REF] have been shown to outperform the HMM approach as they do not suppose the observation are independent. Structural Support Vector Machines (Struct-SVM), which are SVMs that learn a mapping from structured input to structured output, have also been considered for signal segmentation [START_REF] Tsochantaridis | Large margin methods for structured and interdependent output variables[END_REF]. Signal sequence labeling can also be viewed from a very different perspective by considering a change detection method coupled with a supervised classifier. For instance, a Kernel Change Detection algorithm [START_REF] Desobry | An online kernel change detection algorithm[END_REF] can be used for detecting abrupt changes in a signal and afterwards a classifier applied for labeling the segmented regions.

In order to preprocess the signal, a filtering is often applied and the resulting filtered samples are used as training examples for learning. Such an approach poses the issue of the filter choice, which is oftenly based on prior knowledge on the information brought by the signals. Moreover, measured signals and extracted features may not be in phase with the labels and a time-lag due to the acquisition process appears in the signals. For example, in the problem of decoding arm movements from brain signals, there exists a natural time shift between these two entries, hence in their works, Pistohl et al. [START_REF] Pistohl | Prediction of arm movement trajectories from ecog-recordings in humans[END_REF] had to select by a validation method a delay in their signal processing method.

In this work, we address the problem of automated tuning of the filtering stage including its time-lag. Indeed, our objective is to adapt the preprocessing filter and all its properties by including its setting into the learning process. Our hypothesis is that by fitting properly the filter to the classification problem at hand, without relying on ad-hoc prior-knowledge, we should be able to considerably improve the sequence labeling performance. So we propose to take into account the temporal neighborhood of the current sample directly into the decision function and the learning process, leading to an automatic setting of the signal filtering.

For this purpose, we first propose a naive approach based on SVMs which consists in considering, instead of a given time sample, a time-window around the sample. This method named as Window-SVM, allows us to learn a spatio-temporal classifier that will adapt itself to the signal time-lag. Then, we introduce another approach denoted as Filter-SVM which dissociates the filter and the classifier. This novel method jointly learns a SVM classifier and FIR filters coefficients. By doing so, we can interpret our filter as a large-margin filter for the problem at hand. These two methods are tested on a toy dataset and on a real life BCI signal sequence labeling problem from BCI Competition III [START_REF] Blankertz | The BCI competition 2003: progress and perspectives in detection and discrimination of EEG single trials[END_REF].

LARGE MARGIN FILTER

Problem definition

Our concern is a signal sequence labeling problem : we want to obtain a sequence of labels from a multichannel timesample of a signal or from multi-channel features extracted from that signal. We suppose that the training samples are gathered in a matrix X ∈ R N ×d containing d channels and N samples. X i,j is the value of channel j for the i th sample. The vector y ∈ {-1, 1} N contains the class of each sample.

In order to reduce noise in the samples or variability in the features, an usual approach is to filter X before the classifier learning stage. In literature, all channels are usually filtered with the same filter (Savisky-Golay for instance in [START_REF] Pistohl | Prediction of arm movement trajectories from ecog-recordings in humans[END_REF]) although there is no reason for a single filter to be optimal for all channels. Let us define the filters applied to X by the matrix F ∈ R f ×d . Each column of F is a filter for the corresponding channel in X and f is the size of the FIR filters.

We define the filtered data matrix X by:

X i,j = f m=1 F m,j X i+1-m+n0,j (1)
where the sum is a unidimensional convolution of each channel by the filter in the appropriate column of F . n 0 is the delay of the filter, for instance n 0 = 0 corresponds to a causal filter and n 0 = f /2 corresponds to a filter centered on the current sample.

Windowed-SVM (W-SVM)

As highlighted by Equation ( 1), a filtering stage essentially consists in taking into account for a given time i, instead of the sample X i,• , a linear combination of its temporal neighborhood. However, instead of introducing a filter F , it is possible to consider for classification a temporal window around the current sample. Such an approach would lead to this decision function for the i th sample of X:

f W (i, X) = f m=1 d j=1 W m,j X i+1-m+n0,j + w 0 (2)
where W ∈ R f ×d and w 0 ∈ R are the classification parameters and f is the size of the time-window. Note that W plays the role of the filter and the weights of a linear classifier. In a large-margin framework, W and w 0 may be learned by minimizing this functional:

J W SV M (W ) = 1 2 ||W || 2 F + C 2 N i=1 H(y, X, f W , i) 2 (3)
where

||W || 2 F = i,j W 2 i,j
is the squared Frobenius norm of W , C is a regularization term to be tuned and H(y, X, f, i) = max(0, 1y i f (i, X)) is the SVM hinge loss. By vectorizing appropriately X and W , problem (3) may be transformed into a linear SVM. Hence, we can take advantage of many linear SVM solvers existing in the literature such as the one proposed by Chapelle [START_REF] Chapelle | Training a support vector machine in the primal[END_REF]. By using that solver, Window-SVM complexity is about O(N.(f.d) 2 ) which scales quadratically with the filter dimension.

The matrix W weights the importance of each sample value X i,j into the decision function. Hence, channels may have different weights and time-lag. Indeed, W will automatically adapt to a phase difference between the sample labels and the channel signals. However, in this method since space and time are treated independently, W does not take into account the multi-channel structure and the sequentiality of the samples. Since the samples of a given channel are known to be time-dependent due to the underlying physical process, it seems preferable to process them with a filter and to classify the filtered samples. So we propose in the sequel another method that jointly learns the time-filtering and a linear classifier on the filtered sample defined by Eq. (1).

