Coaching a convnet with a small dataset

Having to coach an image-classification mannequin utilizing little or no knowledge is a standard state of affairs, which you’ll seemingly encounter in follow when you ever do pc imaginative and prescient in knowledgeable context. A “few” samples can imply wherever from a couple of hundred to some tens of hundreds of pictures. As a sensible instance, we’ll concentrate on classifying pictures as canine or cats, in a dataset containing 4,000 footage of cats and canine (2,000 cats, 2,000 canine). We’ll use 2,000 footage for coaching – 1,000 for validation, and 1,000 for testing.

In Chapter 5 of the Deep Studying with R e-book we evaluation three methods for tackling this drawback. The primary of those is coaching a small mannequin from scratch on what little knowledge you could have (which achieves an accuracy of 82%). Subsequently we use function extraction with a pretrained community (leading to an accuracy of 90%) and fine-tuning a pretrained community (with a closing accuracy of 97%). On this publish we’ll cowl solely the second and third methods.

The relevance of deep studying for small-data issues

You’ll typically hear that deep studying solely works when a lot of knowledge is obtainable. That is legitimate partly: one elementary attribute of deep studying is that it might discover attention-grabbing options within the coaching knowledge by itself, with none want for guide function engineering, and this could solely be achieved when a lot of coaching examples can be found. That is very true for issues the place the enter samples are very high-dimensional, like pictures.

However what constitutes a lot of samples is relative – relative to the dimensions and depth of the community you’re making an attempt to coach, for starters. It isn’t attainable to coach a convnet to resolve a posh drawback with just some tens of samples, however a couple of hundred can probably suffice if the mannequin is small and properly regularized and the duty is straightforward. As a result of convnets study native, translation-invariant options, they’re extremely knowledge environment friendly on perceptual issues. Coaching a convnet from scratch on a really small picture dataset will nonetheless yield cheap outcomes regardless of a relative lack of knowledge, with out the necessity for any customized function engineering. You’ll see this in motion on this part.

What’s extra, deep-learning fashions are by nature extremely repurposable: you may take, say, an image-classification or speech-to-text mannequin educated on a large-scale dataset and reuse it on a considerably totally different drawback with solely minor modifications. Particularly, within the case of pc imaginative and prescient, many pretrained fashions (normally educated on the ImageNet dataset) at the moment are publicly accessible for obtain and can be utilized to bootstrap highly effective imaginative and prescient fashions out of little or no knowledge. That’s what you’ll do within the subsequent part. Let’s begin by getting your arms on the information.

Downloading the information

The Canines vs. Cats dataset that you just’ll use isn’t packaged with Keras. It was made accessible by Kaggle as a part of a computer-vision competitors in late 2013, again when convnets weren’t mainstream. You’ll be able to obtain the unique dataset from https://www.kaggle.com/c/dogs-vs-cats/knowledge (you’ll have to create a Kaggle account when you don’t have already got one – don’t fear, the method is painless).

The images are medium-resolution colour JPEGs. Listed here are some examples:

Unsurprisingly, the dogs-versus-cats Kaggle competitors in 2013 was received by entrants who used convnets. The very best entries achieved as much as 95% accuracy. Beneath you’ll find yourself with a 97% accuracy, although you’ll practice your fashions on lower than 10% of the information that was accessible to the rivals.

This dataset comprises 25,000 pictures of canine and cats (12,500 from every class) and is 543 MB (compressed). After downloading and uncompressing it, you’ll create a brand new dataset containing three subsets: a coaching set with 1,000 samples of every class, a validation set with 500 samples of every class, and a check set with 500 samples of every class.

Following is the code to do that:

original_dataset_dir <- "~/Downloads/kaggle_original_data"

base_dir <- "~/Downloads/cats_and_dogs_small"
dir.create(base_dir)

train_dir <- file.path(base_dir, "practice")
dir.create(train_dir)
validation_dir <- file.path(base_dir, "validation")
dir.create(validation_dir)
test_dir <- file.path(base_dir, "check")
dir.create(test_dir)

train_cats_dir <- file.path(train_dir, "cats")
dir.create(train_cats_dir)

train_dogs_dir <- file.path(train_dir, "canine")
dir.create(train_dogs_dir)

validation_cats_dir <- file.path(validation_dir, "cats")
dir.create(validation_cats_dir)

