Recently, In some papers face recognition approaches are being evaluated through a new proposed protocol, names as closed-set and open-set face identification over LFW dataset. For open-set one, the Rank-1 accuracy is reported as Detection and Identification Rate (DIR) at a fixed False Alarm/Acceptance Rate (FAR). I have a gallery and a probe set and am using KNN for classification, however I don't know how to compute the DIR#FAR1%.
Update:
Specifically, what is ambiguous to me is fixating the FAR at a fixed threshold, or how the curves such as ROC, precision-recall and etc are plotted for face recognition. What does the threshold in the following paragraph mean?
Hence the performance is evaluated based on (i) Rank-1 detection and identification rate (DIR), which is the fraction of genuine probes matched correctly at Rank-1, and not rejected at a given threshold, and (ii) the false alarm rate (FAR) of the rejection step (i.e. the fraction of impostor probe images which are not rejected). We report the DIR vs. FAR curve describing the trade-off between true Rank-1 identifications and false alarms.
The reference paper is downloadable here.
Any help would be welcome.
I guess the DIR metric was established by the Biometrics society. This metric includes both the detection (exceeding some threshold) and the identification (rank). Let the gallery consists of a set of enrolled users in a biometric
database and the probe set may contain users who may or may not be present
in the database. Let g and p are two elements of the gallery and probe sets respectively. Moreover, let the probe set include two disjoint subsets: P1 including the samples of those who belong to the gallery subjects and P0 including those who do not.
Assume s(p,g) is a similarity score between a probe and a gallery elements, t is a threshold and k is the identification rank. Then DIR is given by:
You can find the complete formula in this reference:
Poh, N., et al. "Description of Metrics For the Evaluation of Biometric Performance." Seventh Framework Programme of Biometrics Evaluation and Testing (2012): 1-22.
Related
I'm setting up the new Tensorflow Object Detection API to find small objects in large areas of satellite imagery. It works quite well - it finds all 10 objects I want, but I also get 50-100 false positives [things that look a little like the target object, but aren't].
I'm using the sample config from the 'pets' tutorial, to fine-tune the faster_rcnn_resnet101_coco model they offer. I've started small, with only 100 training examples of my objects (just 1 class). 50 examples in my validation set. Each example is a 200x200 pixel image with a labeled object (~40x40) in the center. I train until my precision & loss curves plateau.
I'm relatively new to using deep learning for object detection. What is the best strategy to increase my precision? e.g. Hard-negative mining? Increase my training dataset size? I've yet to try the most accurate model they offer faster_rcnn_inception_resnet_v2_atrous_coco as i'd like to maintain some speed, but will do so if needed.
Hard-negative mining seems to be a logical step. If you agree, how do I implement it w.r.t setting up the tfrecord file for my training dataset? Let's say I make 200x200 images for each of the 50-100 false positives:
Do I create 'annotation' xml files for each, with no 'object' element?
...or do I label these hard negatives as a second class?
If I then have 100 negatives to 100 positives in my training set - is that a healthy ratio? How many negatives can I include?
I've revisited this topic recently in my work and thought I'd update with my current learnings for any who visit in the future.
The topic appeared on Tensorflow's Models repo issue tracker. SSD allows you to set the ratio of how many negative:postive examples to mine (max_negatives_per_positive: 3), but you can also set a minimum number for images with no postives (min_negatives_per_image: 3). Both of these are defined in the model-ssd-loss config section.
That said, I don't see the same option in Faster-RCNN's model configuration. It's mentioned in the issue that models/research/object_detection/core/balanced_positive_negative_sampler.py contains the code used for Faster-RCNN.
One other option discussed in the issue is creating a second class specifically for lookalikes. During training, the model will attempt to learn class differences which should help serve your purpose.
Lastly, I came across this article on Filter Amplifier Networks (FAN) that may be informative for your work on aerial imagery.
===================================================================
The following paper describes hard negative mining for the same purpose you describe:
Training Region-based Object Detectors with Online Hard Example Mining
In section 3.1 they describe using a foreground and background class:
Background RoIs. A region is labeled background (bg) if its maximum
IoU with ground truth is in the interval [bg lo, 0.5). A lower
threshold of bg lo = 0.1 is used by both FRCN and SPPnet, and is
hypothesized in [14] to crudely approximate hard negative mining; the
assumption is that regions with some overlap with the ground truth are
more likely to be the confusing or hard ones. We show in Section 5.4
that although this heuristic helps convergence and detection accuracy,
it is suboptimal because it ignores some infrequent, but important,
difficult background regions. Our method removes the bg lo threshold.