Large margin filtering (Filter-SVM)

We propose to find the filter F that maximizes the margin of the linear classifier for the filtered samples. In this case, the decision function is:

f F (i, X) = f m=1 d j=1 w j F m,j X i+1-m+n0,j + w 0 (4)
where w and w 0 are the parameters of the linear SVM classifier corresponding to a weighting of the channels. By dissociating the filter and the decision function weights, we expect that some useless channels (non-informative or too noisy) for the decision function get small weights. Indeed, due to the double weighting w j and F .,j , and the specific channel weighting role played by w j , this approach, as shown in the experimental section is able to perform channel selection.

The decision function given in Equation ( 4) can be obtained by minimizing:

J F SV M = 1 2 ||w|| 2 + C 2 n i=1 H(y, X, f F , i) 2 + λ 2 ||F || 2 F (5)
w.r.t. (F, w, w 0 ) where ||F || F is the Frobenius norm, and λ is a regularization term to be tuned. Note that without the regularization term ||F || 2 F , the problem is ill-posed. Indeed, in such a case, one can always decrease ||w|| 2 while keeping the empirical hinge loss constant by multiplying w by α < 1 and F by 1 α . The cost defined in Equation ( 5) is differentiable and provably non-convex when jointly optimized with respect to all parameters. However, J F SV M is differentiable and convex with respect to w and w 0 when F is fixed as it corresponds to a linear SVM with squared hinge loss. Hence, for a given value of F , we can define

J(F ) = min w,w0 1 2 ||w|| 2 + C 2 n i=1 H(y, X, f F , i) 2
which according to Bonnans et al. [START_REF] Bonnans | Optimization problems with pertubation : A guided tour[END_REF] is differentiable. Then if w * and w * 0 are the optimal values for a given F * , the gradient of the second term of J(•) with respect to F at the point

F * is: ∇ Fm,j J(F * ) = - N i=1 y i (w * j X i-m+1+n0,j )×H(y, X, f F * , i)
Now, since J(F ) is differentiable and since its value can be easily computed by a linear SVM, we choose for learning the decision function to minimize J(F ) + λ 2 F 2 F with respects to F instead of minimizing problem [START_REF] Tsochantaridis | Large margin methods for structured and interdependent output variables[END_REF]. Note that due to the objective function non-convexity in problem ( 5), these two minimization problems are not strictly equivalent, but our approach has the advantage of taking into account the intrinsic large-margin structure of the problem.

Algorithm 1 Filter-SVM solver

Set

F l,k = 1/f for k = 1 • • • d and l = 1 • • • f repeat D F ← gradient of J F SV M with respect to F (F, w * , w * 0 ) ← Line-Search along D F until Stopping criterion is reached
For solving the optimization problem, we propose a gradient descent algorithm along F with a line search method for finding the optimal step. The method is detailed in algorithm 1. Note that at each computation of J(F ) in the line search, the optimal w * and w * 0 are found by solving a linear SVM. The iterations in the algorithm may be stopped by two stopping criteria: a threshold on the relative variation of J(F ) or a threshold on variations of F norm.

Due to the non-convexity of the objective function, it is difficult to provide an exact evaluation of the solution complexity. However, we know that the gradient computation has order of O(N.f.d) and that when J(F ) is computed at each step of the line search, a O(N.d 2 ) linear SVM is solved and a O(N.f.d) filtering is applied.

RESULTS

Toy Example

We use a toy example that consists of nbtot channels, only nbrel of them being discriminative. Discriminative channels have a switching mean {-1, 1} controlled by the label and corrupted by a gaussian noise of deviation σ. The length of the regions with constant label follows a uniform distribution law between [30, 40] samples and different time-lags are applied to the channels. We selected f = 21 and n 0 = 11 corresponding to a good average filtering centered on the current sample. Figure 1 shows how the samples are transformed thanks to the filter F for a unidimensional signal. In this case, the mean test error due to the noise is 16% for the unfiltered signal, while only 2% for the optimally filtered signal.

Window-SVM and Filter-SVM are compared to SVM without filtering, SVM with an average filter of size f (Avg-SVM) and HMM with a Viterbi decoding. The regularization The methods are compared for different σ values with (nbtot = 30, nbrel = 3). The test error is plotted on the left of Figure 2. We can see that only Avg-SVM, Window-SVM and Filter-SVM adapt to time-lags between the channels and the labels. Both Window-SVM and Filter-SVM outperform the other methods, even if for a heavy noise, the last one seems to be slightly better. Then we test our methods for a varying number of channels in order to see how dimension is handled (nbrel = 3, σ = 3). even to be similar to Avg-SVM. This comes from the fact that Filter-SVM can more efficiently perform a channel selection thanks to the weighting of w. Figure 3 shows the filters returned by both methods. We observe that only the coefficients of the relevant signals are important and that the other signals tend to be eliminated by small weights for Filter-SVM, explaining the better results in high dimension.