validation_dogs_dir <- file.path(validation_dir, "canine")
dir.create(validation_dogs_dir)

test_cats_dir <- file.path(test_dir, "cats")
dir.create(test_cats_dir)

test_dogs_dir <- file.path(test_dir, "canine")
dir.create(test_dogs_dir)

fnames <- paste0("cat.", 1:1000, ".jpg")
file.copy(file.path(original_dataset_dir, fnames), 
          file.path(train_cats_dir)) 

fnames <- paste0("cat.", 1001:1500, ".jpg")
file.copy(file.path(original_dataset_dir, fnames), 
          file.path(validation_cats_dir))

fnames <- paste0("cat.", 1501:2000, ".jpg")
file.copy(file.path(original_dataset_dir, fnames),
          file.path(test_cats_dir))

fnames <- paste0("canine.", 1:1000, ".jpg")
file.copy(file.path(original_dataset_dir, fnames),
          file.path(train_dogs_dir))

fnames <- paste0("canine.", 1001:1500, ".jpg")
file.copy(file.path(original_dataset_dir, fnames),
          file.path(validation_dogs_dir)) 

fnames <- paste0("canine.", 1501:2000, ".jpg")
file.copy(file.path(original_dataset_dir, fnames),
          file.path(test_dogs_dir))

Utilizing a pretrained convnet

A typical and extremely efficient strategy to deep studying on small picture datasets is to make use of a pretrained community. A pretrained community is a saved community that was beforehand educated on a big dataset, sometimes on a large-scale image-classification activity. If this unique dataset is giant sufficient and common sufficient, then the spatial hierarchy of options discovered by the pretrained community can successfully act as a generic mannequin of the visible world, and therefore its options can show helpful for a lot of totally different computer-vision issues, although these new issues could contain utterly totally different lessons than these of the unique activity. For example, you may practice a community on ImageNet (the place lessons are largely animals and on a regular basis objects) after which repurpose this educated community for one thing as distant as figuring out furnishings objects in pictures. Such portability of discovered options throughout totally different issues is a key benefit of deep studying in comparison with many older, shallow-learning approaches, and it makes deep studying very efficient for small-data issues.

On this case, let’s contemplate a big convnet educated on the ImageNet dataset (1.4 million labeled pictures and 1,000 totally different lessons). ImageNet comprises many animal lessons, together with totally different species of cats and canine, and you may thus anticipate to carry out properly on the dogs-versus-cats classification drawback.

You’ll use the VGG16 structure, developed by Karen Simonyan and Andrew Zisserman in 2014; it’s a easy and broadly used convnet structure for ImageNet. Though it’s an older mannequin, removed from the present cutting-edge and considerably heavier than many different latest fashions, I selected it as a result of its structure is much like what you’re already aware of and is straightforward to know with out introducing any new ideas. This can be your first encounter with considered one of these cutesy mannequin names – VGG, ResNet, Inception, Inception-ResNet, Xception, and so forth; you’ll get used to them, as a result of they are going to come up often when you hold doing deep studying for pc imaginative and prescient.

There are two methods to make use of a pretrained community: function extraction and fine-tuning. We’ll cowl each of them. Let’s begin with function extraction.

Function extraction consists of utilizing the representations discovered by a earlier community to extract attention-grabbing options from new samples. These options are then run by a brand new classifier, which is educated from scratch.

As you noticed beforehand, convnets used for picture classification comprise two components: they begin with a sequence of pooling and convolution layers, they usually finish with a densely linked classifier. The primary half known as the convolutional base of the mannequin. Within the case of convnets, function extraction consists of taking the convolutional base of a beforehand educated community, working the brand new knowledge by it, and coaching a brand new classifier on high of the output.

Why solely reuse the convolutional base? May you reuse the densely linked classifier as properly? Usually, doing so must be averted. The reason being that the representations discovered by the convolutional base are more likely to be extra generic and due to this fact extra reusable: the function maps of a convnet are presence maps of generic ideas over an image, which is more likely to be helpful whatever the computer-vision drawback at hand. However the representations discovered by the classifier will essentially be particular to the set of lessons on which the mannequin was educated – they are going to solely include details about the presence chance of this or that class in your complete image. Moreover, representations present in densely linked layers not include any details about the place objects are positioned within the enter picture: these layers eliminate the notion of house, whereas the thing location remains to be described by convolutional function maps. For issues the place object location issues, densely linked options are largely ineffective.

