RStudio AI Weblog: Audio classification with torch

Variations on a theme

Easy audio classification with Keras, Audio classification with Keras: Wanting nearer on the non-deep studying components, Easy audio classification with torch: No, this isn’t the primary publish on this weblog that introduces speech classification utilizing deep studying. With two of these posts (the “utilized” ones) it shares the overall setup, the kind of deep-learning structure employed, and the dataset used. With the third, it has in widespread the curiosity within the concepts and ideas concerned. Every of those posts has a distinct focus – must you learn this one?

Nicely, in fact I can’t say “no” – all of the extra so as a result of, right here, you’ve got an abbreviated and condensed model of the chapter on this matter within the forthcoming ebook from CRC Press, Deep Studying and Scientific Computing with R torch. By means of comparability with the earlier publish that used torch, written by the creator and maintainer of torchaudio, Athos Damiani, vital developments have taken place within the torch ecosystem, the top consequence being that the code received so much simpler (particularly within the mannequin coaching half). That stated, let’s finish the preamble already, and plunge into the subject!

Inspecting the information

We use the speech instructions dataset (Warden (2018)) that comes with torchaudio. The dataset holds recordings of thirty completely different one- or two-syllable phrases, uttered by completely different audio system. There are about 65,000 audio information total. Our job will likely be to foretell, from the audio solely, which of thirty potential phrases was pronounced.

library(torch)
library(torchaudio)
library(luz)

ds <- speechcommand_dataset(
  root = "~/.torch-datasets", 
  url = "speech_commands_v0.01",
  obtain = TRUE
)

We begin by inspecting the information.

[1]  "mattress"    "chicken"   "cat"    "canine"    "down"   "eight"
[7]  "5"   "4"   "go"     "pleased"  "home"  "left"
[32] " marvin" "9"   "no"     "off"    "on"     "one"
[19] "proper"  "seven" "sheila" "six"    "cease"   "three"
[25]  "tree"   "two"    "up"     "wow"    "sure"    "zero" 

Choosing a pattern at random, we see that the data we’ll want is contained in 4 properties: waveform, sample_rate, label_index, and label.

The primary, waveform, will likely be our predictor.

pattern <- ds[2000]
dim(pattern$waveform)

[1]     1 16000

Particular person tensor values are centered at zero, and vary between -1 and 1. There are 16,000 of them, reflecting the truth that the recording lasted for one second, and was registered at (or has been transformed to, by the dataset creators) a fee of 16,000 samples per second. The latter data is saved in pattern$sample_rate:

[1] 16000

All recordings have been sampled on the similar fee. Their size virtually all the time equals one second; the – very – few sounds which can be minimally longer we are able to safely truncate.

Lastly, the goal is saved, in integer type, in pattern$label_index, the corresponding phrase being out there from pattern$label:

pattern$label
pattern$label_index

[1] "chicken"
torch_tensor
2
[ CPULongType{} ]

How does this audio sign “look?”

library(ggplot2)

df <- information.body(
  x = 1:size(pattern$waveform[1]),
  y = as.numeric(pattern$waveform[1])
  )

ggplot(df, aes(x = x, y = y)) +
  geom_line(dimension = 0.3) +
  ggtitle(
    paste0(
      "The spoken phrase "", pattern$label, "": Sound wave"
    )
  ) +
  xlab("time") +
  ylab("amplitude") +
  theme_minimal()

What we see is a sequence of amplitudes, reflecting the sound wave produced by somebody saying “chicken.” Put in another way, now we have right here a time collection of “loudness values.” Even for consultants, guessing which phrase resulted in these amplitudes is an unattainable job. That is the place area information is available in. The professional could not have the ability to make a lot of the sign on this illustration; however they could know a technique to extra meaningfully symbolize it.

Two equal representations

Think about that as an alternative of as a sequence of amplitudes over time, the above wave had been represented in a method that had no details about time in any respect. Subsequent, think about we took that illustration and tried to get well the unique sign. For that to be potential, the brand new illustration would in some way must comprise “simply as a lot” data because the wave we began from. That “simply as a lot” is obtained from the Fourier Rework, and it consists of the magnitudes and section shifts of the completely different frequencies that make up the sign.