BCI Dataset

We test our method on the BCI Dataset from BCI Competition III [START_REF] Blankertz | The BCI competition 2003: progress and perspectives in detection and discrimination of EEG single trials[END_REF]. The problem is to obtain a sequence of labels out of brain activity signals for 3 human subjects. The data consists in 96 channels containing PSD features (3 training sessions, 1 test session, N ≈ 3000 per session) and the problem has 3 labels (left arm, right arm or feet).

We use Filter-SVM that showed better result in hight dimension for the toy example. The multi-class aspect of the problem is handled by using a One-Against-All strategy. The regularization parameters are tuned using a grid search validation method on the third training set. We compare our method to the best BCI competition results (using only 8 samples) and to the SVM without filtering. Test error for different filter size f and delay n 0 may be seen on Table 1. Results show that one can improve drastically the result by using longer filtering with causal filters (n 0 = 0). Note that Filter-SVM outperform Avg-SVM with a centered filter.

Another advantage of this method is that one can visualize a discriminative space-time map (channel selection, shape of the filter and delays). We show for instance in Figure 4 the discriminative filters F obtained for subject 1, and we can see that the filtering is extremely different depending on the task.

The Matlab code corresponding to these results will be provided on our website for reproducibility.

CONCLUSIONS

We have proposed two methods for automatically learning a spatio-temporal filter used for multi-channel signal classification. Both methods have been tested on a toy example and on a real life dataset from BCI Competition III.

Empirical results clearly show the benefits of adapting the signal filter to the large-margin classification problem despite the non-convexity of the criterion.

In future work, we plan to extend our approach to nonlinear case, we believe that a differentiable kernel can be used instead of inner products at the cost of solving the SVM in the dual space. Another perspective would be to adapt our methods to the multi-task situation, where one wants to jointly learn one matrix F and several classifiers (one per task).

Fig. 1 .σFig. 2 .Fig. 3 .

 123 Fig. 1. Histograms of both labels with and without filtering (vertical axis are different) for a 1 channel signal with σ = 1

Figure 2 (

 2 right) shows the interest of Filter-SVM over Window-SVM in hight dimension as we can see that the last one tends to lose his efficiency, f = 8, n 0 = 0 0.2337 0.3589 0.4937 0.3621 f = 20, n 0 = 0 0.2021 0.2693 0.4381 0.3032 f = 50, n 0 = 0 0.1321 0.2382 0.4395 0.2699 Avg-SVM f = 100, n 0 = 50 0.1544 0.2235 0.3870 0.2550 Filter-SVM f = 100, n 0 = 50 0.0537 0.1659 0.3859 0.2018

Fig. 4 .

 4 Fig. 4. F filters (subject 1) for label 1 against all (left) and label 2 against all (right).

Table 1 .

 1 Test Error for BCI Dataset

This work is funded in part by the FP7-ICT Programme of the European Community, under the PASCAL2 Network of Excellence, ICT-216886 and by the French ANR Project ANR-09-EMER-001.


M.D. Mr Urpo Kinnunen

Hannu Syrjälä

Pasi Ohtonen

M.D Urpo ; Kinnunen
email: urpo.kinnunen@oulu.fi

Riikka Räty

Erkki Elonen

Tapio Nousiainen

Esa Jantunen

Kari Remes

Maija Itälä-Remes

Raija Silvennoinen

Pirjo Koistinen

# Urpo Kinnunen

Nousiainen

Pirjo

Koistinen

Finnish Leukemia

Blood Stream Infections during Chemotherapy-Induced Neutropenia in Adult Patients with Acute Myeloid Leukemia: Treatment cycle matters

Keywords: acute myeloid leukemia, adult, chemotherapeutics, neutropenia, bloodstream infection leukemia, adult, chemotherapeutics, neutropenia, bloodstream 58 infection 59 60 61

Blood stream infections during chemotherapy-induced

neutropenia in adult patients with acute myeloid leukemia: treatment cycle matters

"If more than one micro-organism was recovered from blood cultures of a patient during a chemotherapy cycle, the episode was defined as polymicrobial." is added to the method section in lines 115 -116.

Reviewer #2:

We agree with the reviewer, that the cycle II is a crucial point in the data. As suggested we analyzed the cycle 2 by dividing it in two groups: those with active disease and receiving the 2nd induction (n=80) and those in remission and receiving the 1st consolidation (n=212).

Active disease Remission p (n=80) (n=212) Neutropenia d 27 (22 -36) 25 ( We could not demonstrate any significant differences between the groups. This may partly be due to the limited number of patients (80 + 212). A more powerful study would probably demonstrate difference in amount of VGS and maybe in amount of gastrointestinal toxicity.

The following sentence has been added into the text in the results section to lines 157 -159: "On the other hand, no difference in number of febrile or neutropenic days, in amount of grade 3 & 4 gastrointestinal toxicity, peak CRP-values, or recovery of individual microbial strains was found between those patients with active disease and those in remission in the second cycle".

The reviewer asks about the interpretation about the skin contaminants found in blood cultures. Due to the characteristics of the register data we cannot analyze more specifically these blood culture findings. Unfortunately we have to accept decisions of attending physicians.

We have chanced the text about interpretation of blood cultures in the methods section: "Whether blood culture findings were true or contaminant was accepted by attending physicians." is added to the text in the line 114.