Notice that the extent of generality (and due to this fact reusability) of the representations extracted by particular convolution layers will depend on the depth of the layer within the mannequin. Layers that come earlier within the mannequin extract native, extremely generic function maps (corresponding to visible edges, colours, and textures), whereas layers which are increased up extract more-abstract ideas (corresponding to “cat ear” or “canine eye”). So in case your new dataset differs quite a bit from the dataset on which the unique mannequin was educated, you might be higher off utilizing solely the primary few layers of the mannequin to do function extraction, fairly than utilizing your complete convolutional base.

On this case, as a result of the ImageNet class set comprises a number of canine and cat lessons, it’s more likely to be useful to reuse the data contained within the densely linked layers of the unique mannequin. However we’ll select to not, with a view to cowl the extra common case the place the category set of the brand new drawback doesn’t overlap the category set of the unique mannequin.

Let’s put this in follow by utilizing the convolutional base of the VGG16 community, educated on ImageNet, to extract attention-grabbing options from cat and canine pictures, after which practice a dogs-versus-cats classifier on high of those options.

The VGG16 mannequin, amongst others, comes prepackaged with Keras. Right here’s the checklist of image-classification fashions (all pretrained on the ImageNet dataset) which are accessible as a part of Keras:

• Xception
• Inception V3
• ResNet50
• VGG16
• VGG19
• MobileNet

Let’s instantiate the VGG16 mannequin.

library(keras)

conv_base <- application_vgg16(
  weights = "imagenet",
  include_top = FALSE,
  input_shape = c(150, 150, 3)
)

You cross three arguments to the perform:

• weights specifies the burden checkpoint from which to initialize the mannequin.
• include_top refers to together with (or not) the densely linked classifier on high of the community. By default, this densely linked classifier corresponds to the 1,000 lessons from ImageNet. Since you intend to make use of your individual densely linked classifier (with solely two lessons: cat and canine), you don’t want to incorporate it.
• input_shape is the form of the picture tensors that you just’ll feed to the community. This argument is solely optionally available: when you don’t cross it, the community will be capable to course of inputs of any measurement.

Right here’s the element of the structure of the VGG16 convolutional base. It’s much like the easy convnets you’re already aware of:

Layer (sort)                     Output Form          Param #  
================================================================
input_1 (InputLayer)             (None, 150, 150, 3)   0       
________________________________________________________________
block1_conv1 (Convolution2D)     (None, 150, 150, 64)  1792     
________________________________________________________________
block1_conv2 (Convolution2D)     (None, 150, 150, 64)  36928    
________________________________________________________________
block1_pool (MaxPooling2D)       (None, 75, 75, 64)    0        
________________________________________________________________
block2_conv1 (Convolution2D)     (None, 75, 75, 128)   73856    
________________________________________________________________
block2_conv2 (Convolution2D)     (None, 75, 75, 128)   147584   
________________________________________________________________
block2_pool (MaxPooling2D)       (None, 37, 37, 128)   0        
________________________________________________________________
block3_conv1 (Convolution2D)     (None, 37, 37, 256)   295168   
________________________________________________________________
block3_conv2 (Convolution2D)     (None, 37, 37, 256)   590080   
________________________________________________________________
block3_conv3 (Convolution2D)     (None, 37, 37, 256)   590080   
________________________________________________________________
block3_pool (MaxPooling2D)       (None, 18, 18, 256)   0        
________________________________________________________________
block4_conv1 (Convolution2D)     (None, 18, 18, 512)   1180160  
________________________________________________________________
block4_conv2 (Convolution2D)     (None, 18, 18, 512)   2359808  
________________________________________________________________
block4_conv3 (Convolution2D)     (None, 18, 18, 512)   2359808  
________________________________________________________________
block4_pool (MaxPooling2D)       (None, 9, 9, 512)     0        
________________________________________________________________
block5_conv1 (Convolution2D)     (None, 9, 9, 512)     2359808  
________________________________________________________________
block5_conv2 (Convolution2D)     (None, 9, 9, 512)     2359808  
________________________________________________________________
block5_conv3 (Convolution2D)     (None, 9, 9, 512)     2359808  
________________________________________________________________
block5_pool (MaxPooling2D)       (None, 4, 4, 512)     0        
================================================================
Whole params: 14,714,688
Trainable params: 14,714,688
Non-trainable params: 0

The ultimate function map has form (4, 4, 512). That’s the function on high of which you’ll stick a densely linked classifier.