How, then, does the Fourier-transformed model of the “chicken” sound wave look? We acquire it by calling torch_fft_fft() (the place fft stands for Quick Fourier Rework):

dft <- torch_fft_fft(pattern$waveform)
dim(dft)

[1]     1 16000

The size of this tensor is identical; nonetheless, its values usually are not in chronological order. As an alternative, they symbolize the Fourier coefficients, comparable to the frequencies contained within the sign. The upper their magnitude, the extra they contribute to the sign:

magazine <- torch_abs(dft[1, ])

df <- information.body(
  x = 1:(size(pattern$waveform[1]) / 2),
  y = as.numeric(magazine[1:8000])
)

ggplot(df, aes(x = x, y = y)) +
  geom_line(dimension = 0.3) +
  ggtitle(
    paste0(
      "The spoken phrase "",
      pattern$label,
      "": Discrete Fourier Rework"
    )
  ) +
  xlab("frequency") +
  ylab("magnitude") +
  theme_minimal()

From this alternate illustration, we may return to the unique sound wave by taking the frequencies current within the sign, weighting them in line with their coefficients, and including them up. However in sound classification, timing data should absolutely matter; we don’t actually need to throw it away.

Combining representations: The spectrogram

In actual fact, what actually would assist us is a synthesis of each representations; some type of “have your cake and eat it, too.” What if we may divide the sign into small chunks, and run the Fourier Rework on every of them? As you’ll have guessed from this lead-up, this certainly is one thing we are able to do; and the illustration it creates is known as the spectrogram.

With a spectrogram, we nonetheless hold some time-domain data – some, since there may be an unavoidable loss in granularity. However, for every of the time segments, we find out about their spectral composition. There’s an essential level to be made, although. The resolutions we get in time versus in frequency, respectively, are inversely associated. If we break up up the alerts into many chunks (known as “home windows”), the frequency illustration per window is not going to be very fine-grained. Conversely, if we need to get higher decision within the frequency area, now we have to decide on longer home windows, thus shedding details about how spectral composition varies over time. What seems like an enormous drawback – and in lots of instances, will likely be – received’t be one for us, although, as you’ll see very quickly.

First, although, let’s create and examine such a spectrogram for our instance sign. Within the following code snippet, the dimensions of the – overlapping – home windows is chosen in order to permit for cheap granularity in each the time and the frequency area. We’re left with sixty-three home windows, and, for every window, acquire 200 fifty-seven coefficients:

fft_size <- 512
window_size <- 512
energy <- 0.5

spectrogram <- transform_spectrogram(
  n_fft = fft_size,
  win_length = window_size,
  normalized = TRUE,
  energy = energy
)

spec <- spectrogram(pattern$waveform)$squeeze()
dim(spec)

[1]   257 63

We are able to show the spectrogram visually:

bins <- 1:dim(spec)[1]
freqs <- bins / (fft_size / 2 + 1) * pattern$sample_rate 
log_freqs <- log10(freqs)

frames <- 1:(dim(spec)[2])
seconds <- (frames / dim(spec)[2]) *
  (dim(pattern$waveform$squeeze())[1] / pattern$sample_rate)

picture(x = as.numeric(seconds),
      y = log_freqs,
      z = t(as.matrix(spec)),
      ylab = 'log frequency [Hz]',
      xlab = 'time [s]',
      col = hcl.colours(12, palette = "viridis")
)
primary <- paste0("Spectrogram, window dimension = ", window_size)
sub <- "Magnitude (sq. root)"
mtext(aspect = 3, line = 2, at = 0, adj = 0, cex = 1.3, primary)
mtext(aspect = 3, line = 1, at = 0, adj = 0, cex = 1, sub)

We all know that we’ve misplaced some decision in each time and frequency. By displaying the sq. root of the coefficients’ magnitudes, although – and thus, enhancing sensitivity – we had been nonetheless capable of acquire an inexpensive consequence. (With the viridis shade scheme, long-wave shades point out higher-valued coefficients; short-wave ones, the other.)

Lastly, let’s get again to the essential query. If this illustration, by necessity, is a compromise – why, then, would we need to make use of it? That is the place we take the deep-learning perspective. The spectrogram is a two-dimensional illustration: a picture. With pictures, now we have entry to a wealthy reservoir of methods and architectures: Amongst all areas deep studying has been profitable in, picture recognition nonetheless stands out. Quickly, you’ll see that for this job, fancy architectures usually are not even wanted; an easy convnet will do an excellent job.