The reviewer points to the possible inability of the WHO criteria to detect gastrointestinal toxicity caused by chemotherapy. "Another explanation to our surprising findings may be that measuring toxicity by the WHO method is not sensitive enough for identifying this kind of changes in gastrointestinal tract." is added in the text into the discussion section to lines 212 -214.

The question, whether the patients who died, did so before acquiring BSI was analyzed in cycles one and two: During the first cycle 13 patients died of whom BSI data of 11 patients were available and five had BSI. During the second cycle, eleven patients with induction treatment died, of whom eight had BSI. Taken together, the interesting idea made by the reviewer, did not seem to explain our results.

INTRODUCTION

63

As early as in the sixties, the importance of severe gram-negative bacterial blood stream infections (BSI) during 64 intensive chemotherapy of acute myeloid leukemia (AML) was identified [START_REF] Bodey | Quantitative relationships 265 between circulating leukocytes and infection in patients with acute leukemia[END_REF]. In the seventies, empirical 65 treatment protocols were introduced to treat BSIs caused by gram-negative microorganism in neutropenic fever 66 patients [START_REF] Schimpff | Empiric therapy with 268 carbenicillin and gentamicin for febrile patients with cancer and 269 granulocytopenia[END_REF]. During the next two decades, the causes of BSIs shifted from gram-negative rods to gram-positive 67 cocci [START_REF] Baden | Prophylactic antimicrobial agents and the importance of 271 fitness[END_REF][START_REF] Cometta | Piperacillin-tazobactam plus 273 amikacin versus ceftazidime plus amikacin as empiric therapy for fever in 274 granulocytopenic patients with cancer. The International Antimicrobial Therapy 275 Cooperative Group of the European Organization for Research and Treatment of 276 Cancer[END_REF][START_REF] Cometta | Monotherapy with meropenem 278 versus combination therapy with ceftazidime plus amikacin as empiric therapy 279 for fever in granulocytopenic patients with cancer[END_REF][START_REF] Edmond | Nosocomial bloodstream infections in United States hospitals: a three-283 year analysis[END_REF][START_REF] Hammond | Antibiotic prophylaxis for patients with acute 285 leukemia[END_REF][START_REF] Wisplinghoff | Current trends in the 287 epidemiology of nosocomial bloodstream infections in patients with hematological malignancies and solid neoplasms in hospitals in the United 289 States[END_REF][START_REF] Zinner | Changing epidemiology of infections in patients with 291 neutropenia and cancer: emphasis on gram-positive and resistant bacteria[END_REF]. The most important reason for this change has been explained to be due to the use of 68 antibiotic prophylaxis during periods of neutropenia in AML patients. Interestingly, the newest results suggest 69 that the proportion of gram-negative infections is once again increasing [START_REF] Cattaneo | Recent changes in bacterial 294 epidemiology and the emergence of fluoroquinolone-resistant Escherichia coli 295 among patients with haematological malignancies: results of a prospective study 296 on 823 patients at a single institution[END_REF].

70

According to the knowledge of the authors, little attention has been paid to BSI rate during 71 different chemotherapy cycles. When the febrile episodes of the so called SIGNIFICANT study [START_REF] Cullen | Antibacterial prophylaxis after 298 chemotherapy for solid tumors and lymphomas[END_REF] were later 72 evaluated, it was found that during the chemotherapy of solid tumors and lymphomas the risk of a febrile 73 episode, as a sign of possible BSI and an indication for empirical antibiotic treatment, was highest during the 74 first treatment cycle, especially in testicular and small-cell lung cancers [START_REF] Cullen | Rational selection of 300 patients for antibacterial prophylaxis after chemotherapy[END_REF]. It was also noted that if the patient 75 had a febrile episode during the first chemotherapy cycle, he or she would have an increased risk of a febrile 76 episode during the subsequent cycles [START_REF] Cullen | Rational selection of 300 patients for antibacterial prophylaxis after chemotherapy[END_REF].

77

In solid tumors and lymphomas patients receive repeated cycles of the same chemotherapeutics, 78 whereas in AML different chemotherapeutics are administrated in consecutive cycles in order to achieve a 79 favorable outcome. As has been seen earlier in a small, one center study, during AML treatment with an 80 idarubicin, conventional-dose cytarabine and thioquanine schedule, the BSI rate was lower than after other 81 regimens [START_REF] Kinnunen | Influence of 303 chemotherapy courses on the rate of bloodstream infections during therapy-304 induced neutropenia in adult acute myeloid leukemia[END_REF] whereas high-dose cytarabine treatment was associated with a high BSI rate. The present study 82 was based on the nationwide AML-92 register data collected by the Finnish leukemia group [START_REF] Koistinen | Long-term outcome of intensive 307 chemotherapy for adults with de novo acute myeloid leukaemia (AML): the 308 nationwide AML-92 study by the Finnish Leukaemia Group[END_REF], in which 327

83

AML patients with 956 chemotherapy episodes were included for the evaluation of BSI rates. None of the 84 patients had received any antibiotic prophylaxis during chemotherapy-induced neutropenia, which allowed us to 85 observe the real BSI results in four consecutive chemotherapeutic cycles. 86 87

MATERIALS AND METHODS

88

Background. The study protocol and hematological results of this nationwide study population of 327 89 consecutive intensive chemotherapy-treated patients, of whom 82% experienced complete remission, has earlier 90 been published elsewhere [START_REF] Koistinen | Long-term outcome of intensive 307 chemotherapy for adults with de novo acute myeloid leukaemia (AML): the 308 nationwide AML-92 study by the Finnish Leukaemia Group[END_REF].