In fact this paper is referenced and its ideas are used in Tensorflow's object detection losses.py code for hard mining:
class HardExampleMiner(object):
"""Hard example mining for regions in a list of images.
Implements hard example mining to select a subset of regions to be
back-propagated. For each image, selects the regions with highest losses,
subject to the condition that a newly selected region cannot have
an IOU > iou_threshold with any of the previously selected regions.
This can be achieved by re-using a greedy non-maximum suppression algorithm.
A constraint on the number of negatives mined per positive region can also be
enforced.
Reference papers: "Training Region-based Object Detectors with Online
Hard Example Mining" (CVPR 2016) by Srivastava et al., and
"SSD: Single Shot MultiBox Detector" (ECCV 2016) by Liu et al.
"""
Based on your model config file, the HardMinerObject is returned by losses_builder.py in this bit of code:
def build_hard_example_miner(config,
classification_weight,
localization_weight):
"""Builds hard example miner based on the config.
Args:
config: A losses_pb2.HardExampleMiner object.
classification_weight: Classification loss weight.
localization_weight: Localization loss weight.
Returns:
Hard example miner.
"""
loss_type = None
if config.loss_type == losses_pb2.HardExampleMiner.BOTH:
loss_type = 'both'
if config.loss_type == losses_pb2.HardExampleMiner.CLASSIFICATION:
loss_type = 'cls'
if config.loss_type == losses_pb2.HardExampleMiner.LOCALIZATION:
loss_type = 'loc'
max_negatives_per_positive = None
num_hard_examples = None
if config.max_negatives_per_positive > 0:
max_negatives_per_positive = config.max_negatives_per_positive
if config.num_hard_examples > 0:
num_hard_examples = config.num_hard_examples
hard_example_miner = losses.HardExampleMiner(
num_hard_examples=num_hard_examples,
iou_threshold=config.iou_threshold,
loss_type=loss_type,
cls_loss_weight=classification_weight,
loc_loss_weight=localization_weight,
max_negatives_per_positive=max_negatives_per_positive,
min_negatives_per_image=config.min_negatives_per_image)
return hard_example_miner
which is returned by model_builder.py and called by train.py. So basically, it seems to me that simply generating your true positive labels (with a tool like LabelImg or RectLabel) should be enough for the train algorithm to find hard negatives within the same images. The related question gives an excellent walkthrough.
In the event you want to feed in data that has no true positives (i.e. nothing should be classified in the image), just add the negative image to your tfrecord with no bounding boxes.
I think I was passing through the same or close scenario and it's worth it to share with you.
I managed to solve it by passing images without annotations to the trainer.
On my scenario I'm building a project to detect assembly failures from my client's products, at real time.
I successfully achieved very robust results (for production env) by using detection+classification for components that has explicity a negative pattern (e.g. a screw that has screw on/off(just the hole)) and only detection for things that doesn't has the negative pattens (e.g. a tape that can be placed anywhere).
On the system it's mandatory that the user record 2 videos, one containing the positive scenario and another containing the negative (or the n videos, containing n patterns of positive and negative so the algorithm can generalize).
After a while testing I found out that if I register to detected only tape the detector was giving very confident (0.999) false positive detections of tape. It was learning the pattern where the tape was inserted instead of the tape itself. When I had another component (like a screw on it's negative format) I was passing the negative pattern of tape without being explicitly aware of it, so the FPs didn't happen.
So I found out that, in this scenario, I had to necessarily pass the images without tape so it could differentiate between tape and no-tape.
I considered two alternatives to experiment and try to solve this behavior:
Train passing an considerable amount of images that doesn't has any annotation (10% of all my negative samples) along with all images that I have real annotations.
On the images that I don't have annotation I create a dummy annotation with a dummy label so I could force the detector to train with that image (thus learning the no-tape pattern). Later on, when get the dummy predictions, just ignore them.
Concluded that both alternatives worked perfectly on my scenario.
The training loss got a little messy but the predictions work with robustness for my very controlled scenario (the system's camera has its own box and illumination to decrease variables).