Coaching a neural community on spectrograms

We begin by making a torch::dataset() that, ranging from the unique speechcommand_dataset(), computes a spectrogram for each pattern.

spectrogram_dataset <- dataset(
  inherit = speechcommand_dataset,
  initialize = operate(...,
                        pad_to = 16000,
                        sampling_rate = 16000,
                        n_fft = 512,
                        window_size_seconds = 0.03,
                        window_stride_seconds = 0.01,
                        energy = 2) {
    self$pad_to <- pad_to
    self$window_size_samples <- sampling_rate *
      window_size_seconds
    self$window_stride_samples <- sampling_rate *
      window_stride_seconds
    self$energy <- energy
    self$spectrogram <- transform_spectrogram(
        n_fft = n_fft,
        win_length = self$window_size_samples,
        hop_length = self$window_stride_samples,
        normalized = TRUE,
        energy = self$energy
      )
    tremendous$initialize(...)
  },
  .getitem = operate(i) {
    merchandise <- tremendous$.getitem(i)

    x <- merchandise$waveform
    # be sure that all samples have the identical size (57)
    # shorter ones will likely be padded,
    # longer ones will likely be truncated
    x <- nnf_pad(x, pad = c(0, self$pad_to - dim(x)[2]))
    x <- x %>% self$spectrogram()

    if (is.null(self$energy)) {
      # on this case, there may be an extra dimension, in place 4,
      # that we need to seem in entrance
      # (as a second channel)
      x <- x$squeeze()$permute(c(3, 1, 2))
    }

    y <- merchandise$label_index
    record(x = x, y = y)
  }
)

Within the parameter record to spectrogram_dataset(), observe energy, with a default worth of two. That is the worth that, until informed in any other case, torch’s transform_spectrogram() will assume that energy ought to have. Below these circumstances, the values that make up the spectrogram are the squared magnitudes of the Fourier coefficients. Utilizing energy, you’ll be able to change the default, and specify, for instance, that’d you’d like absolute values (energy = 1), some other optimistic worth (reminiscent of 0.5, the one we used above to show a concrete instance) – or each the actual and imaginary components of the coefficients (energy = NULL).

Show-wise, in fact, the total complicated illustration is inconvenient; the spectrogram plot would wish an extra dimension. However we could properly wonder if a neural community may revenue from the extra data contained within the “complete” complicated quantity. In any case, when decreasing to magnitudes we lose the section shifts for the person coefficients, which could comprise usable data. In actual fact, my exams confirmed that it did; use of the complicated values resulted in enhanced classification accuracy.

Let’s see what we get from spectrogram_dataset():

ds <- spectrogram_dataset(
  root = "~/.torch-datasets",
  url = "speech_commands_v0.01",
  obtain = TRUE,
  energy = NULL
)

dim(ds[1]$x)

[1]   2 257 101

Now we have 257 coefficients for 101 home windows; and every coefficient is represented by each its actual and imaginary components.

Subsequent, we break up up the information, and instantiate the dataset() and dataloader() objects.

train_ids <- pattern(
  1:size(ds),
  dimension = 0.6 * size(ds)
)
valid_ids <- pattern(
  setdiff(
    1:size(ds),
    train_ids
  ),
  dimension = 0.2 * size(ds)
)
test_ids <- setdiff(
  1:size(ds),
  union(train_ids, valid_ids)
)

batch_size <- 128

train_ds <- dataset_subset(ds, indices = train_ids)
train_dl <- dataloader(
  train_ds,
  batch_size = batch_size, shuffle = TRUE
)

valid_ds <- dataset_subset(ds, indices = valid_ids)
valid_dl <- dataloader(
  valid_ds,
  batch_size = batch_size
)

test_ds <- dataset_subset(ds, indices = test_ids)
test_dl <- dataloader(test_ds, batch_size = 64)

b <- train_dl %>%
  dataloader_make_iter() %>%
  dataloader_next()

dim(b$x)

[1] 128   2 257 101

The mannequin is an easy convnet, with dropout and batch normalization. The actual and imaginary components of the Fourier coefficients are handed to the mannequin’s preliminary nn_conv2d() as two separate channels.