Study design.

The study protocol is briefly explained as follows (for a more extensive description, see ref. [START_REF] Koistinen | Long-term outcome of intensive 307 chemotherapy for adults with de novo acute myeloid leukaemia (AML): the 308 nationwide AML-92 study by the Finnish Leukaemia Group[END_REF]: 92

To be included the patient had to have de novo AML diagnosed by standard cytological criteria according to 93

French-American-British (FAB) classification [START_REF] Bennett | Proposed revised criteria for the classification of acute myeloid[END_REF], and be between 16 an 65 years old. The study protocol was 94 approved by the ethical committees of all five participating centers. Moreover, the National Agency for 95

Medicines scrutinized the protocol before the beginning of the study. All patients provided informed consent.

96

During the first induction course the chemotherapeutics used were idarubicin, conventional-dose 114

The microorganisms were identified by standard microbiological methods based on growth conditions and 115 appearance on solid media, fermentation of sugars and other organic compounds as well as the use of 116 commercial kits. Wheter blood culture findings were true or contaminant was accepted by attending physicians.

117

If more than one micro-organism was recovered from blood cultures of a patient during a chemotherapy cycle, 118 the episode was defined as polymicrobial.

119

Statistical analysis. and whether the patients had received antibiotic prophylaxis during neutropenia. For example, in a large multi-196 center study with solid tumors and lymphomas, the BSI rate was 6.2% in the levofloxacin group and 7.9% in the 197 placebo group [START_REF] Cullen | Antibacterial prophylaxis after 298 chemotherapy for solid tumors and lymphomas[END_REF]. In another multi-center study, patients having acute leukemia and a duration of neutropenia 198 of at least 7 days, BSI rate was 20.6% in the levofloxacin group and 38.8% in the placebo group [START_REF] Bucaneve | Levofloxacin to prevent 330 bacterial infection in patients with cancer and neutropenia[END_REF]. In our 199 study, the median duration of neutropenia was more than three weeks in each cycle, which is a well-known and 200 real risk of higher BSI rate [START_REF] Bodey | Quantitative relationships 265 between circulating leukocytes and infection in patients with acute leukemia[END_REF]. In one of our centers, the BSI rate during neutropenia among AML patients 201 increased from 21% to 40% when a manual blood culture system was replaced by a CMBCS [START_REF] Kinnunen | Continuous-343 monitoring blood culture screening system improves the detection of bacteremia 344 in neutropenic patients[END_REF]. Taken 202 together, we consider that our BSI rate is realistic and moreover, our BSI incidence rate of 13.2 per 1000 203 patient-days is rather near to the corresponding figure of 10.2 published earlier [START_REF] Velasco | Prospective evaluation of the epidemiology, microbiology, and outcome 347 of bloodstream infections in hematologic patients in a single cancer center[END_REF].

204

When the BSI results were analyzed separately in each cycle, the recovery of micro-organisms 205 during the first chemotherapy-induced neutropenia was clearly lower than in other cycles. This phenomenon was 206 relevant when also incidence rate per 1000 patient-days or per 1000 neutropenia-days was calculated. Our result 207 was rather surprising , when gastrointestinal toxicity (WHO grade III and IV) was taken into account. High-208 dose cytarabine is well-known for its gastrointestinal toxicity. In the present data, the toxicity was highest in the It has been recently noted that the knowledge of polymicrobial infections among cancer patients 239 is sparse [START_REF] Rolston | Polymicrobial infection in patients 366 with cancer: an underappreciated and underreported entity[END_REF]: In trials involving neutropenic patients, the proportion of polymicrobial BSIs has varied from 8% 240 to 32% [START_REF] Giamarellou | Monotherapy with 369 intravenous followed by oral high-dose ciprofloxacin versus combination 370 therapy with ceftazidime plus amikacin as initial empiric therapy for 371 granulocytopenic patients with fever[END_REF][START_REF] Harter | Piperacillin/tazobactam vs 374 ceftazidime in the treatment of neutropenic fever in patients with acute leukemia 375 or following autologous peripheral blood stem cell transplantation: a prospective 376 randomized trial[END_REF]. Our overall figure of polymicrobial BSIs was 28.3%. However, there was once again substantial 241 inter-cycle variation. In three-fourths of the episodes, polymicrobial BSIs were caused by two microorganisms.

242

The most common combination included both gram-positive and gram-negative microorganisms and the second 243 most common included at least two gram-positive microorganisms together.

244

When polymicrobial BSIs were also taken into account in our study, which included the series of 245 AML patients recruited between 1992 and 2001, the portion of gram-positive microorganisms in BSIs was even 246 higher (79.6%) than in the earlier-mentioned study from the USA: their highest figure (76%) was from the year 247 2000 [START_REF] Wisplinghoff | Current trends in the 287 epidemiology of nosocomial bloodstream infections in patients with hematological malignancies and solid neoplasms in hospitals in the United 289 States[END_REF]. The result of 50.9%of gram-negative organisms when polymicrobial BSIs were also included, is quite 248 similar to a recent study [START_REF] Velasco | Comparative study of clinical characteristics of neutropenic and non-379 neutropenic adult cancer patients with bloodstream infections[END_REF], patients were also treated without antibiotic prophylaxis. In another study the 249 proportion of gram-negatives was 52% without and 25% with antibiotic prophylaxis [START_REF] Klastersky | Bacteraemia in febrile 336 neutropenic cancer patients[END_REF].

