Posit 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 elements, Easy audio classification with torch: No, this isn’t the primary put up on this weblog that introduces speech classification utilizing deep studying. With two of these posts (the “utilized” ones) it shares the final 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 special focus – do you have to learn this one?

Effectively, after all I can’t say “no” – all of the extra so as a result of, right here, you’ve gotten an abbreviated and condensed model of the chapter on this subject within the forthcoming e book from CRC Press, Deep Studying and Scientific Computing with R torch. By the use of comparability with the earlier put up that used torch, written by the creator and maintainer of torchaudio, Athos Damiani, important developments have taken place within the torch ecosystem, the tip consequence being that the code obtained lots 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 totally different one- or two-syllable phrases, uttered by totally different audio system. There are about 65,000 audio information total. Our process can be to foretell, from the audio solely, which of thirty attainable 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"    "hen"   "cat"    "canine"    "down"   "eight"
[7]  "5"   "4"   "go"     "completely satisfied"  "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 knowledge we’ll want is contained in 4 properties: waveform, sample_rate, label_index, and label.

The primary, waveform, can 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 at all times equals one second; the – very – few sounds which might be minimally longer we are able to safely truncate.

Lastly, the goal is saved, in integer kind, in pattern$label_index, the corresponding phrase being accessible from pattern$label:

pattern$label
pattern$label_index

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

How does this audio sign “look?”

library(ggplot2)

df <- knowledge.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 “hen.” Put in a different way, we now have right here a time sequence of “loudness values.” Even for specialists, guessing which phrase resulted in these amplitudes is an inconceivable process. That is the place area data is available in. The professional might not be capable to make a lot of the sign on this illustration; however they could know a approach 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 recuperate the unique sign. For that to be attainable, the brand new illustration would by some means must comprise “simply as a lot” data because the wave we began from. That “simply as a lot” is obtained from the Fourier Remodel, and it consists of the magnitudes and part shifts of the totally different frequencies that make up the sign.

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

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, akin to the frequencies contained within the sign. The upper their magnitude, the extra they contribute to the sign:

magazine <- torch_abs(dft[1, ])

df <- knowledge.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 Remodel"
    )
  ) +
  xlab("frequency") +
  ylab("magnitude") +
  theme_minimal()

From this alternate illustration, we might 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 certainly matter; we don’t actually wish to throw it away.

Combining representations: The spectrogram

In reality, what actually would assist us is a synthesis of each representations; some kind of “have your cake and eat it, too.” What if we might divide the sign into small chunks, and run the Fourier Remodel on every of them? As you will 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 preserve some time-domain data – some, since there may be an unavoidable loss in granularity. Then again, for every of the time segments, we study their spectral composition. There’s an necessary 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 won’t be very fine-grained. Conversely, if we wish to get higher decision within the frequency area, we now have to decide on longer home windows, thus shedding details about how spectral composition varies over time. What appears like an enormous drawback – and in lots of circumstances, can be – gained’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 scale 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 will 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")
)
predominant <- paste0("Spectrogram, window dimension = ", window_size)
sub <- "Magnitude (sq. root)"
mtext(facet = 3, line = 2, at = 0, adj = 0, cex = 1.3, predominant)
mtext(facet = 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 in a position to acquire an affordable consequence. (With the viridis colour 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 wish 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 photographs, we now 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 process, 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 = perform(...,
                        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$initialize(...)
  },
  .getitem = perform(i) {
    merchandise <- tremendous$.getitem(i)

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

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

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

Within the parameter checklist to spectrogram_dataset(), word 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 possibly can change the default, and specify, for instance, that’d you’d like absolute values (energy = 1), some other optimistic worth (equivalent to 0.5, the one we used above to show a concrete instance) – or each the true and imaginary elements of the coefficients (energy = NULL).

Show-wise, after all, the total complicated illustration is inconvenient; the spectrogram plot would wish an extra dimension. However we might effectively ponder whether a neural community might revenue from the extra data contained within the “entire” complicated quantity. In spite of everything, when decreasing to magnitudes we lose the part shifts for the person coefficients, which could comprise usable data. In reality, my checks 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

We now have 257 coefficients for 101 home windows; and every coefficient is represented by each its actual and imaginary elements.

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

mannequin <- nn_module(
  initialize = perform() {
    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$classifier <- nn_sequential(
      nn_linear(512, 512),
      nn_batch_norm1d(512),
      nn_relu(),
      nn_dropout(p = 0.5),
      nn_linear(512, 30)
    )
  },
  ahead = perform(x) {
    x <- self$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 = checklist(luz_metric_accuracy())
  )

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

Based mostly 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 = checklist(
      luz_callback_early_stopping(endurance = 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 courses to tell apart between, a remaining validation-set accuracy of ~0.94 seems like a really first rate consequence!

We will verify this on the check set:

consider(fitted, test_dl)

loss: 0.2373
acc: 0.9324

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

Wrapup

That’s it for right this moment! Within the upcoming weeks, anticipate extra posts drawing on content material from the soon-to-appear CRC e book, Deep Studying and Scientific Computing with R torch. Thanks for studying!

Photograph by alex lauzon on Unsplash