I had to make two little modifications for the first alternative to work:
All images that didn't had any annotation I passed a dummy annotation (class=None, xmin/ymin/xmax/ymax=-1)
When generating the tfrecord files I use this information (xmin == -1, in this case) to add an empty list for the sample:
def create_tf_example(group, path, label_map):
with tf.gfile.GFile(os.path.join(path, '{}'.format(group.filename)), 'rb') as fid:
encoded_jpg = fid.read()
encoded_jpg_io = io.BytesIO(encoded_jpg)
image = Image.open(encoded_jpg_io)
width, height = image.size
filename = group.filename.encode('utf8')
image_format = b'jpg'
xmins = []
xmaxs = []
ymins = []
ymaxs = []
classes_text = []
classes = []
for index, row in group.object.iterrows():
if not pd.isnull(row.xmin):
if not row.xmin == -1:
xmins.append(row['xmin'] / width)
xmaxs.append(row['xmax'] / width)
ymins.append(row['ymin'] / height)
ymaxs.append(row['ymax'] / height)
classes_text.append(row['class'].encode('utf8'))
classes.append(label_map[row['class']])
tf_example = tf.train.Example(features=tf.train.Features(feature={
'image/height': dataset_util.int64_feature(height),
'image/width': dataset_util.int64_feature(width),
'image/filename': dataset_util.bytes_feature(filename),
'image/source_id': dataset_util.bytes_feature(filename),
'image/encoded': dataset_util.bytes_feature(encoded_jpg),
'image/format': dataset_util.bytes_feature(image_format),
'image/object/bbox/xmin': dataset_util.float_list_feature(xmins),
'image/object/bbox/xmax': dataset_util.float_list_feature(xmaxs),
'image/object/bbox/ymin': dataset_util.float_list_feature(ymins),
'image/object/bbox/ymax': dataset_util.float_list_feature(ymaxs),
'image/object/class/text': dataset_util.bytes_list_feature(classes_text),
'image/object/class/label': dataset_util.int64_list_feature(classes),
}))
return tf_example
Part of the traning progress:
Currently I'm using tensorflow object detection along with tensorflow==1.15, using faster_rcnn_resnet101_coco.config.
Hope it will solve someone's problem as I didn't found any solution on the internet. I read a lot of people telling that faster_rcnn is not adapted for negative training for FPs reduction but my tests proved the opposite.
I am playing some demos about recurrent neural network.
I noticed that the scale of my data in each column differs a lot. So I am considering to do some preprocess work before I throw data batches into my RNN. The close column is the target I want to predict in the future.
open high low volume price_change p_change ma5 ma10 \
0 20.64 20.64 20.37 163623.62 -0.08 -0.39 20.772 20.721
1 20.92 20.92 20.60 218505.95 -0.30 -1.43 20.780 20.718
2 21.00 21.15 20.72 269101.41 -0.08 -0.38 20.812 20.755
3 20.70 21.57 20.70 645855.38 0.32 1.55 20.782 20.788
4 20.60 20.70 20.20 458860.16 0.10 0.48 20.694 20.806
ma20 v_ma5 v_ma10 v_ma20 close
0 20.954 351189.30 388345.91 394078.37 20.56
1 20.990 373384.46 403747.59 411728.38 20.64
2 21.022 392464.55 405000.55 426124.42 20.94
3 21.054 445386.85 403945.59 473166.37 21.02
4 21.038 486615.13 378825.52 461835.35 20.70
My question is, is preprocessing the data with, say StandardScaler in sklearn necessary in my case? And why?
(You are welcome to edit my question)
It will be beneficial to normalize your training data. Having different features with widely different scales fed to your model will cause the network to weight the features not equally. This can cause a falsely prioritisation of some features over the others in the representation.
Despite that the whole discussion on data preprocessing is controversial either on when exactly it is necessary and how to correctly normalize the data for each given model and application domain there is a general consensus in Machine Learning that running a Mean subtraction as well as a general Normalization preprocessing step is helpful.
In the case of Mean subtraction, the mean of every individual feature is being subtracted from the data which can be interpreted as centering the data around the origin from a geometric point of view. This is true for every dimensionality.