250

In

  97 cytarabine and thioguanine. The second course, which was either first postremission or second induction course, 98 included high-dose cytarabine and idarubicin. The third course included etoposide, high-dose cytarabine and 99 mitoxantrone and the fourth course amsacrine and high-dose cytarabine. The use of supportive treatments (i.e. 100 growth factors, antibiotics, alimentation and blood products) were administered according to the policies of each 101 of the five hematological university centers. All patients had a central venous access. The infections were treated 102 according to generally accepted guidelines [16, 17]. The patients did not receive any antibiotic prophylaxis 103 during chemotherapy-induced neutropenia. For this study the following information was used from the 104 prospectively gathered register data of the AML patients recruited for the original study between September 105 1992 and December 2001: age at the time of diagnosis, sex, treatment faculty, FAB classification of AML, 106 whether or not the patient had an infection at the time of AML diagnosis and whether or not the patient had a 107 positive blood culture (in ten episodes data was missing). Moreover, the duration of hospital stays, neutropenia 108 (days when absolute neutrophil count was less than 500/μL), febrile days (body temperature > 38 °C), peak C-109 reactive protein level (mg/L) and outcome of the patients were analyzed. Furthermore, gastrointestinal toxicity 110 and the severity of infection categorized according to WHO criteria was recorded in each episode [18]. 111 Microbiological methods. Blood was cultured at participating hospitals using automated continuous-112 monitoring blood culture systems (CMBCS): in two centers with BacT/Alert ™ (bioMérieux INDUSTRY, 113 Hazelwood, MS) and in three centers with Bactec 9240 ™ (BD Diagnostics, Diagnostic Systems, Sparks, MD).

FIGURE 1 .

 1 FIGURE 1. Positive blood culture findings (%) during four chemotherapy cycles among adult

FIGURE 2 .

 2 FIGURE 2. Comparison of positive blood culture findings in cycle I between patients having (Inf

  Figure 1.

Figure 2 .

 2 Figure 2.

  The summary measurements for continuous and ordinal variables are expressed as medians with 25 th and 75 th 121 percentiles unless otherwise stated. Fisher's exact test was used to analyze simple categorical data. The 122 generalized linear mixed model approach was utilized in comparison of presence of positive BSI and toxicity in If the number of hospital days or neutropenic days was missing it was replaced by the cycle average. . 7 of them had BSI. Only 4 patients treated with consolidation treatment in cycle II died because of 143 infection. 1 of those infections was BSI. In cycle III, five deaths were due to infections, of which three were 144 BSIs. In cycle IV four patients died due to infection, with two BSIs among them. III and IV than in cycle I (Table1). The odds ratio for BSI (compared to cycle I) was 5.8, 5.5 and 4.8 in 151 cycles II, III and IV, respectively (P < .001, in all) (Table1). Severe gastrointestinal toxicity (WHO grade III and 152 IV) was highest during cycle I and decreased significantly in successive cycles, the odds ratios compared to Our statistical approach with linear and generalized linear mixed models took into account that the 188 same subjects were evaluated repeatedly, i.e., the measurements of the same patients are not independent. On the 189 other hand, our register data did not include the detection day of BSI from the onset of neutropenia. The other 190 weakness of this study was that gathered data did not include the resistance patterns of detected microorganisms 191 or systematic information regarding the mucositis of the oral cavity of the study subjects.

	180	Our results show that during the chemotherapy courses of adult AML patients, the BSI rate and yielded
	181	microorganisms vary greatly from cycle to cycle, probably reflecting the tendency of different
	123 153 182	chemotherapeutics to predispose patients to infections. Thus, the BSI results in AML should be evaluated based
	124 154 183	different chemotherapy cycles and the linear mixed model approach was used when comparing continuous cycle I being 0.65 at cycle II (P = .041), 0. 43 at cycle III (P < .001) and 0.33 at cycle IV (P < .001) (Table 1, on cycles rather than on the overall results.
	125 155 184	variables (maximum CRP, duration of neutropenia, length of hospital stay and duration of fever days) between Figure 1). Our study has several strengths: It was a prospective multi-center study with a large
	126 156 185	chemotherapy cycles. Both mixed-model approaches take into account that measurements are repeatedly taken During the first chemotherapy cycle, the number of BSI was slightly higher, if the patients did not have homogenous study population of 327 adult de novo AML patients treated according to the same schedule of
	127 157 186	from the same subjects and these within-subject measurements are not independent [19]. Furthermore, both infections at the time of AML diagnosis (25.6%) than those patients having infections (19.3%, P = .17; Figure chemotherapeutic protocol [14]. The patients had not received any prophylactic antibiotics for neutropenia,
	128 158 187	methods use all data available, i.e., subjects with missing information are not dropped out from analyses. 2). During the second cycle, the BSI rate was still slightly higher in the patients who had already achieved which allowed us to study the real influence of different chemotherapeutic cycles on BSI rates during
	129 159	Incidence rates (per 1000 hospital days or 1000 neutropenic days) with 95% confidence intervals were remission (64.6%) than among those who received the second induction course of chemotherapy (53.6%, P = neutropenia.
	.11; Figure 2). On the other hand, no difference in number of febrile or neutropenic days, in amount of grade 3 & 4 gastrointestinal toxicity, peak CRP-values, or recovery of individual microbial strains was found between those calculated. 145 160 161 patients with active disease and those in remission in the second cycle.
	146	In total there were 956 treatment episodes with 456 positive blood cultures, constituting a rate of
	147	47.7% of BSI. The overall incidence rate (per 1000 hospital days) for BSI was 13.2 (95% confidence interval
	148	12.0 to 14.5). When the cycles were compared, the median peak C-reactive protein level did not differ between