At this level, there are two methods you can proceed:

• Operating the convolutional base over your dataset, recording its output to an array on disk, after which utilizing this knowledge as enter to a standalone, densely linked classifier much like these you noticed partly 1 of this e-book. This answer is quick and low-cost to run, as a result of it solely requires working the convolutional base as soon as for each enter picture, and the convolutional base is by far the costliest a part of the pipeline. However for a similar cause, this method received’t assist you to use knowledge augmentation.

• Extending the mannequin you could have (conv_base) by including dense layers on high, and working the entire thing finish to finish on the enter knowledge. This may assist you to use knowledge augmentation, as a result of each enter picture goes by the convolutional base each time it’s seen by the mannequin. However for a similar cause, this method is much dearer than the primary.

On this publish we’ll cowl the second approach intimately (within the e-book we cowl each). Notice that this method is so costly that you must solely try it in case you have entry to a GPU – it’s completely intractable on a CPU.

As a result of fashions behave similar to layers, you may add a mannequin (like conv_base) to a sequential mannequin similar to you’ll add a layer.

mannequin <- keras_model_sequential() %>% 
  conv_base %>% 
  layer_flatten() %>% 
  layer_dense(items = 256, activation = "relu") %>% 
  layer_dense(items = 1, activation = "sigmoid")

That is what the mannequin seems to be like now:

Layer (sort)                     Output Form          Param #  
================================================================
vgg16 (Mannequin)                    (None, 4, 4, 512)     14714688                                     
________________________________________________________________
flatten_1 (Flatten)              (None, 8192)          0        
________________________________________________________________
dense_1 (Dense)                  (None, 256)           2097408  
________________________________________________________________
dense_2 (Dense)                  (None, 1)             257      
================================================================
Whole params: 16,812,353
Trainable params: 16,812,353
Non-trainable params: 0

As you may see, the convolutional base of VGG16 has 14,714,688 parameters, which may be very giant. The classifier you’re including on high has 2 million parameters.

Earlier than you compile and practice the mannequin, it’s crucial to freeze the convolutional base. Freezing a layer or set of layers means stopping their weights from being up to date throughout coaching. Should you don’t do that, then the representations that had been beforehand discovered by the convolutional base will probably be modified throughout coaching. As a result of the dense layers on high are randomly initialized, very giant weight updates could be propagated by the community, successfully destroying the representations beforehand discovered.

In Keras, you freeze a community utilizing the freeze_weights() perform:

size(mannequin$trainable_weights)

[1] 30

freeze_weights(conv_base)
size(mannequin$trainable_weights)

[1] 4

With this setup, solely the weights from the 2 dense layers that you just added will probably be educated. That’s a complete of 4 weight tensors: two per layer (the primary weight matrix and the bias vector). Notice that to ensure that these modifications to take impact, you have to first compile the mannequin. Should you ever modify weight trainability after compilation, you must then recompile the mannequin, or these modifications will probably be ignored.

Utilizing knowledge augmentation

Overfitting is brought on by having too few samples to study from, rendering you unable to coach a mannequin that may generalize to new knowledge. Given infinite knowledge, your mannequin could be uncovered to each attainable facet of the information distribution at hand: you’ll by no means overfit. Information augmentation takes the strategy of producing extra coaching knowledge from present coaching samples, by augmenting the samples through various random transformations that yield believable-looking pictures. The objective is that at coaching time, your mannequin won’t ever see the very same image twice. This helps expose the mannequin to extra features of the information and generalize higher.

In Keras, this may be performed by configuring various random transformations to be carried out on the photographs learn by an image_data_generator(). For instance:

train_datagen = image_data_generator(
  rescale = 1/255,
  rotation_range = 40,
  width_shift_range = 0.2,
  height_shift_range = 0.2,
  shear_range = 0.2,
  zoom_range = 0.2,
  horizontal_flip = TRUE,
  fill_mode = "nearest"
)

These are just some of the choices accessible (for extra, see the Keras documentation). Let’s rapidly go over this code:

• rotation_range is a price in levels (0–180), a spread inside which to randomly rotate footage.
• width_shift and height_shift are ranges (as a fraction of whole width or peak) inside which to randomly translate footage vertically or horizontally.
• shear_range is for randomly making use of shearing transformations.
• zoom_range is for randomly zooming inside footage.
• horizontal_flip is for randomly flipping half the photographs horizontally – related when there are not any assumptions of horizontal asymmetry (for instance, real-world footage).
• fill_mode is the technique used for filling in newly created pixels, which might seem after a rotation or a width/peak shift.