Normalizing the data after the Mean subtraction step results in a normalization of the data dimensionality to approximately the same scale. Note that the different features will loose any prioritization over each other after this step as mentioned above. If you have good reasons to think that the different scales in your features bear important information that the network may need to truly understand the underlying patterns in your dataset, then a normalization will be harmful. A standard approach would be to scale the inputs to have mean of 0 and a variance of 1.
Further preprocessing operations may be helpful in specific cases such as performing PCA or Whitening on your data. Look into the awesome notes of CS231n (Setting up the data and the model) for further reference on these topics as well as for a more detailed explenation of the topics above.
Definetly yes. Most of neural networks work best with data beetwen 0-1 or -1 to 1(depends on output function). Also when some inputs are higher then others network will "think" they are more important. This can make learning very long. Network must first lower weights in this inputs.
I found this https://arxiv.org/abs/1510.01378
If you normalize it may improve convergence so you will get lower training times.
I am a master student working with localization in VANEts
in this moment I am working on a trilateration method based on RSSI for
Cooperative Positioning (CP).
I am considering the Analogue Model : Simple Path Loss Model
But I have some doubts in how to calculate the distance correctly for a determined Phy Model.
I spent some time (one day) reading some papers of Dr. Sommer about the PHY models included in veins.
Would anyone help-me with this solution?
I need a way to:
1) Measure the power of an receiver when its receive a beacon (I found this in the Decider class).
In the Decider802.11p the received Power can be obtained with this line in method Decider80211p::processSignalEnd(AirFrame* msg):
double recvPower_dBm = 10*log10(signal.getReceivingPower()->getValue(start));
2) Apply a formula of RSSI accordingly the phy model in order to achieve a distance estimation between transmiter and receiver.
3) Asssociate this measure (distance by RSSI) with the Wave Short Message to be delivered in AppLayer of the receiver (that is measuring the RSSI).
After read the paper "On the Applicability of Two-Ray Path Loss Models for Vehicular Network Simulation"
and the paper "A Computationally Inexpensive Empirical Model of IEEE 802.11p Radio Shadowing in Urban Environments"
and investigating how it works in the veins project. I noticed that each analogue model have your own path loss model
with your own variables to describe the model.
For example for the SimplePathLossModel we have these
variables defined on AnalogueModels folder of veins modules:
lambda = 0.051 m (wave length to IEEE 802.11p CCH center frequency of 5.890 GHz)
A constant alpha = 2 (default value used)
a distance factor given by pow(sqrDistance, -pathLossAlphaHalf) / (16.0 * M_PI * M_PI);
I found one formula for indoor environments in this link, but I am in doubt if it is applicable for vehicular environments.
Any clarification is welcome. Thanks a lot.
Technically, you are correct. Indeed, you could generate a simple look-up table: have one vehicle drive past another one, record distance and RSSIs, and you have a table that can map RSSI to mean distance (without knowing how the TX power, antenna gains, path loss model, fading models, etc, are configured).
In the simplest case, if you assume that antennas are omnidirectional, that path loss follows the Friis transmission equation, that no shadow fading occurs, and that fast fading is negligible, your table will be perfect.
In a more complicated case, where your simulation also includes probabilistic fast fading (say, a Nakagami model), shadow fading due to radio obstacles (buildings), etc. your table will still be roughly correct, but less so.
It is important to consider a real-life application, though. Consider if your algorithm still works if conditions change (more reflective road surface changing reflection parameters, buildings blocking more or less power, antennas with non-ideal or even unknown gain characteristics, etc).
I have a large dataset I am trying to do cluster analysis on using SOM. The dataset is HUGE (~ billions of records) and I am not sure what should be the number of neurons and the SOM grid size to start with. Any pointers to some material that talks about estimating the number of neurons and grid size would be greatly appreciated.
Thanks!
Quoting from the som_make function documentation of the som toolbox
It uses a heuristic formula of 'munits = 5*dlen^0.54321'. The
'mapsize' argument influences the final number of map units: a 'big'
map has x4 the default number of map units and a 'small' map has
x0.25 the default number of map units.
dlen is the number of records in your dataset
You can also read about the classic WEBSOM which addresses the issue of large datasets
http://www.cs.indiana.edu/~bmarkine/oral/self-organization-of-a.pdf
http://websom.hut.fi/websom/doc/ps/Lagus04Infosci.pdf
Keep in mind that the map size is also a parameter which is also application specific. Namely it depends on what you want to do with the generated clusters. Large maps produce a large number of small but "compact" clusters (records assigned to each cluster are quite similar). Small maps produce less but more generilized clusters. A "right number of clusters" doesn't exists, especially in real world datasets. It all depends on the detail which you want to examine your dataset.