130 Statistical analysis was performed using SPSS (SPSS, version 14.0, SPSS Inc, Chicago, IL) and SAS (version 131 9.1.3, SAS Institute Inc., Cary, NC) statistical software. 132 133 RESULTS

134

The study population included 327 AML patients and their most common FAB-types were M2 135 with 32.1%, M1 with 23.9% and M4 with 23.9%. There were 166 men and 161 women. Their median age was 136 47.7 yrs with a range from 16 to 66 years of age. More detailed hematological results are presented elsewhere 137

[START_REF] Koistinen | Long-term outcome of intensive 307 chemotherapy for adults with de novo acute myeloid leukaemia (AML): the 308 nationwide AML-92 study by the Finnish Leukaemia Group[END_REF]

. WHO grade IV infections with signs of organ failure, were observed among 22 patients in cycle I (6.7%), 138 12 patients in cycle II (4.1%), 13 patients in cycle III (6.1%) and 9 patients in cycle IV (7.4%).

139

During the study period, there were 40 deaths (12.2%), of which 35 (87.5%) were due to 140 infection. 12 patients died due to infection during cycle I. Five of these deaths were due to BSIs. Of the 14 141 patients who died due to infection in cycle II, 10 were treated with the second induction treatment for active 142 diseasethe cycles, but the duration of febrile days was longest during the first cycle (Table

1

). The length of hospital 149 stay, the incidence rate for BSI per 1000 patient days or per 1000 neutropenia days were clearly higher in cycles II, 162

There was a great inter-cycle variation among positive blood cultures (from 23.3% to 61.6%) as 163 well as for monomicrobial BSIs (from 62.2% to 83.3%) and for polymicrobial BSIs (from 16.7% to 37.2%). In 164 monomicrobial BSIs, the proportion of gram-positive microorganisms decreased from cycle I (71.7%) to cycle 165 IV (36.6%), whereas the change was in opposite direction among gram-negatives; from 21.7% in cycle I to 166 46.9% in cycle IV (Table

2

). The most common gram-positive microorganisms in monomicrobial BSIs were 167 CoNSs and viridans group streptococci; the latter was most frequently detected during cycle II. The most 168 common gram-negative microorganisms were E. coli (in cycle III and IV) and Klebsiella species (in cycles II 169 and III). Anaerobic microorganisms were seen only in cycle I and some yeasts in cycles I-III (table

2

).

192

Our BSI proportion of 47.7% is higher than has been thus far reported; the figures in other 193 studies have varied from 10% to 38.8%

[START_REF] Cullen | Antibacterial prophylaxis after 298 chemotherapy for solid tumors and lymphomas[END_REF][START_REF] Bow | A randomized, open-label, 326 multicenter comparative study of the efficacy and safety of piperacillin-327 tazobactam and cefepime for the empirical treatment of febrile neutropenic 328 episodes in patients with hematologic malignancies[END_REF][START_REF] Bucaneve | Levofloxacin to prevent 330 bacterial infection in patients with cancer and neutropenia[END_REF][START_REF] Gaytán-Martínez | Microbiological findings in 334 febrile neutropenia[END_REF][START_REF] Klastersky | Bacteraemia in febrile 336 neutropenic cancer patients[END_REF][START_REF] Madani | Clinical infections and bloodstream isolates associated with 338 fever in patients undergoing chemotherapy for acute myeloid leukemia[END_REF][START_REF] Pizzo | Management of fever in patients with cancer and treatment-341 induced neutropenia[END_REF]

. The crucial questions from the point of view 194 of BSI frequency are study population (only leukemia patients or also patients with solid tumor and lymphomas) 195

TABLE 1 . Length of hospital stay, duration of febrile episodes and neutropenia, the serum peak value of C-reactive protein, incidence rate (IR) of blood stream infections (BSI) and odds ratios (OR) for the risk of BSI and gastrointestinal toxicity in different treatment cycles (cycle I as a reference);

 1 conclusion, our AML patients had a high overall BSi rate during chemotherapy regimen-

	251
	252	induced neutropenia. However, there was great variation in BSI findings in four treatment cycles with different
	253	chemotherapeutics: BSI rate was lowest in cycle I and proportions of microorganisms and polymicrobial BSIs
	254	varied greatly from cycle to cycle. Therefore, in order to obtain more precise information concerning BSIs
	255	during the intensive chemotherapeutic treatments of AML, the analysis of BSI results should be focused on
	256	different chemotherapy cycles rather than by analyzing the overall results.

cytarabine and idarubicin, cycle III; etoposide cytarabine and mitoxantrone, Cycle IV; amsacrine and high-dose cytarabin.