Now we will practice our mannequin utilizing the picture knowledge generator:

# Notice that the validation knowledge should not be augmented!
test_datagen <- image_data_generator(rescale = 1/255)  

train_generator <- flow_images_from_directory(
  train_dir,                  # Goal listing  
  train_datagen,              # Information generator
  target_size = c(150, 150),  # Resizes all pictures to 150 × 150
  batch_size = 20,
  class_mode = "binary"       # binary_crossentropy loss for binary labels
)

validation_generator <- flow_images_from_directory(
  validation_dir,
  test_datagen,
  target_size = c(150, 150),
  batch_size = 20,
  class_mode = "binary"
)

mannequin %>% compile(
  loss = "binary_crossentropy",
  optimizer = optimizer_rmsprop(lr = 2e-5),
  metrics = c("accuracy")
)

historical past <- mannequin %>% fit_generator(
  train_generator,
  steps_per_epoch = 100,
  epochs = 30,
  validation_data = validation_generator,
  validation_steps = 50
)

Let’s plot the outcomes. As you may see, you attain a validation accuracy of about 90%.

Fantastic-tuning

One other broadly used approach for mannequin reuse, complementary to function extraction, is fine-tuning
Fantastic-tuning consists of unfreezing a couple of of the highest layers of a frozen mannequin base used for function extraction, and collectively coaching each the newly added a part of the mannequin (on this case, the totally linked classifier) and these high layers. That is known as fine-tuning as a result of it barely adjusts the extra summary
representations of the mannequin being reused, with a view to make them extra related for the issue at hand.

I acknowledged earlier that it’s essential to freeze the convolution base of VGG16 so as to have the ability to practice a randomly initialized classifier on high. For a similar cause, it’s solely attainable to fine-tune the highest layers of the convolutional base as soon as the classifier on high has already been educated. If the classifier isn’t already educated, then the error sign propagating by the community throughout coaching will probably be too giant, and the representations beforehand discovered by the layers being fine-tuned will probably be destroyed. Thus the steps for fine-tuning a community are as follows:

• Add your customized community on high of an already-trained base community.
• Freeze the bottom community.
• Prepare the half you added.
• Unfreeze some layers within the base community.
• Collectively practice each these layers and the half you added.

You already accomplished the primary three steps when doing function extraction. Let’s proceed with step 4: you’ll unfreeze your conv_base after which freeze particular person layers inside it.

As a reminder, that is what your convolutional base seems to be like:

Layer (sort)                     Output Form          Param #  
================================================================
input_1 (InputLayer)             (None, 150, 150, 3)   0        
________________________________________________________________
block1_conv1 (Convolution2D)     (None, 150, 150, 64)  1792     
________________________________________________________________
block1_conv2 (Convolution2D)     (None, 150, 150, 64)  36928    
________________________________________________________________
block1_pool (MaxPooling2D)       (None, 75, 75, 64)    0        
________________________________________________________________
block2_conv1 (Convolution2D)     (None, 75, 75, 128)   73856    
________________________________________________________________
block2_conv2 (Convolution2D)     (None, 75, 75, 128)   147584   
________________________________________________________________
block2_pool (MaxPooling2D)       (None, 37, 37, 128)   0        
________________________________________________________________
block3_conv1 (Convolution2D)     (None, 37, 37, 256)   295168   
________________________________________________________________
block3_conv2 (Convolution2D)     (None, 37, 37, 256)   590080   
________________________________________________________________
block3_conv3 (Convolution2D)     (None, 37, 37, 256)   590080   
________________________________________________________________
block3_pool (MaxPooling2D)       (None, 18, 18, 256)   0        
________________________________________________________________
block4_conv1 (Convolution2D)     (None, 18, 18, 512)   1180160  
________________________________________________________________
block4_conv2 (Convolution2D)     (None, 18, 18, 512)   2359808  
________________________________________________________________
block4_conv3 (Convolution2D)     (None, 18, 18, 512)   2359808  
________________________________________________________________
block4_pool (MaxPooling2D)       (None, 9, 9, 512)     0        
________________________________________________________________
block5_conv1 (Convolution2D)     (None, 9, 9, 512)     2359808  
________________________________________________________________
block5_conv2 (Convolution2D)     (None, 9, 9, 512)     2359808  
________________________________________________________________
block5_conv3 (Convolution2D)     (None, 9, 9, 512)     2359808  
________________________________________________________________
block5_pool (MaxPooling2D)       (None, 4, 4, 512)     0        
================================================================
Whole params: 14714688