I have written a function that, with the data set as input, returns the grid size. I rewrote it from the som_topol_struct() function of Matlab's Self Organizing Maps Toolbox into a R function.
topology=function(data)
{
#Determina, para lattice hexagonal, el número de neuronas (munits) y su disposición (msize)
D=data
# munits: número de hexágonos
# dlen: número de sujetos
dlen=dim(data)[1]
dim=dim(data)[2]
munits=ceiling(5*dlen^0.5) # Formula Heurística matlab
#munits=100
#size=c(round(sqrt(munits)),round(munits/(round(sqrt(munits)))))
A=matrix(Inf,nrow=dim,ncol=dim)
for (i in 1:dim)
{
D[,i]=D[,i]-mean(D[is.finite(D[,i]),i])
}
for (i in 1:dim){
for (j in i:dim){
c=D[,i]*D[,j]
c=c[is.finite(c)];
A[i,j]=sum(c)/length(c)
A[j,i]=A[i,j]
}
}
VS=eigen(A)
eigval=sort(VS$values)
if (eigval[length(eigval)]==0 | eigval[length(eigval)-1]*munits<eigval[length(eigval)]){
ratio=1
}else{
ratio=sqrt(eigval[length(eigval)]/eigval[length(eigval)-1])}
size1=min(munits,round(sqrt(munits/ratio*sqrt(0.75))))
size2=round(munits/size1)
return(list(munits=munits,msize=sort(c(size1,size2),decreasing=TRUE)))
}
hope it helps...
Iván Vallés-Pérez
I don't have a reference for it, but I would suggest starting off by using approximately 10 SOM neurons per expected class in your dataset. For example, if you think your dataset consists of 8 separate components, go for a map with 9x9 neurons. This is completely just a ballpark heuristic though.
If you'd like the data to drive the topology of your SOM a bit more directly, try one of the SOM variants that change topology during training:
Growing SOM
Growing Neural Gas
Unfortunately these algorithms involve even more parameter tuning than plain SOM, but they might work for your application.
Kohenon has written on the issue of selecting parameters and map size for SOM in his book "MATLAB Implementations and Applications of the Self-Organizing Map". In some cases, he suggest the initial values can be arrived at after testing several sizes of the SOM to check that the cluster structures were shown with sufficient resolution and statistical accuracy.
my suggestion would be the following
SOM is distantly related to correspondence analysis. In statistics, they use 5*r^2 as a rule of thumb, where r is the number of rows/columns in a square setup
usually, one should use some criterion that is based on the data itself, meaning that you need some criterion for estimating the homogeneity. If a certain threshold would be violated, you would need more nodes. For checking the homogeneity you would need some records per node. Agai, from statistics you could learn that for simple tests (small number of variables) you would need around 20 records, for more advanced tests on some variables at least 8 records.
remember that the SOM represents a predictive model. So validation is the key, absolutely mandatory. Yet, validation of predictive models (see typeI / II error entry in Wiki) is a subject on its own. And the acceptable risk as well as the risk structure also depend fully on your purpose.
You may test the dynamics of the error rate of the model by reducing its size more and more. Then take the smallest one with acceptable error.
It is a strength of the SOM to allow for empty nodes. Yet, there should not be too much of them. Let me say, less than 5%.
Taken all together, from experience, I would recommend the following criterion a minimum of the absolute number of 8..10 records, but those should not be more than 5% of all clusters.
Those 5% rule is of of course a heuristics, which however can be justified by the general usage of the confidence level in statistical tests. You may choose any percentage from 1% to 5%.
I want to classify documents (composed of words) into 3 classes (Positive, Negative, Unknown/Neutral). A subset of the document words become the features.
Until now, I have programmed a Naive Bayes Classifier using as a feature selector Information gain and chi-square statistics. Now, I would like to see what happens if I use Odds ratio as a feature selector.