TABLE 2 . Detected microorganisms during different chemotherapy cycles; the number (%) of positive blood cultures per treatment episodes in each cycle.

 2

		Cycle I	Cycle II	Cycle III	Cycle IV	All (n=956)
		(n= 323)	(n=292)	(n=219)	(n=122)
	Blood culture positive,	72 (22.3)	180 (61.6)	133 (60.7)	71 (58.2)	456 (47.7)
	number (%)
	Monomicrobial	60 (83.3)	113 (62.2)	105 (78.9)	49 (69.0)	327 (71.7)
	Gram-positive	43 (71.7)	71 (62.8)	56 (53.3)	26 (36.6)	197 (43.2)
	-CoNS	23 (38.3)	28 (24.8)	34 (32.4)	15 (30.6)	100 (30.6)
	-VGS	5 (8.3)	23 (20.4)	12 (11.4)	6 (12.2)	46 (14.1)
	-Enterococci	7 (11.7)	9 (8.0)	7 (6.7)	4 (8.2)	27 (8.3)
	Gram-negative	13 (21.7)	41 (36.3)	48 (45.7)	23 (46.9)	124 (37.9)
	-E. coli	3 (5.0)	7 (6.2)	15 (14.3)	12 (24.5)	37 (11.3)
	-Klebsiella sp.	2 (3.3)	16 (14.2)	20 (19.0)	5 (10.2)	43 (13.1)
	-Enterobacter sp.	1 (1.7)	7 (6.2)	6 (5.7)	2 (4.1)	16 (4.9)
	-Pseudomonas	3 (5.0)	7 (6.2)	1 (1.0)	3 (6.1)	14 (4.3)
	aeruginosa
	Anaerobic	3 (5.0)	-	-	-	3 (0.9)
	microorganisms
	Yeast	1 (1.7)	1 (0.9)	1 (1.0)	-	3 (0.9)
	Polymicrobial	12 (16.7)	67 (37.2)	28 (21.1)	22 (31.0)	129 (28.3)

NOTE.

CoNS, coagulase-negative staphylococci; VGS, viridans group streptococci. Among grampositives and gram-negatives, only three most common microbes are mentioned, and among gramnegatives also the presence of Pseudomonas.

TABLE 3 . Characterization of microorganisms of polymicrobial bloodstream infections in different chemotherapy cycles

 3

	Blood stream	Cycle I	Cycle II	Cycle III	Cycle IV	All (n=129)
	infections	(n=12)	(n=67)	(n=28)	(n=22)
	Number of
	microorganisms
	-Two	8 (66.7)	49 (73.1)	24 (85.7)	16 (72.7)	97 (75.2)
	-More than two	4 (33.3)	18 (26.9)	4 (14.3)	6 (27.3)	32 (24.8)
	Combinations of
	microorganisms
	-Gram-positives only	5 (41.7)	27 (40.3)	5 (17.9)	3 (13.6)	40 (31.0)
	-Gram-positive and	-	4 (6.0)	-	-	4 (3.1)
	anaerobic
	-Gram-positive and	-	1 (1.5)	-	2 (9.1)	3 (2.3)
	yeast
	-Gram-positive and	6 (50.0)	28 (41.8)	18 (64.3)	11 (50.0)	63 (48.8)
	gram-negative
	-Gram-negatives only	1 (8.3)	4 (6.0)	3 (10.7)	5 (22.7)	13 (10.1)
	-Gram-negative and	-	3 (4.5)	2 (7.1)	1 (4.5)	6 (4.7)
	yeast

Most polymicrobial BSIs contained two microorganisms (Table3). The most common

combination included both gram-positive and gram-negative microorganisms in each cycle (41.8% to 64.3%).

Although there was once again great variability between the cycles; the proportion of gram-negative

microorganisms was always higher than 50% (from 52.3% to 82.1%).

When the BSI results obtained by two different automated blood systems were compared, there

was not any statistical difference between them concerning the cycles or individual microorganisms (data not

shown).

cycle with high-dose cytarabine and idarubicin and clearly lower in cycle IV, which also included high-dose

cytarabine and amsacrine. Thus, the combination of chemotherapeutics and not only the high-dose cytarabine

per se seems to be important for BSIs caused by viridans group streptococci.

leukemia. A report of the French-American-British Cooperative Group. Ann

Dis 36:149-158.

Microbiol Infect Dis 25:1-7.

b P-time according to Linear mixed model. c values are medians with 25 th -75 th percentiles. d values are means with 95% confidence intervals (95%CI).e P-time according to the generalized linear mixed model[START_REF] Hammond | Antibiotic prophylaxis for patients with acute 285 leukemia[END_REF].

Acknowledgements 258

No financial support was obtained for this study. 259

Appendix 28 29 The other investigators and centers of the Finnish Leukemia Group collaborated in this study : 30 Liisa Volin and Tapani Ruutu, Helsinki; Timo Siitonen and Eeva-Riitta Savolainen, Oulu; 31 Vesa Lindström, Tampere; Tarja-Terttu Pelliniemi, Turku. 32

DISCUSSION

Conflict of Interest 261

The authors declare that they have no conflict of interest. 262