You’ll fine-tune the entire layers from block3_conv1 and on. Why not fine-tune your complete convolutional base? You would. However you might want to contemplate the next:

• Earlier layers within the convolutional base encode more-generic, reusable options, whereas layers increased up encode more-specialized options. It’s extra helpful to fine-tune the extra specialised options, as a result of these are those that must be repurposed in your new drawback. There could be fast-decreasing returns in fine-tuning decrease layers.
• The extra parameters you’re coaching, the extra you’re prone to overfitting. The convolutional base has 15 million parameters, so it will be dangerous to aim to coach it in your small dataset.

Thus, on this state of affairs, it’s a superb technique to fine-tune solely a few of the layers within the convolutional base. Let’s set this up, ranging from the place you left off within the earlier instance.

unfreeze_weights(conv_base, from = "block3_conv1")

Now you may start fine-tuning the community. You’ll do that with the RMSProp optimizer, utilizing a really low studying fee. The explanation for utilizing a low studying fee is that you just need to restrict the magnitude of the modifications you make to the representations of the three layers you’re fine-tuning. Updates which are too giant could hurt these representations.

mannequin %>% compile(
  loss = "binary_crossentropy",
  optimizer = optimizer_rmsprop(lr = 1e-5),
  metrics = c("accuracy")
)

historical past <- mannequin %>% fit_generator(
  train_generator,
  steps_per_epoch = 100,
  epochs = 100,
  validation_data = validation_generator,
  validation_steps = 50
)

Let’s plot our outcomes:

You’re seeing a pleasant 6% absolute enchancment in accuracy, from about 90% to above 96%.

Notice that the loss curve doesn’t present any actual enchancment (in reality, it’s deteriorating). You could surprise, how might accuracy keep secure or enhance if the loss isn’t reducing? The reply is straightforward: what you show is a median of pointwise loss values; however what issues for accuracy is the distribution of the loss values, not their common, as a result of accuracy is the results of a binary thresholding of the category chance predicted by the mannequin. The mannequin should be enhancing even when this isn’t mirrored within the common loss.

Now you can lastly consider this mannequin on the check knowledge:

test_generator <- flow_images_from_directory(
  test_dir,
  test_datagen,
  target_size = c(150, 150),
  batch_size = 20,
  class_mode = "binary"
)

mannequin %>% evaluate_generator(test_generator, steps = 50)

$loss
[1] 0.2158171

$acc
[1] 0.965

Right here you get a check accuracy of 96.5%. Within the unique Kaggle competitors round this dataset, this could have been one of many high outcomes. However utilizing trendy deep-learning methods, you managed to achieve this outcome utilizing solely a small fraction of the coaching knowledge accessible (about 10%). There’s a enormous distinction between with the ability to practice on 20,000 samples in comparison with 2,000 samples!

Take-aways: utilizing convnets with small datasets

Right here’s what you must take away from the workout routines up to now two sections:

• Convnets are the most effective sort of machine-learning fashions for computer-vision duties. It’s attainable to coach one from scratch even on a really small dataset, with respectable outcomes.
• On a small dataset, overfitting would be the primary challenge. Information augmentation is a strong method to combat overfitting while you’re working with picture knowledge.
• It’s simple to reuse an present convnet on a brand new dataset through function extraction. It is a priceless approach for working with small picture datasets.
• As a complement to function extraction, you should utilize fine-tuning, which adapts to a brand new drawback a few of the representations beforehand discovered by an present mannequin. This pushes efficiency a bit additional.

Now you could have a stable set of instruments for coping with image-classification issues – specifically with small datasets.