My problem is that I don't know hot to implement Odds-ratio. Should I:
1) Calculate Odds Ratio for every word w, every class:
E.g. for w:
Prob of word as positive Pw,p = #positive docs with w/#docs
Prob of word as negative Pw,n = #negative docs with w/#docs
Prob of word as unknown Pw,u = #unknown docs with w/#docs
OR(Wi,P) = log( Pw,p*(1-Pw,p) / (Pw,n + Pw,u)*(1-(Pw,n + Pw,u)) )
OR(Wi,N) ...
OR(Wi,U) ...
2) How should I decide if I choose or not the word as a feature ?
Thanks in advance...
Since it took me a while to independently wrap my head around all this, let me explain my findings here for the benefit of humanity.
Using the (log) odds ratio is a standard technique for filtering features prior to text classification. It is a 'one-sided metric' [Zheng et al., 2004] in the sense that it only discovers features which are positively correlated with a particular class. As a log-odds-ratio for the probability of seeing a feature 't' given the class 'c', it is defined as:
LOR(t,c) = log [Pr(t|c) / (1 - Pr(t|c))] : [Pr(t|!c) / (1 - Pr(t|!c))]
= log [Pr(t|c) (1 - Pr(t|!c))] / [Pr(t|!c) (1 - Pr(t|c))]
Here I use '!c' to mean a document where the class is not c.
But how do you actually calculate Pr(t|c) and Pr(t|!c)?
One subtlety to note is that feature selection probabilities, in general, are usually defined over a document event model [McCallum & Nigam 1998, Manning et al. 2008], i.e., Pr(t|c) is the probability of seeing term t one or more times in the document given the class of the document is c (in other words, the presence of t given the class c). The maximum likelihood estimate (MLE) of this probability would be the proportion of documents of class c that contain t at least once. [Technically, this is known as a Multivariate Bernoulli event model, and is distinct from a Multinomial event model over words, which would calculate Pr(t|c) using integer word counts - see the McCallum paper or the Manning IR textbook for more details, specifically on how this applies to a Naive Bayes text classifier.]
One key to using LOR effectively is to smooth these conditional probability estimates, since, as #yura noted, rare events are problematic here (e.g., the MLE of Pr(t|!c) could be zero, leading to an infinite LOR). But how do we smooth?
In the literature, Forman reports smoothing the LOR by "adding one to any zero count in the denominator" (Forman, 2003), while Zheng et al (2004) use "ELE [Expected Likelihood Estimation] smoothing" which usually amounts to adding 0.5 to each count.
To smooth in a way that is consistent with probability theory, I follow standard practices in text classification with a Multivariate Bernoulli event model. Essentially, we assume that we have seen each presence count AND each absence count B extra times. So our estimate for Pr(t|c) can be written in terms of #(t,c): the number of times we've seen t and c, and #(t,!c): the number of times we've seen t without c, as follows:
Pr(t|c) = [#(t,c) + B] / [#(t,c) + #(t,!c) + 2B]
= [#(t,c) + B] / [#(c) + 2B]
If B = 0, we have the MLE. If B = 0.5, we have ELE. If B = 1, we have the Laplacian prior. Note this looks different than smoothing for the Multinomial event model, where the Laplacian prior leads you to add |V| in the denominator [McCallum & Nigam, 1998]
You can choose 0.5 or 1 as your smoothing value, depending on which prior work most inspires you, and plug this into the equation for LOR(t,c) above, and score all the features.
Typically, you then decide on how many features you want to use, say N, and then choose the N highest-ranked features based on the score.
In a multi-class setting, people have often used 1 vs All classifiers and thus did feature selection independently for each classifier and thus each positive class with the 1-sided metrics (Forman, 2003). However, if you want to find a unique reduced set of features that works in a multiclass setting, there are some advanced approaches in the literature (e.g. Chapelle & Keerthi, 2008).
References:
Zheng, Wu, Srihari, 2004
McCallum & Nigam 1998
Manning, Raghavan & Schütze, 2008
Forman, 2003
Chapelle & Keerthi, 2008
Odd ratio is not good measure for feature selection, because it is only shows what happen when feature present, and nothing when it is not. So it will not work for rare features and almost all features are rare so it not work for almost all features. Example feature with 100% confidence that class is positive which present in 0.0001 is useless for classification. Therefore if you still want to use odd ratio add threshold on frequency of feature, like feature present in 5% of cases. But I would recommend better approach - use Chi or info gain metrics which automatically solve those problems.