mannequin <- nn_module(
  initialize = operate() {
    self$options <- nn_sequential(
      nn_conv2d(2, 32, kernel_size = 3),
      nn_batch_norm2d(32),
      nn_relu(),
      nn_max_pool2d(kernel_size = 2),
      nn_dropout2d(p = 0.2),
      nn_conv2d(32, 64, kernel_size = 3),
      nn_batch_norm2d(64),
      nn_relu(),
      nn_max_pool2d(kernel_size = 2),
      nn_dropout2d(p = 0.2),
      nn_conv2d(64, 128, kernel_size = 3),
      nn_batch_norm2d(128),
      nn_relu(),
      nn_max_pool2d(kernel_size = 2),
      nn_dropout2d(p = 0.2),
      nn_conv2d(128, 256, kernel_size = 3),
      nn_batch_norm2d(256),
      nn_relu(),
      nn_max_pool2d(kernel_size = 2),
      nn_dropout2d(p = 0.2),
      nn_conv2d(256, 512, kernel_size = 3),
      nn_batch_norm2d(512),
      nn_relu(),
      nn_adaptive_avg_pool2d(c(1, 1)),
      nn_dropout2d(p = 0.2)
    )

    self$classifier <- nn_sequential(
      nn_linear(512, 512),
      nn_batch_norm1d(512),
      nn_relu(),
      nn_dropout(p = 0.5),
      nn_linear(512, 30)
    )
  },
  ahead = operate(x) {
    x <- self$options(x)$squeeze()
    x <- self$classifier(x)
    x
  }
)

We subsequent decide an acceptable studying fee:

mannequin <- mannequin %>%
  setup(
    loss = nn_cross_entropy_loss(),
    optimizer = optim_adam,
    metrics = record(luz_metric_accuracy())
  )

rates_and_losses <- mannequin %>%
  lr_finder(train_dl)
rates_and_losses %>% plot()

Primarily based on the plot, I made a decision to make use of 0.01 as a maximal studying fee. Coaching went on for forty epochs.

fitted <- mannequin %>%
  match(train_dl,
    epochs = 50, valid_data = valid_dl,
    callbacks = record(
      luz_callback_early_stopping(persistence = 3),
      luz_callback_lr_scheduler(
        lr_one_cycle,
        max_lr = 1e-2,
        epochs = 50,
        steps_per_epoch = size(train_dl),
        call_on = "on_batch_end"
      ),
      luz_callback_model_checkpoint(path = "models_complex/"),
      luz_callback_csv_logger("logs_complex.csv")
    ),
    verbose = TRUE
  )

plot(fitted)

Let’s examine precise accuracies.

"epoch","set","loss","acc"
1,"practice",3.09768574611813,0.12396992171405
1,"legitimate",2.52993751740923,0.284378862793572
2,"practice",2.26747255972008,0.333642356819118
2,"legitimate",1.66693911248562,0.540791100123609
3,"practice",1.62294889937818,0.518464153275649
3,"legitimate",1.11740599192825,0.704882571075402
...
...
38,"practice",0.18717994078312,0.943809229501442
38,"legitimate",0.23587799138006,0.936418417799753
39,"practice",0.19338578602993,0.942882159044087
39,"legitimate",0.230597475945365,0.939431396786156
40,"practice",0.190593419024368,0.942727647301195
40,"legitimate",0.243536252455384,0.936186650185414

With thirty lessons to tell apart between, a ultimate validation-set accuracy of ~0.94 seems to be like a really respectable consequence!

We are able to affirm this on the check set:

consider(fitted, test_dl)

loss: 0.2373
acc: 0.9324

An attention-grabbing query is which phrases get confused most frequently. (In fact, much more attention-grabbing is how error chances are associated to options of the spectrograms – however this, now we have to depart to the true area consultants. A pleasant method of displaying the confusion matrix is to create an alluvial plot. We see the predictions, on the left, “circulation into” the goal slots. (Goal-prediction pairs much less frequent than a thousandth of check set cardinality are hidden.)

Wrapup

That’s it for at present! Within the upcoming weeks, count on extra posts drawing on content material from the soon-to-appear CRC ebook, Deep Studying and Scientific Computing with R torch. Thanks for studying!

Picture by alex lauzon on Unsplash